Lonergan and Mathematics
DavidB
I stumbled across Lonergan about eight years ago, and have been impressed with his remarkable precision in the way he addresses complex problems.
What struck me was the strong affinity between his method and the mathematical way of thinking, which led me to inquire what connections there could exist between Lonergan and mathematics. The result was quite startling at times, and I have outlined my findings (still in need of tidying up and probably full of mistakes) below.
Your thoughts will be appreciated.
Many thanks,
David
Jaray...@aol.com
A Directed Scale-Free Network Approach to Lonergan’s Generic Model of Development
Michael Bretz
Department of Physics
University of Michigan
mbr...@umich.edu
1.1 Introduction
An intriguing heuristic model of development, decline, and change conceived by Bernard J.F. Lonergan (BL) in the late 1940’s was laid out in a manner now recognizable as representing an early model of complexity. This report is a first effort toward eventually translating that qualitative vision, designated Emergent Probability* (EP), into a viable network computer study.
In his study of human understanding, Lonergan [1992] saw the task of constructing a cohesive body of explanatory knowledge as a convoluted building process of recurrent schemes (RS) that act as foundational elements to further growth. Although BL’s kernal RS was composed of the cognitional dynamics surrounding Insight [Bretz, 2002], other examples of recurrent growth schemes abound in nature: resource cycles, motor skills, biological routines, autocatalytic processes, etc. The corresponding growing generic World Process can alternatively be thought of as chemical, environmental, evolutionary, social, organizational, economical, psychological, or ethical [Melchin, 2001], and its generality might be of particular interest to complex systems researchers.
Schemes of Recurrence are conjoined dynamic activities where, in simplest form, each element generates the next action, which in turn generates the next, until the last dynamic regenerates the first one again, locking the whole scheme into long term stable equilibrium. BL modeled generic growth as the successive appearance of conditioned Recurrent Schemes (RS), each of which comes into function with high probabilistically once all required prior schemes have become functional. RS’s can be treated as dynamic black cells of activity which themselves may contain internal structures and dynamic schemes of arbitrary complexity. Emergent Probability is a generic heuristic model. Applications to specific physical problems requires detailed knowledge of the recurrent schemes’ makeup and of their interrelationships (an elementary example is provided in the Appendix).
The universe of possibilities available to any open-ended development process is vast, and the interrelations among the elements can become arbitrarily convoluted as the process proceeds. All growth in that universe, no matter how complex, depends upon a suitable underlying environmental “situation”, and an ecology, or niche, in order to thrive. Any full simulation of EP must allow for adaptation to a changing situation and ecology, so that recovery can occur when events disrupt underlying schemes, or when separate growths vie among themselves for dominance within a stressed environment
Here, I present first results obtained from an exploratory toy model of EP development. This MATLAB simulation uses a scale-free, directed network (nodes as RS’s, inward links from the conditional RS’s) to represent the universe of relational possibilities. Growth occurs when nodes of the network are sequentially activated to functionality. The appearance of RS clusters (Things), their dependence on the underlying ecology and situation, and their interplay are sought.
1.2 Modeling the Potential World
A sparse adjacency matrix was grown that defines all of the possible nodes of the toy model simulation, their link dependencies on selected previously grown nodes and their role in constraining younger nodes. Each row/column number names a specific, unique node and values of 1 in the sparse matrix elements represent individual links between adjacent nodes of the network. The network was grown from 3 core nodes by combining aspects of the scale-free growing network methods of [Dorogovtsey, 2000] and [ Krapivsky, 2001]. For each succeeding iteration, with probability q = .83, a new node without links was created having an attractiveness A = 1. With the complementary probability, p = .17, m = 3 new links were added between statistically chosen existing nodes. Selection of the m target nodes and of originating nodes used weightings directly proportional to (kin +A) and (kout +A), where the k’s refer to the number of inward and outward links associated with individual nodes, respectively.
The resulting square matrix containing a total of 700,000 undirected nodes was altered to ensure that all of the links pointed toward younger nodes. This was accomplished by superimposing the transpose of the upper triangular portion of the matrix onto its lower triangular portion before isolated nodes and nodes having zero or one in-link were winnowed from the matrix. After compacting, the final triangular adjacency matrix representing the universe of possibilities for our toy model contained 99,059 nodes and 277,493 directed links, with zeros along the diagonal. Although not huge, the adjacency matrix, named WORLD, is still large enough that elements of the RS growth activity can be explored before being unduly quenched by finite size limitations
.
2
1.3 Characterizing the WORLD Matrix
The node link distributions, P(k), representing the total number of nodes having specific kin and kout are presented in a log-log graph shown in Fig. 1. Both distributions follow power law behavior from k ≅ 4 with exponents γ ~ 1.64 and γ ~ 8 for the out-link and in-link distributions, respectively. Significantly, the oldest two nodes possesses an appreciably larger number of outlinks than is consistent with the out-degree scale-free trend. These are interpreted as defining the ‘situation’ under which the recurrent scheme nodes will grow upon WORLD. Traversing all directed link paths emanating from node 1 reveals a degree of separation, d, of 5 steps to all existing nodes in WORLD. Following the link paths from node 6 gives d = 7 steps. Probing other link paths indicates a maximum of d ≅ 18 directed steps for the WORLD matrix.
Another parameter that characterizes networks is the correlation coefficient, CC = (# links between parent nodes)/(# possible links), which measures the local connectivity between constraining in-link (or out-link) nodes. A coefficient near 1 would indicate a highly connected network. The WORLD matrix, however, possesses very low correlation coefficients for parent nodes and also for child nodes, with values CCin = .0028, CCout = 7.0 x 10-6, respectively.
2.1 Development as World Process
Our World Process in Emergent Probability is the probabilistic activation to functionality of nodes upon the WORLD matrix as the situation, ecology (to be defined), and node conditioning permit. Recurrent Schemes become virtually unconditioned toward activation when all of their conditions have been satisfied by the actual functioning of their originating in-link nodes. Starting from the three formally unconditioned WORLD nodes, #’s 1, 2 and 6 that possess no in-links, each iteration of EP visits and interrogates all non-functioning nodes.
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From: bibby...@yahoo.com
To: Jaray...@aol.com
CC: tjcq...@gmail.com, pmcs...@shaw.ca, raymake...@googlemail.com
Sent: 10/7/2017 4:23:19 PM Mitteleuropäische Sommerzeit
Subj: Re: Lonergan and MathematicsDear John,Thank you for your email. Nice to meet you all.I was good at maths at school, but perhaps for that very reason I didn't study it at university. Instead, I took a Masters in Chemistry, and currently I am working for an independent market research agency in their data processing department. It's a day job, but I enjoy working together with my colleagues to get the jobs that we need out on time.You could say that I still have more than a passing interest in mathematics, and when I was introduced to Lonergan by a friend, I immediately felt that he had something significant to say. But what that is, is laboriously difficult to explain. I soon discovered in my conversations with other people that I wasn't getting anywhere in communicating what Lonergan meant to them. This led to a process where I started asking myself the questions, and the essay I posted is the product of about seventeen months of direct reflection on mathematics. During this time, I sought advice from professional mathematicians, and ended up on this discussion forum.Why mathematics? I think Lonergan answers this question when he explains the motives that led him to concentrate on mathematical examples in his early chapters of Insight. If we are to communicate what Lonergan means about the social surd, for example, then we need clear and precisely defined terms, and mathematics is the field where the greatest precision is reached.What I used to like about mathematics is that is possible to know when one has reached the answer to a problem. It is either right or wrong. But in Lonergan's analysis, this is merely an instance of the virtually unconditioned. That is why Lonergan is so interestingto me, and it would be interesting to know whether his penetrating insights could be brought to shed light on some more obscure regions of modern mathematics.Best wishes,DavidDavid,I started reading your long, detailed message on Lonergan and math. Our google_L discussion group has some 12 to 15 active participants and none of us are as deep into math as you are.Terry Quinn is a professional math professor. He's president of another Lonergan, venue, SGEME of which Phil McShane, a close associate of Lonergan until his death, is a prominent-founding member. Phil knows much about physics. Wonder what they might have to say. I'll reread your post (link below) when I have a bit more time.I moderate the google site, so I certainly want to follow up on your searching observations and, hopefully, Phil and Terry will respond. Please let us know a bit more about yourself,John
From: loner...@googlegroups.com
To: loner...@googlegroups.com
Sent: 10/7/2017 10:37:50 AM Mitteleuropäische Sommerzei
Subj: [lonergan_l] Lonergan and Mathematics
Dear all,
I stumbled across Lonergan about eight years ago, and have been impressed with his remarkable precision in the way he addresses complex problems.
What struck me was the strong affinity between his method and the mathematical way of thinking, which led me to inquire what connections there could exist between Lonergan and mathematics. The result was quite startling at times, and I have outlined my findings (still in need of tidying up and probably full of mistakes) below.
https://docs.google.com/document/d/e/2PACX-1vTG-fYJZfmx4AxNut9GDOXrJmKCLEDyvJigy8r3vawv12dumw5nSQY9K7mFfntiE250z5BRjRtmlBb1/pub
Your thoughts will be appreciated.
Many thanks,
David
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DavidB
Thanks for your reply. A very interesting article on emergent probability, and I like the appendix that applies it to the probability of learning to ride a bike. How we learn to ride a bike has always puzzled me, especially the balancing bit. It's beginning to make more sense now.
I think learning mathematics can be very much like riding a bike. If we start at the deep end, it can all seem like a mystery of arcane symbols. But if we start from simple examples, we can build up our proficiency gradually. The technique of solving complex problems then becomes a matter of breaking it down into smaller problems, each of which we can solve.
Emergent probability may also be connected with the foundations of mathematics. Abstractly, a probability is a ratio of numbers, of occurrences to occasions. But concretely, what is it? Schemes of recurrence form part of an explanatory view, but emergent probability is in the world around us, even before we stop to think what it is. Mathematical expression may be an instance of basic schemes of recurrence that follow a pattern of, consciousness, number, insight. But I still need to think this through.
Regards,
David
Doug Mounce
Nice presentation of Lonergan's thought, congratulations! It seems to me that Lonergan’s analysis of insight revealing three levels of consciousness is integral to the level methods explained in MiT, but do you think the analysis also relates to the precepts?
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DavidB
Thanks for your question and kind comments.
By the precepts, do you mean the directives, 'Be Attentive! Be Intelligent! Be Reasonable! Be Responsible! Be Loving!' ? There certainly appears to be a parallel between the first three and the levels of consciousness, so I would say, yes, the precepts do arise from Lonergan's analysis of insight. But we might bear in mind that the structure is only relatively invariant. Changes to Lonergan's analysis of consciousness may lead to changes in the precepts that the rational self-conscious subject issues to him or herself.
@John, thanks for running my post past Phil McShane, I will contact him at that address you gave me.
Best wishes,
David
Jaray...@aol.com
Hello David and John,
It has been a huge weekend of various teaching duties, grading papers, and what not.
So it is only now, after my Monday evening lectures have ended, that I am getting around to responding to John’s request to comment on David’s work.
First, though, some context: The other night I sent off a small note about a vital new focus, a focus on a solution to a major historical problem affecting all areas, globally. Discovering the main structuring of the solution was a crowning achievement of Lonergan, a discovery that so far has mainly been ignored by Lonerganism. Please know that I am not singling out any individuals here, but refer to a trend that has been undermining Lonergan Studies. I hope that Lonergan Studies eventually breaks free of that trend. A gradually growing group of scholars interested in Lonergan’s work are now beginning to realize something of the major significance of his discovery, what he called functional specialization. But, we are all in the boat of being beginners, struggling to slowly work out a few aspects of how what he envisioned not only can work, but also, we want to start making it work! For David’s article:
David, I don’t want to get into it too much . .. But, since I’ve got your document now, I didn't want you to think that I didn't give some time to it. So, I thought that I might share a few thoughts.
I hope that you're not put out by my remarks, since, as you'll read below, I can't go along with your main approach.
But, read your article, and thought that I should share a few things, some of which you might be interested in.
Having spent much of my career so far in the mathematics community, I enjoyed seeing your end-topic, Riemann’s hypothesis. You seem to have an interest in how Lonergan’s work might “bear fruit” in the sciences, in particular, in mathematics. That problem, the problem of bearing fruit is, in fact, part of the justification for functional collaboration. See, e.g. Chapter 14 of Method in Theology.
But, leaving that large topic for now, I thought that I could at least jot down some questions and comments.
Questions: Where do you see your work contributing? To what community? For what progress? To help in what way? What audience? What do see as possibly coming from your approach? Partly I ask because the questions, I think, are important, and at the same time not usually asked with traditional philosophical work.
See, e.g., Socrates' Tenured, for a glimpse into that non-interest in progress that is part of the present philosophical ethos.
But, I also ask because a problem that I see with your approach is that you seem to have attempted a kind of brief “summary” of Lonergan’s book Insight; and, ..., are attempting some kind of analytic deduction, very much in keeping with the Lonerganism tradition:
“To illustrate how these combine in the concrete context of the human mind, we can apply the canons to an empirical analysis of the human mind itself, and since consciousness operates on three successive levels, there will be three successive applications of the canons.”
Your article, a kind of attempt at summary might, as an outline for your own purposes, be a handy thing to have. I mean this in the sense of, when reading a challenging book, simply organizing topics can sometimes be helpful.
But, if you intend your summary as something more, as an actual “summary of Lonergan's ideas,” then who might that be for? And is it really plausible? On that approach, one is falling into the damaging tradition of “negative haute vulgarization,” a tradition invented by Fontanelle, a tradition of philosophy that has been bluffing philosophy and philosophy of science for centuries. With that said, that is though, at present, an accepted mode of scholarship. But, where does it go? That is part of the historical problem.
Regarding Insight, instead of something to summarize, you would be better to think of it not unlike an advanced graduate text in, say, physical chemistry. A student needs several years of chemistry and quantum chemistry to be able to use such a book profitably. Insight is such a book, but more so. And so one needs to begin with the elementary exercises, years’ worth, and, eventually, as only a first cut through the book, attempt to reach a preliminary and descriptive control of meaning with one’s own examples. Getting beyond description to explanatory work is a remote future possibility for the academic community. See, e.g., the heavy hitting Section 17.3 of Insight that sets, or rather identifies, an enormously high bar for a very remote future.
I would encourage you not to work so much at what “Lonergan considers.” There is the challenge of trying to make a little progress in one’s own “considerings.” I get the impression that you may well have done some of the elementary exercises I am referring to. But, a good beginning, would be the first example in Insight. Have you had the time to ponder over your own puzzlement and then work at identifying elements of your understanding of Archimedes’ principle with, say, an actual floating body! Data, description, question, wonder, insight, correlation of correlation, ...., further wonder, and so on. I know that you have developed a chart of “canons,” but I mean something very down to earth. The homely exercise is extremely challenging! For Lonergan, such examples are already familiar territory. Just as with an advanced graduate text in chemistry, though, that they were familiar for the leading author of the advanced graduate text does not mean that we, readers, can skip them. But, it is true that that is a very tough demand on us, at this time in history.
As McShane has observed, the necessary several years of undergraduate work in the sciences and arts, and in self-attention, the work that would prepare one to work through exercises in Insight, are lacking.
Your end topic on the Rimeann hypothesis shows that you’ve done some serious homework on becoming familiar with the hypothesis. But, I couldn’t be sure what level of mathematical detail you have worked through yourself in the context. For someone doing that math of Riemann's series, can you imagine, perhaps, the enormous challenge – years worth of exercises in self-attention – of reaching familiarity with the many layerings of key questions, key insights of various sorts, layerings of diagrams and symbolisms, transitions of contexts and developments, various routes up through from the Pythagorean Theorem, ...., to Calculus and later, Green’s theorem, to Cauchy’s work on integration and on into convergence theory of complex series and then Riemann’s work on the complex plane? Chapter 10 of Lonergan’s book Insight is a short chapter. But, if the results of one's climb are to be at the level of the near-present times, if e.g, one hope to reach a control of meaning with Riemann's hypothesis, that chapter points to years’ worth of empirical work needed. Lonergan was a genius and reported on his results about the entire historical development of mathematical understanding, and did so in utter crystalline density. For someone who is at home in the mathematics, a first serious of reading Chapter 10 of Insight is at least a several year project, and that as a first cut through only. That single chapter is a foundational mountain climb recorded on a postage stamp, namely, the few pages of Chapter 10. I could say a Post Chapters 1-9 stamp, since the exercises asked of the reader in the book are written cumulatively!
A main key and core challenge put to us by Insight is not reach for philosophical analysis in, e.g, the analytic tradition, but self-knowledge.
In as much as any of us slow pokes can manage (I mean all of us slow compared Lonergan), that is a life-long empirical problem.
And, by the way, even if someone were to attain some level of control comparable to Lonergan’s, what would be the point in attempting to summarize an already ultra dense book of empirical exercises?
How would such summary help the community? A different kind of summary will be normative and needed, but for that see Functional Dialectics in Method in Theology.
This might all sound too much. Please know that I don't mean to discourage you. But, I felt that I should be straight with you about the enormity of the challenge.
You might also have a look at Lonergan’s definition of “generalized empirical method,” p. 141 of the first edition of A Third Collection.
The paragraph there hints at a long term goal for the academy.
You may have noticed that he also uses the name "generalized empirical method" in the earlier book Insight, but he doesn’t say much about it there.
The precise definition needed is the later one that he gave in A Third Collection.
The book Insight partly is an invitation to all of
history, for the Academy to climb toward competence in generalized empirical
method.
But, the book is far far far too advanced to be read "straight on," especially at this time in history.
I was lucky to have had a couple of good teachers who kept forcing me back to “simple problems.”
But, I certainly don't claim any serious mastery. And, frankly, that is much of what I still struggle with, elementary problems.
It would be quite amazing if you were open to the possibility of shifting to a different approach, an empirical approach.
Two books that you might helpful are Philip McShane’s book from 1973, Wealth of Self and Wealth of Nations.
It’s available for free download on his website. http://www.philipmcshane.org/ There is also the co-authored book Introducing Critical Thinking, published by Axial Publishing. Introducing Critical Thinking (with Alexandra Drage and John Benton), Axial Press, 2005. Neither of these two books will encourage traditional philosophical analysis. Both books invite readers, among other things, to grow in self-attention.
Wealth of Self can help one get some initial clarification on the meanings of probability, needed if one is to eventually climb to precision needed to handle advanced problems in advanced contexts, such as, say, the Riemann hypothesis. Even after many years, I find gems in Wealth of Self. McShane has gone on since then, of course, and is still climbing.
But, the precision of that early book is remarkable and the examples remain remarkably helpful.
Wishing all the best in your searching,
Terry
Quinn. PS I hope David will share with us his thoughts as he
"revises" a la Lonergan-Quinn
Dear all,
I stumbled across Lonergan about eight years ago, and have been impressed with his remarkable precision in the way he addresses complex problems.
What struck me was the strong affinity between his method and the mathematical way of thinking, which led me to inquire what connections there could exist between Lonergan and mathematics. The result was quite startling at times, and I have outlined my findings (still in need of tidying up and probably full of mistakes) below.
https://docs.google.com/document/d/e/2PACX-1vTG-fYJZfmx4AxNut9GDOXrJmKCLEDyvJigy8r3vawv12dumw5nSQY9K7mFfntiE250z5BRjRtmlBb1/pub
Your thoughts will be appreciated.
Many thanks,
David
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Q. Where do you see your work contributing? A. Primarily to myself, to grow in self knowledge. But there is a hope that others too may be able to gain some small thing from that journey.
Q. To what community? A. The mathematical community. The background question on my mind throughout was, what is a number? I feel I still haven't plumbed the depths of that question, and a still more extended exploration awaits.
Q. For what progress? A. To prove the Riemann Hypothesis. In my mind, mathematics is about proving theorems, and with Lonergan's compelling genius, I cannot believe it would not be possible to make a breakthrough using his systematic and methodical approach.
Q. To help in what way? A. To demonstrate the potential of a method. When I began, I didn't know how different elements of Lonergan's work would combine into something that approximates to a deductive inference of the Riemann Hypothesis. A more conclusive and precise exposition may follow.
Q. What audience? A. Essentially, anyone who is prepared to engage with the issues. A person who is curious about numbers and wants to solve the Riemann Hypothesis. A person who is rationally self-aware and wants to understand the nature of their consciousness.
Q. What do see as possibly coming from your approach? A. I don't know! I have hopes, I see challenges, but maybe the best outcome is a recognition of these things and a meeting of minds who share the same concerns. From the initial meeting, collaboration should follow.
“To illustrate how these combine in the concrete context of the human mind, we can apply the canons to an empirical analysis of the human mind itself, and since consciousness operates on three successive levels, there will be three successive applications of the canons.”
DavidB
Jaray...@aol.com
Limits Imposed by Today’s Machiavellian Power Politics--the Hope a Pascal Brings
Needless to say, we realize that our hope that people in general live Kingdom values is severely limited by the realities of self-serving and power politics. Today’s nation-states have replaced feudal face-to-face relationships. Machiavelli's The Prince emboldens political leaders to disregard morality. We now live in an all-too a nihilist culture that promotes selfishness. Still, a century after Machiavelli, the Christian genius Blaise Pascal explored the heart and its reasons. In the section “Faith” of Method, Lonergan writes that the heart’s reasons are “feelings that are intentional responses to values” felt by persons “in the dynamic state of being in love.” It includes the kind of knowledge reached through the “discernment of value and the judgments of value of a person in love.” (Method, 115). Faith is a further knowledge experienced when God’s love floods our heart; “to our apprehension of vital, social, cultural and personal values, faith adds an apprehension of transcendent value” leading to “towards the mystery of love and awe” (Ibid). How relate this “eye of love” to power politics or mathematics?
“Faith and progress have a common root in man’s cognitional and moral self-transcendence. To promote either is to promote the other indirectly.” (Ibid). Here again Pascal is a role model. With his role in the discovery of probability theory,[1] Pascal solved “the problem of bringing the superficial lawlessness of pure chance under the domination of law, order and regularity. Man could use the theory of probability to explain rationally things and events that had before been attributed to magic and mysticism.”[2] Pascal and Lonergan help us reconcile heart and reason in the face of the paradoxes in human affairs. Compassion lies at the heart of religion and spirituality. This book focuses on Kingdom-of-God oriented persons and communities. Karen Armstrong has shown that in our secular age governed by reason and technology, fundamentalism has emerged as an overwhelming force in every major world religion. Her approach to compassion[3] reinforces the “optimism” of the present book’s two dialectics by promoting loving hearts and communities. With Gibson Winter, we hold that in our secularized societies, ethics is indispensable to sharing the good news about the kingdom of God (Mark 1:14-15.[4] Exponents of liberation theology, using a see-judge act method, have also argued along those lines.[5] We shall touch on their see-judge-act strategies in Part III as part of our intention to avoid the trap of falsifying Christianity with all-too parochial, privatized forms of “feel-good” escapism which would shield us from social responsibilities. First, we must prepare in Part II the ground for this with a dialectic of persons within communities. Since Part II mainly restricts itself to abbreviated comments on philosophical dialectics, we shall delay until Part III the impact of Lonergan’s views on the religious, theological, mystical aspects of interiority.
PART II The Human Self, Community and Dialectic: How the Kingdom Might Influence the World
CHAPTER 2 Meaning and the Human Good as Constitutive of Human Community[1] Fermat and Pascal created probability theory which has influenced a wide variety of areas of studies requiring the quantitative analysis of large sets of data such as in statistics, finance, insurance, science and philosophy.
[3] Karen Armstrong, The Battle for God: A History of Fundamentalism (New York, Ballantine, 2001); Twelve Steps to a Compassionate Life (Anchor 2010). Every great religious and spiritual tradition teaches that life’s ultimate truth lies within us. Jesus urges “Seek ye first the kingdom of God and His righteousness and all shall be added unto you” (Matthew 6:33). This inner treasure of life has had many names. Plato refers to it as the Good and the Beautiful, Aristotle as Being, Plotinus as the Infinite, Ralph Waldo Emerson as the Oversoul. In Taoism it is called the Tao, in Judaism Ein Sof. See http://www.worldwisdom.com/public/viewpdf/default.aspx?article-title=Faith_and_Modernity_by_Karen_Armstrong.pdf
[4] Gibson Winter, The New Creation as Metropolis (New York: Macmillan, 1963). See also J. Raymaker, Theory-Praxis of Social Ethics: The Complementarity of Bernard Lonergan's and Gibson Winter's Theological Foundations (Marquette Univ. 1977) which correlates these two scholars’ views in terms of relevant value judgments.
[5] Victor Figueroa-Villarreal, Gustavo Gutierrez's Understanding of the Kingdom of God in the Light of the Second Vatican Council, http://digitalcommons.andrews.edu/cgi/viewcontent.cgi?article=1048&context=dissertations.
Catherine Blanche King
David:
I have read over the recent notes here, from you and John and Terry Quinn and, If I may offer just a brief comment: The remarkable openness of mind demonstrated in your writing is refreshing.
Though we all aim at knowing, your "I don't know," like Socrates, reaches back to the lively-ness of unlearned consciousness that is present before any knowledge accrues.
Catherine
Sent: Wednesday, October 11, 2017 1:38 AM
To: Lonergan_L
Subject: [lonergan_l] Re: Lonergan and Mathematics
DavidB
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Pierre Whalon
Catherine Blanche King
John, David, and Terry:
Thank you for publishing this note here. I'm full of questions about it but will limit my inquiry to just three: (1) the "undermining trend"; (2) David's introduction; and (3) haute vulgarization.
First, Terry says: "Discovering the main structuring of the solution was a crowning achievement of Lonergan, a discovery that so far has mainly been ignored by Lonerganism. Please know that I am not singling out any individuals here, but refer to a trend that has been undermining Lonergan Studies. I hope that Lonergan Studies eventually breaks free of that trend. A gradually growing group of scholars interested in Lonergan’s work are now beginning to realize something of the major significance of his discovery, what he called functional specialization."
CBK: Does Terry mean by the "undermining trend" the absence, or even avoidance, in our narratives and presentations of the functional specialties? Or is there something more in this "trend"? It sounds like there's more to it and I would like to know more exactly what that is so that we all here who are interested can avoid it.
Second, Terry writes: "But, if you intend your summary as something more, as an actual 'summary of Lonergan's ideas,' then who might that be for? And is it really plausible? On that approach, one is falling into the damaging tradition of 'negative haute vulgarization,' a tradition invented by Fontanelle, a tradition of philosophy that has been bluffing philosophy and philosophy of science for centuries. With that said, that is though, at present, an accepted mode of scholarship. But, where does it go? That is part of the historical problem."
CBK: At the very least, it goes to a good reference, should readers want to pursue it? But if Terry is talking about the beginning of David's paper and that assumed "going," then I thought it rather good--though of course it's not a comprehensive treatise on Lonergan's Insight. I never thought it was meant to be that. I assumed it to be merely setting up the philosophical background of the writer's "this is where I'm coming from" introduction to what was to come later in the paper. In my view, this pattern (philosophically setting-up) is as best as can be done for a treatment that is not ABOUT that background, but where the writer still wants to poke a few holes, so to speak, and raise a few questions against the reader's own assumptions that (we can also assume) readers will most probably bring to their reading of a document giving treatment to, for instance, mathematics or some other-than-philosophical exploration. (Actually, I think this foundational-context setting-up narrative is what is called for in developing authentic humanities or liberal arts/sciences courses or papers and, perhaps later, even "hard" science papers. If anything has been systematically ignored for the last century and beyond, it's been the foundations of the writer or even the recognition that there even IS such a background. At least such papers won't just begin by assuming some philosophical polymorphic form or other, while they claim some kind of Absolute Objectivity, understood as having no subjective influence at all, as they have for so long.
Having said that, I think Terry's questions point to the many questions and problems with communicating (FS8) Lonergan's work, and the age old problem (as Terry suggests in his reference to Fontanelle) of communicating complex ideas to those who don't like to think that way; and even (potentially) initiating a new paradigm with the hopes of a large shift-of-thought at the level that no one likes to admit. But it is one thing to be incorrect in what you say or write in such abreviated cases, and quite another merely to be brief about it.
But the main point is that, if "we" who want to write in another field but from our albeit-developing Lonergan-inspired influence, need to wait until the general public, or even other fields, are up-to-speed philosophically, nothing in any other field will ever get said or even hinted at, at least by those who are involved with understanding the significance of Lonergan's contributions to at least the philosophical foundations of those fields (if not the religious-theological).
3) But that brings me to my third question which is about Terry's mention of the problem of haute vulgarization ala Lonergan's references to it--which (briefly) have to do with the lack of theoretical consciousness (so important today) and the "appropriation" of complex ideas rooted in theoretical developments, by a commonsense consciousness that has no clue about theory or its import, needs to, and in fact may be biased against theory (general bias).
But let's contrast that with Mirriam-Webster where the definition is about a more general state of affairs that overtly refers to no lacking: "high popularization . . . effective presentation of a difficult subject to a general audience."
"Let's also juxtapose this to two commonly known Lonergan points, paraphrased here: (1) that never was the need more acute than now for qualified communications to commonsense; and (2) from Phil's note on his site where he quotes from a Lonergan letter from 1936 about the massive philosophical and theological problems he recognized: "What on earth is to be done?"
My question: Do you see a conflict here and where the Mirriam Webster definition of HV refers to the "EFFECTIVE presentation" of difficult material to a general audience? Is there such a thing as "effective" where Lonergan's definition and Terry's "negative haute vulgarization" are concerned, where purveying complex ideas, theory itself, or Lonergan's work is concerned? or are we who try to speak to commonsense about such things, just bringing it into the arena of accepted thought, just purveying distortions and "lackings," . . . are we merely tinkling bells and sounding brass?
OR in our albeit small way, are we trying to prepare the way for a change that is already written in the universe. I think the latter, and am willing to swim through the rhetorical excrement that's "out there," even in our own "field," to get there; but I wonder what Terry's take on the matter is?
Catherine
Jaray...@aol.com
"In one of the courses, my job is to help seniors (4th year students) climb into what is called "real analysis."
That course is to help prepare them for the next semester (which I will also teach), a first year graduate school course climb into "modern analysis."
It is also actually quite subtle, working such diverse group of students from various countries, cultures and mathematical backgrounds.
I've students from the Middle East, N. America, Europe, USA and a group of 10 students from S. East China.
There are universities in Chine with which my university has some kind of exchange program going, so we are getting more and more students from there.
Working with the Chinese students this semester has been a hoot because they hardly speak any English and of course, I don't speak any of their Chinese dialects.
Although, two of them taught me a word, which a few days later I can no longer "say" correctly. The subtleties of tone. Wow!
We're managing, though, and most in the Chinese part of the class are excellent students and now "top of the class"!
Anyway, that's my day taking shape! :-)
To your question: Yes, certainly, I have no problem with you sharing my note that I wrote to you and David, if you think it will be of some use.
By the way, you seemed curious about Fontenelle.
Of course, I've nothing against the man.
And, by all accounts, he was a popular and kindly fellow.
The problem that I'm referring to is a tradition of philosophy of science that he promoted (perhaps initiated?) and that pretty soon thereafter became the norm.
He didn't get through his university degree in the sciences and, in particular, wasn't up on the science and mathematics of the day.
But, amusingly in a way, although ultimately part of his damaging influence, he was naive enough to take issue with Newton's work!
Charles B. Paul sheds some light on that "hiatus" in Fontenelle's work (Charles B. Paul, Science and Immortality: The Éloges of the Paris Academy, 1699 - 1791, (Oakland: University of California Press, 2008), 31-32.)
But, you can see something of the problem being expressed by Fontenelle himself. He wrote philosophy for the “worldly salons, …, (whom) he regarded … as his essential audience” (Steven F Rendall, “Fontenelle and his Public,” Modern Language Notes 86 (4) (1971), 496-508.) In the Preface of his famous Entretiens sur la pluralité des mondes (1686), Fontenelle explains:
My purpose is to discourse Philosophy, but not directly in a Philosophical Manner; and to raise it to such a Pitch, that it shall not be too dry and insipid a Subject to please Gentlemen; nor too mean and trifling to entertain Scholars. … If I should acquaint those who are to read this Book, and have any Knowledge of Natural Philosophy, that I do not pretend to instruct, but only to Divert them, by presenting to their View, in a gay and pleasing Dress, what they have already seen in a more grave and solid Habit. Not but They, to whom the Subject is New, may be both Diverted and Instructed: The first will act contrary to my intention, if they look for Profit, and the second, if they seek for nothing but Pleasure (Bernard le Bovier, M. de Fontenelle, Conversations on the Plurality of Worlds, trans. William Gardiner, Esq. London: A. Bettesworth, 1715, page A3. Classic eBook Collection, Open Library, https://openlibrary.org.)
Later in the Preface to that, his book, Fontenelle writes:
To penetrate into things either obscure in themselves, or but darkly expressed, requires deep Meditation, and an earnest application of the Mind; but here nothing more is requisite than to Read, and to imprint an idea of what is read, in the Fancy, which will certainly be clear enough. I shall desire no more of the Fair Sex, than that they will peruse this System of Philosophy with the same application that they do a Romance, or a Novel when they would retain the Plot, or find out all its Beauties (M. de Fontenelle, Conversations, page A4).
The approach became mainstream and continues to influence contemporary philosophy and philosophy of science.
Catherine Blanche King
John:
Well, thanks. But that further discussion, as charming as it is, doesn't address the question about haute vulgarization that I asked.
Also, the migration of mis-takes from Fontelle's time to ours sees the advent of (what I would call) hard-core positivism, which solidified naive realism and is what has been at the core of so many of our problems in the last century.
Catherine
Sent: Wednesday, October 11, 2017 12:19 PM
To: loner...@googlegroups.com
Subject: [lonergan_l] Lonergan and Mathematics--Some Questions
"In one of the courses, my job is to help seniors (4th year students) climb into what is called "real analysis."
That course is to help prepare them for the next semester (which I will also teach), a first year graduate school course climb into "modern analysis."
It is also actually quite subtle, working such diverse group of students from various countries, cultures and mathematical backgrounds.
I've students from the Middle East, N. America, Europe, USA and a group of 10 students from S. East China.
There are universities in Chine with which my university has some kind of exchange program going, so we are getting more and more students from there.
Working with the Chinese students this semester has been a hoot because they hardly speak any English and of course, I don't speak any of their Chinese dialects.
Although, two of them taught me a word, which a few days later I can no longer "say" correctly. The subtleties of tone. Wow!
We're managing, though, and most in the Chinese part of the class are excellent students and now "top of the class"!
Anyway, that's my day taking shape! :-)
To your question: Yes, certainly, I have no problem with you sharing my note that I wrote to you and David, if you think it will be of some use.
By the way, you seemed curious about Fontenelle.
Of course, I've nothing against the man.
And, by all accounts, he was a popular and kindly fellow.
The problem that I'm referring to is a tradition of philosophy of science that he promoted (perhaps initiated?) and that pretty soon thereafter became the norm.
He didn't get through his university degree in the sciences and, in particular, wasn't up on the science and mathematics of the day.
But, amusingly in a way, although ultimately part of his damaging influence, he was naive enough to take issue with Newton's work!
Charles B. Paul sheds some light on that "hiatus" in Fontenelle's work (Charles B. Paul, Science and Immortality: The Éloges of the Paris Academy, 1699 - 1791, (Oakland: University of California Press, 2008), 31-32.)
But, you can see something of the problem being expressed by Fontenelle himself. He wrote philosophy for the “worldly salons, …, (whom) he regarded … as his essential audience” (Steven F Rendall, “Fontenelle and his Public,” Modern Language Notes 86 (4) (1971), 496-508.) In the Preface of his famous Entretiens sur la pluralité des mondes (1686), Fontenelle explains:
My purpose is to discourse Philosophy, but not directly in a Philosophical Manner; and to raise it to such a Pitch, that it shall not be too dry and insipid a Subject to please Gentlemen; nor too mean and trifling to entertain Scholars. … If I should acquaint those who are to read this Book, and have any Knowledge of Natural Philosophy, that I do not pretend to instruct, but only to Divert them, by presenting to their View, in a gay and pleasing Dress, what they have already seen in a more grave and solid Habit. Not but They, to whom the Subject is New, may be both Diverted and Instructed: The first will act contrary to my intention, if they look for Profit, and the second, if they seek for nothing but Pleasure (Bernard le Bovier, M. de Fontenelle, Conversations on the Plurality of Worlds, trans. William Gardiner, Esq. London: A. Bettesworth, 1715, page A3. Classic eBook Collection, Open Library, https://openlibrary.org.)
Jaray...@aol.com
DavidB
DavidB
re...@yahoo.com
Jaray...@aol.com
Jaray...@aol.com
)! See Proof of Riemann hypothesis
We prove Riemann hypothesis. Method is to show the convexity of function which has zeros critical strip the same as zeta function.
| Comments: | detailed proof |
| Subjects: | General Mathematics (math.GM) |
| Cite as: | arXiv:1703.03827 [math.GM] |
| (or arXiv:1703.03827v5 [math.GM] for this version) |
Submission history
From: Vladimir Blinovsky M [view email][v1] Mon, 13 Mar 2017 15:04:13 GMT (3kb)
[v2] Wed, 15 Mar 2017 09:58:20 GMT (3kb)
[v3] Fri, 24 Mar 2017 14:28:34 GMT (2kb)
[v4] Mon, 3 Apr 2017 16:14:52 GMT (2kb)
[v5] Mon, 1 May 2017 05:57:26 GMT (6kb)
Catherine Blanche King
Hello David:
Speaking of interpretation, I need to clarify what I meant by "the liveliness of unlearned consciousness." That is, I didn't mean "untutored consciousness." (I never even thought that about your paper!)
What I meant, and was not very clear about, was that "I don't know" "reaches back," behind our experience and learning to the open dynamism of the basic structure of consciousness as intentional, which is not learned but natural to human intelligence or, to use Lonergan's term, it's "given."
Thanks,
Catherine
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
DavidB
DavidB
Doug Mounce
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Catherine Blanche King
Hello David:
Thank you again for your thoughtful response. I'll respond by copying your text first and responding at CK:
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Good question. My response would be no.
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Catherine Blanche King
Hello again David:
Profound or not, I fear I have inadvertently misled you by using the term "unlearned." I do not mean anything even near being ignorant (or untutored) by the common meaning of those terms. What I mean is the condition for learning any content whatsoever, or, as you say: "the dynamic intentional core." We can learn ABOUT it but, when we do, we use it to do so. Whereas "untutored" implies a state of being in need of learning, like being obtuse, "unlearned" means (in my use of it) that about us which comes with being human--that core. It's not knowledge, but what we learn all knowledge with, including about itself. We come with a set of intentions and a structured-in set of questions (namely: What is it?, Is it so?)--we don't get those by learning--they are, then, "unlearned." And I WANTED you to disregard knowledge content.
Also, children have wonder long before they acquire language--they acquire language through the process of wondering and having insights. (Early pre-language insights produce images, on which we build our more formal language patterns.)
But the "unlearned" comment was an afterthought in my original note about your openness and willingness to say: I don't know. In my own writing, I'll find another way to express the "given" of consciousness, for sure.
Thanks--you need not respond again unless you wish. We've probably beaten this to death more than enough already!
Catherine
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Thomas J. McPartland, Lonergan and the Philosophy of Historical Existence (Univ. of Missouri, 2000), 20 writes that “If Lonergan posits a level of symbolic consciousness because the psychic level of integration is precisely the link between unconscious energy and conscious intentionality, his positing of a spiritual level strains the metaphor even more, perhaps to the point where it may be counterproductive. On the one hand, Lonergan does define levels of integration with the mathematical level of operators and the existence of a spiritual operator (unrestricted loving), would in a move reminiscent of Kiergegaard, be a distinct operator beyond that of the moral. This retains the theological idea of Aquinas that the supernatural sublates (that is perfects) natural existence. On the other hand, the principle of this operator for Lonergan, is not a new set of conscious and intentional operations. The principle is, rather, “conversion”, the vertical exercise of liberty that transforms a horizon and perforce sublates (transforms) the operations within his horizon—but not by a new set of operations.” McPartland pursues this transformation of horizons in term of faith, hope and charity. See https://books.google.de/books?id=DLqDFc54qgYC&pg=PA20&lpg=PA20&dq=lonergan+the+intentional+operators+operate+consciously&source=bl&ots=fbmrJ7w_br&sig=7rYTG-yJ2oBEJYqIRjqXp_yBHTo&hl=en&sa=X&ved=0ahUKEwiewqSy8-zWAhWJmBoKHdIaBk0Q6AEINjAC#v=onepage&q=lonergan%20the%20intentional%20operators%20operate%20consciously&f=false
Hi Doug and Dave,"If a number is one of anything, but there's no one around to count it, is it a number? (George Berkeley?)"
Good question. My response would be no.The counterposition would argue that if a number is one of anything, it doesn't matter whether there is anyone around or not. There were dinosaurs on this planet, and there was no one around at the time. If there was one dinosaur, it is still a number.But one doesn't need to be around at the time to count it. We know there were dinosaurs because we have discovered their bones and fossils. We may not know precisely how many there were or when they lived, but if a number is one of anything, then the fact that we know there were dinosaurs means there is a number. The counterposition argument is unsound, because we are around now to count it.Let's suppose next there is life on some planet millions of light years away where no one has or ever will be around to count it. Is it a number? On Lonergan's position, the real is the intelligently grasped and reasonably affirmed. We can understand the basic meaning of the structures of life. As astronomy becomes more advanced, we may be able to estimate the probability that life would develop on some planet at some time somewhere in the universe. Therefore, the possibility of extraterrestrial life lies within our understanding. But can we reasonably affirm it? If we accept the premise that we cannot count it, we will never know, and such speculation is not scientific. The best we can settle for is not a number, but a concrete probability.A concrete probability is not a number. Rather, it is a feature of the emergent universe in Lonergan's worldview. As soon as we are able to count it, it becomes a number, or rather, a ratio of two numbers. So if a number is one of anything, but there's no one around to count it, there can be no numbers, only concrete probabilities.
Best wishes,David
On Thursday, 12 October 2017 21:39:17 UTC+1, relyo wrote:
Hi Doug and DavidWith regard to Doug's first question, I would say yes With regard to the second there is some truth to it since what a number is, is understood via the relations it is in.With regard to David's questions, I say that numbers per se are formal and real. Things exist, events occur. A number is neither a thing or an event. (so it is not a central or conjugate act). Numbers also can be understood as properties of things and events but that is different from understanding them per se. See MIT pages 75 to 76 on limited spheres of being to get Lonergan's approach to the ontological issue.
More good questions! I'd like to add two items that Lonergan indirectly addresses, but that specifically concern those who study the nature of math.If a number is one of anything, but there's no one around to count it, is it a number? (George Berkley?)The meaning of a number in formal context is the game of arithmetic created to give us insight about qualitatively countable things. (John Casti)PS - EO Wilson maintains that counting is a genetic inclination because everyone learns how to count in the same way (four rules) around the age of 3-5, and we never change the way we count.
On Thu, Oct 12, 2017 at 9:02 AM, 'DavidB' via Lonergan_L <loner...@googlegroups.com> wrote:
Dear Dave,Thank you for sharing this article. There are many helpful thoughts and insights which I shall probably need to spend some time studying. I also enjoyed the broader context of the chapter on language, conceptualisation etc.The problem I had was reconciling my notion of numbers with Lonergan's characterisation of the real. You say, "We speak of numbers as if they exist," and most of the effort we put into understanding them generally takes this starting point for granted. It is a matter of studying the relations, the operations, the material differences, and then having the insight which puts two and two together, and grasps the meaning of a number in its formal context.Does this mean that a number must be formal, since it is abstracted from material difference? The natural answer would be yes, except that it involves the counterpositions. The real is what is intelligibly grasped, and reasonably affirmed. On what do we base our grasp of formal systems? Or in other words, what makes a number a number? And can we reasonably affirm it? I think there is something in what you say about "the insight that there can be one of anything", and "the insight which yields the operators and operands as interrelated". Could we use these to speak of numbers in terms of central and conjugate acts?Good luck with your website development, it is looking really good so far.
Best wishes,David
On Thursday, 12 October 2017 01:49:43 UTC+1, relyo wrote:
Hi David - Though I am not quite ready to generally advertise it, I have developed a website at davidoyler.org. If you go there and select the "Mind and Performance" tab and scroll down you will find a paper titled "Intelligibility, Meaning and Language". The section of that paper titled "Difference and Intelligibility" has some reflections on the nature of numbers you may find of interest.Dave Oyler
On Wednesday, October 11, 2017, 2:44:30 PM MST, 'DavidB' via Lonergan_L <loner...@googlegroups.com> wrote:
Dear Catherine,Some thoughts on the questions you raised.1. "undermining trend". I can't comment on this unfortunately, as I'm not sure what "major historical problem" Terry was referring to, nor what he meant by "Lonergan's crowning achievement." I imagine it's to do with functional specialisation.2. My introduction. I think you are spot on about my intentions, setting the background rather than aiming for a complete exposition of Lonergan's work. Professor McShane has drawn attention to the paragraph that spans pages 609-610 in Insight, which outlines three elements that fuse in an explanatory interpretation, the third element of which is the differentiation and specialisation of modes of expression and which conditions the discoverers own grasp of his or her discovery. So if I am attempting to communicate what I have discovered in Lonergan, then the opening paragraphs reveal the limitations of what I know.Basically, there is still work to be done. The introduction is inadequate, but why? I think you are right about the importance of the foundational context, and that is what I am searching for. I agree with what you said about communicating in other fields and/or the general public, but in mathematics, the communication is connected with the problem. The three elements of the explanatory interpretation, the genetic sequence of insights of discovery, the dialectical alternatives in which they are formulated, and the differentiation and specialisation of modes of expression, must fuse into one.3. Haute vulgarisation. Are we tinkling bells, purveying distortions, or preparing the way for change? Without love, we are indeed merely tinkling bells or sounding brass. Without the clarity of an intellectual conversion, we are indeed purveying our own distortions and misconceptions. But in love, and in truth, we may prepare the way for change.Best wishes,David
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Catherine Blanche King
David:
You say: "If we speak of the unlearned state of dynamic intentionality, disregarding knowledge content, then there is no self-knowledge of its dynamic state."
I'm not saying that, concretely, we don't or cannot have knowledge content, or that our reflection and self-reflection cannot and does not result in knowledge and self-knowledge. I'm just generalizing--distinguishing (a) the basic dynamic structure from (b) its content. Rather than confusing, differentiating often leads to its opposite.
The same applies to your next paragraph. But also in that paragraph, you refer to "the bewildering fact of polymorphism." Now that's a huge topic; and we can be polymorphic in many different arenas and aspects of our learning, e.g., psychologically, socially, politically, spiritually. But in Lonergan's work he often refers specifically to philosophical polymorphism.
In that context, I would consider that term refers also to learning or, in this case, to learning badly.
So that polymorphism occurs **as a result** of the question-to-insight-to-understanding process.
But as polymorphic, we can have insights that flow from oversights and we can have erred insights. But the "many forms" of philosophical thought, ideas, and ideologies refer to what we have learned but where that learning does not correspond with the actual "what" that we asked about at some point in our learning career. Our present understanding, then, doesn't accurately reflect the actual philosophical (cognitional, epistemological, metaphysical) activities of our core consciousness and the assumptions that flow from it's actual activities. Those omissions and erred insights become a set of assumptions that, in turn and if not corrected, do not overcome the core and its activities, but rather continue to conflict with it. They become the source of much internal tension. They are the source of not only the philosophical mess we are in today but they extend themselves into all areas of thought.
It's because our core still works, AND our polymorphism comes into play, that we can say with Einstein: do not listen to what scientists say about their knowing, but watch what they actually do.
The core continues to work; but what scientists think about it and about their own knowing adds the "poly" to the forms of philosophical knowing that are, with that bad learning still in place and influencing our further thought, "bewildering."
Much more to it, of course, but if you need a reference for Lonergan on the above distinction, see Lectures 1 and 7 in Collection 5.)
I don't know if or how the above relates to your last paragraph, but nuf said.
Catherine
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https://docs.google.com/document/d/e/2PACX-1vTG-fYJZfmx4AxNut9GDOXrJmKCLEDyvJigy8r3vawv12dumw5nSQY9K7mFfntiE250z5BRjRtmlBb1/pub
"To illustrate how the canon operates, we will attempt to apply it to the three interpretations of 1+1=2 discussed so far, the conceptual, the formal and the historical. In each case, the goal is to marshal the evidence for the proposition into a form of the virtually unconditioned. Since a virtually unconditioned supposes the fulfilment of other conditions, if there is not to be vicious circle of mutually conditioning affirmations, each interpretation ultimately derives its validity from a form of the absolutely unconditioned.
First, the conceptual interpretation can be summarised as follows.
- 1+1=2 if and only if 1’+1’=2’, where 1’, 2’, are cognitional elements corresponding to 1, 2 respectively;
- The expression 1’+1’=2’ is verified in subjective awareness;
- Hence 1+1=2.
In this interpretation, 1 and 2 are abstract elements that are added to the cognitional contents, 1’, 2’. They could be considered as congruence classes of sets equal under bijection. The major proposition is analytic, it follows from the definition of its terms when 1, 2, have been identified with elements of cognitional awareness. The minor proposition is an experimental issue. The equation has to be verified using subjective concepts. If an insight occurs and the equation is verified, then the conclusion reaches the shape of the virtually unconditioned, and 1+1=2 is known to be true as a matter of fact.
The absolutely unconditioned lies in the realm of subjective awareness. For what is given to empirical consciousness is merely given, and the empirical data that is merely given originates from the reality of rational consciousness. But the given is not explained, it is prior to the questioning of intellectual consciousness, and therefore it is unconditioned not merely as a matter of fact, but absolutely in the field of subjective awareness.
Next, the formal interpretation can be cast as follows.
- 1+1=2 if and only if it is a member of the set T of theorems for which there exists a proof P from the set of axioms A.
- But there is a proof P that 1+1=2 belongs to T.
- Hence 1+1=2.
The expression 1+1=2 is cast into the form of the virtually unconditioned by a chain of deductive reasoning, that relates it to its axiomatic premises. The axioms A are themselves absolutely unconditioned, for they are considered to be self-evident truths.
Third, the historical interpretation relates mathematical expressions to the occurrence of mathematical insights.
- 1+1=2 if and only if it is grasped as virtually unconditioned by the mathematical community.
- But 1+1=2 is grasped as virtually unconditioned by the mathematical community.
- Hence 1+1=2.
The major premise (a) of the argument can be established as follows. For 1+1=2 to be virtually unconditioned, it is not enough for it to be verified in my subjective consciousness. It is not enough for the equation to follow logically from axioms which claim to be self-evident, for what really counts is the choice of axioms that are supposed significant. Rather, it follows from the rational reflection of the mathematical community. Interpretations are subject to scrutiny, questions are raised. There is a process of checking and revision, until the insight on which the expression rests proves to be invulnerable, meaning that there are no further relevant questions. When this happens, it is grasped as virtually unconditioned, and then judgement follows with rational necessity.
The minor premise (b) follows from the principles of criticism we have considered. The interpretation falls within the universal viewpoint, for the mathematical community studies the variety of potential viewpoints and orders them into a genetic and dialectical sequence. It satisfies the principle of equivalence, for it relates the expression to the insights of the mathematical community and this gives it an explanatory formulation. Within the genetic sequence of modes of expression, it stands as a higher viewpoint to the formal interpretation in which the expression 1+1=2 is verified by the mathematical community. Finally, there is the criterion of truth. If the historical interpretation answers all relevant questions, and all the evidence is valid, then in fact it is true, and a failure to judge would be an abandonment of the dictates of rational consciousness.
But the virtually unconditioned rests on the absolutely unconditioned, which in this interpretation is the existence of God. For the existence of a completely intelligible universe in which a mathematical community can develop, supposes the existence of a complete intelligibility which can be shown to have all the attributes of an absolutely necessary being that we name God. And the universe is completely intelligible, for it is the objective of the pure desire to know, which arises within the limits of rational consciousness. Hence 1+1=2 is true virtually through the reflection of the mathematical community, whose existence is true absolutely through the free decision of a creator God.
In the fifth place, there is a canon of residues. It is the acknowledgement of an incidental component in all interpretation, due to limitations of the re-enactment of meaning in one mind by another. This brings us back to Lonergan’s division between classical and statistical heuristic structures of empirical method. The premise of classical method is that similars are similarly understood. In the expression 1+1=2, the dynamism of the human mind is contained in the symbol ‘+’, the pure question in the symbol ‘=’, but the numbers 1, 2, are merely heuristic notions. The one thing that is significant in the numerical symbolism of the expression is the repetition of the number 1, and the single occurrence of the number 2. Indeed, any symbols could have been used, and the expression could be taken as a definition of the number 2.
Classically, numbers are defined implicitly by the heuristic anticipations of inquiring intelligence. For a number is abstract, but it is given a concrete expression by the heuristic symbol x, and the anticipations of intelligence both define the operations with which numbers are manipulated, and the rules which relate them to one another. Within this framework, the definitions of the number ‘1’ as unity and ‘2’ as the sum of two unities arise naturally, and by further insights the definitions extend to projections of the number line, and the fields of rational, real and complex numbers.
Statistically, however, numbers emerge in a context in which abstract laws define the background in which particular instances of numbers occur. For example, the numbers 1, 2, are particular instances of the classical heuristic structure that denotes any number x. The statistical occurrence is the insight that consists of experiencing an aspect of the concrete universe, such as the symbol, 1, the understanding that grasps its similarity to other instances of previously grasped instances of 1, and the judgement that concludes that this is the number, 1.
The contrast between classical and statistical heuristic structures can be illustrated by considering the expression 1+1=2 in a new light. Classically, the elements have definite meanings, either subjectively in terms of cognitional concepts, or formally as an expression within an abstract system. The meaning is conditional on the grasping of the relevant heuristic structure within consciousness. But statistically, what is significant is not processes, but events. 1+1=2 can therefore be interpreted as the definition of the occurrence of an event, an event of insight. The mathematical expression must be true for the event to occur, but if it is, then it is possible for the following to occur: a) concrete experience of the mathematical expression, as written down or in imagination; b) abstract understanding of the mathematical laws, and their combination in the particular expression; c) judgement of the truth of the mathematical expression. The latter component constitutes the final, complete increment in human knowledge, and it is occasioned by the occurrence of insight.
Lonergan considers the nature of statistical heuristic structures, and relates it to their mode of abstraction. His basic theory is that abstraction is not impoverishing, but enriching. The abstract symbol ‘1’ is not simply an impoverished replica that is common to all concrete instances of sets of one. Rather, it reveals the anticipations of intelligence that there is something to be understood in the data. Abstraction is enriching the concrete data by setting up heuristic structures, and the formulation of their intelligibility by specifying their significant aspects, and as a corollary, neglecting the insignificant. Classical and statistical heuristic structures are complementary because of the differing anticipations of intelligibility to be revealed in concrete data. Classical anticipations are of a direct intelligibility to be understood. Statistical anticipations are a denial of a direct intelligibility, but the discovery of an indirect intelligibility in which abstract formulations set up the boundaries from which the concrete diverges, but non-systematically. This indirect intelligibility is called probability.
It is a general feature of classical laws that they are necessarily abstract. Language uses words to refer to concrete objects, but the reference is mediated by an insight that grasps the meaning of a word and its applicability to a concrete object. All mathematical expressions are abstract, and to understand them depends on an insight that grasps the meaning of the abstract symbols and the way they combine in a concrete manner. But the abstractness of classical laws also renders them indeterminate. The expression 1+1=2 is indeterminate inasmuch as we have found different interpretations for the same thing. The nature of the interpretation is determined by the mode of abstraction used.
Lonergan considers the possibility that world process as a whole can be determined completely by classical laws, but concludes that there must be statistical laws too, revealed in the existence of statistical residues. We have determined that classical laws are conditioned by the occurrence of an insight, and the insight itself has conditions which must be fulfilled. If each of the conditions could be determined by a further classical law, then they too would rest on an insight which has further conditions, and in general, the series of conditions diverges. In principle, it is possible to calculate any event Z from the prior sequence of events A, B, C, … that lead up to it, and the prior events can be calculated to the nth degree. But even if the means existed for determining the initial situation to sufficient accuracy, the labour of calculation would only lead to an inference of the event Z, and would not be a firm basis for prediction of the course of events from a slightly different initial situation.
Lonergan refers to the set of diverging series of conditions for different events Z as a non-systematic aggregate. While classical laws determine the intelligibility of systematic processes, theoretical considerations can equally construct what are called non-systematic processes, meaning they are devoid of abstract law. When there is a non-systematic aggregate devoid of abstract relations, then classical laws do not apply, but they can be studied statistically. Statistical theories are explanatory of the numbers and distributions in world process, by considering the relative frequencies of events through the measure of probability.
To interpret 1+1=2 statistically is to recognise it as a true occurrence of insight, but nothing more. Statistical theories do not concern individual events, but events considered in aggregate. A possible application in mathematics might be to solve the Riemann Hypothesis, which states that all the complex values which make a particular function, the ζ function vanish, have a real part equal to ½, because in the critical strip (when the real part lies between 0 and 1) the functional expression of ζ is a diverging series. It could be proved by an insight into the following chain of reasoning:
- If the zeroes of the ζ function form a statistical heuristic structure, then the Riemann Hypothesis is true.
- But the zeroes of the ζ function form a statistical heuristic structure.
- Therefore the Riemann Hypothesis is true.
To know the impossibility of any counter example of the Riemann Hypothesis requires Lonergan’s notion of transcendental knowledge, which means lying beyond human experience. It is possible for humans to calculate any finite number of zeroes, and to verify they all lie on the critical line (real part equal to ½), but the Riemann Hypothesis concerns an infinite number of zeroes. Moreover, there is not known any finite set of insights that brings all the zeroes to heel under an abstract law, and shows they must all lie on the critical line. This is inconclusive, but shows that transcendent knowledge is required for relations involving all the zeroes of the ζ function.
Studying the properties of transcendent knowledge leads Lonergan to conclude to the existence of an unrestricted act of understanding, that grasps everything about everything. Such an understanding would grasp the full range of zeroes of the ζ function, and would know whether or not they all fell on the critical line. But suppose the zeroes formed part of a statistical heuristic structure. What happens to the non-systematic element in the unrestricted act of understanding? Lonergan answers that it vanishes, which leads to a consideration of how the non-systematic element arises in human knowledge in the first place.
The basic distinction is between abstract laws and concrete situations. Abstract laws can demonstrate complete intelligibility, but they cannot be applied to the concrete without further determinations, and the concrete patterns of the further determinations form an enormous non-systematic manifold. Hence there results what Lonergan calls “the peculiar type of impossibility that arises from mutual conditioning.” Granted complete information on the totality of zeroes of the ζ function, one could work out the concrete pattern in which all the diverging series relate the zeroes in the totality. Conversely, granted complete information of the concrete pattern of diverging series, one could use it as a guide to find the zeroes. But both are merely theoretical possibilities. If the zeroes form a statistical heuristic structure, then the diverging series form a non-systematic aggregate, and there is no possibility of deducing one from the other.
Now the ζ function has a reflection formula, which implies that if ζ(s) = 0 then ζ(1-s) = 0 too. But if, by hypothesis, the diverging series form a non-systematic aggregate, then the diverging series for ζ(1-s) cannot be deduced from the diverging series for ζ(s), and vice versa. The only possibility for the simultaneous vanishing of ζ(s) and ζ(1-s) is if the concrete patterns for the diverging series are the same, which implies that s and 1-s are either equal or complex conjugates. If they are equal, then s=½ which is known not to be a zero of the ζ function. But if s and 1-s are complex conjugates, then the real part of s equals ½. This proves the first step a), that if the zeroes form a statistical heuristic structure, then the Riemann Hypothesis is true.
The first step is what Lonergan calls analytic, that is, it can be deduced from the definitions and meanings of its terms. The second step, however, b) is concrete. It has to be determined whether or not, in fact, the zeroes of the ζ function form a statistical heuristic structure. This calls for an empirical analysis of the properties of functions. Such empirical analysis involves a transition from descriptive conjugates, relating things to us, to explanatory conjugates, relating things among themselves." End quote
That is a very ambitious and I must admirable piece of work which has now been professionally evaluated by Terry and Phil. In the light of these evaluations, would you have further comments on e. g. the fact that Riemann's hypothesis has been proved--at least that is what I read on the Net and submitted here a couple of days ago. Specifically, any comments on the following:
"It has been proven that there an infinite number of non-trivial zeros. Of the ten trillion (give or take) found so far, all of them seem to have a real part of exactly 1/2.
Given that evidence, most mathematicians think the Riemann hypothesis is true. But trillions of confirmations do not a proof make.
One
way to get some idea of why 
Each
term is just 
Jaray...@aol.com
David, I'm sorry that I misspoke. Clearly you have read Method in Theology in some depth. In the Ms I'm writing with Father Mombula, PhD, on the subject of language, interiority, community in the light of BL's method etc. we have this footnote--see below. I submit it because of your present conversation with Catherine and invite her or any one's comments. (Sorry, I cannot find a way to enlarge the small print). (John)
In the Philosophical Investigations, Wittgenstein, 19e, set himself the task of refuting Augustine’s view of language: “Augustine describes the learning … of human language as if the child came into a foreign country and did not understand the language of the country; that is, as if he already had a language, only not this one. Or again, as if the child could already think, only not yet speak. And ‘think’ would here mean something like ‘talk to himself.” Since the notion of interiority is the center-piece of Augustine’s thought and writings, it is easy to see why he would write as follows: “It was not that grown-up people instructed me by presenting me with words in certain order by formal teaching, as I was to learn the letters of the alphabet. I, myself, acquired this power of speech with intelligence which you gave me, my God.” (Confessions I.8.13). Wittgenstein rejects this approach since he is not concerned with issues such as interior versus exterior, private versus public. While Augustine does stress the interior and the private, Wittgenstein opts for reductionism; only ordinary, public language matters. Commenting on this topic, David G. Stern, Wittgenstein’s Philosophical Investigations, 181, notes that “Wittgenstein has reminded us that language is a practice, and a practice cannot be super-private.”
David and all,
Doug Mounce
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DavidB
DavidB
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Doug Mounce
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DavidB
Catherine Blanche King
Hello David:
As an aside, Lonergan has some interesting things to say about mathematics in his "discussion" section of collection 5, Understanding and Being. but to your note:
51) Yes--to make distinctions between the core structure and its content is to a move towards theory. However, you say ". . . which is without self-knowledge because we have made the differentiation between structure and content." Such knowledge (of the core sans its content) can be merely a conceptual exercise. However, (and if I understand your comment rightly) that knowledge is also a central part of the process of self-understanding/knowledge.
For example, one way to "catch myself in the process" is to say to myself, **while I'm raising a concrete question** about, say, "who's that on the phone?" That question with content is also a "what is it?" kind of question. In this case, I can pay attention to the content, or who is calling; but I can also pay attention to myself in the process of asking "what." In doing so, I am enacting my core structure: as I intend intelligibility and meaning with any-x content but, in this case, it's the content of: WHO is actually on the phone? In this case of my "catching," I also can focus on the fact that I raised a what-KIND of question that is identical with the theoretical account of cognition as referential (general empirical method); and which relates that conscious order to my own constitutional core. That core is made up of generalized kinds of questions, one of which is the kind that asks "what is it?" intending insights of intelligibility and meaning.
In the case of cognitional theory, the generalization of the theory becomes identical with the concreteness of my actually asking questions. So in the case of both verifying a cognitional theory and consummating an aspect of constitutional self-knowledge, we need not lose anything in the movement from the abstraction of the theory to the concreteness of philosophical self-knowledge: our core. The other core questions are similarly operative and knowable.
2) on polymorphism, you say: "My understanding of polymorphism is that it is prior to the self-knowledge that follows from the concrete subject becoming rationally aware and capable of issuing the transcendental precepts to him/herself."
CK: Philosophical polymorphism issues from an **incorrect** self-understanding, about how we actually learn (cognitional), what knowledge is (epistemological), reality (metaphysics) and where all extends to several other philosophical issues (like ethics). The error can become ideological and assumptive, and can actually block the questions and insights that would develop and/or correct that view. In this way, we can actively reject even discussing such issues. In these cases, the philosophical questions have been raised at some point in our past and, as polymorphic, answered in "latent" and/or "problematic" form.
In that sense, polymorphic consciousness comes "before" an **adequate** understanding/self-knowledge. But again, NOT before the structure itself.
Then you say: "Confusion precedes clarification. The polymorphism is just as much a native feature of the human mind as the liveliness of its dynamic intentionality."
CK: I think not. Though it IS rampant now and over history. That's the value of isolating the core structure as a generalized set of questions, and finding (catching) them operative in ourselves in concrete fashion (like who is on the phone/what is it-type question), from **whatever** content that goes into that structure. As Lonergan says, the question of the subject "is a personal question that will not be the same for everyone." That's where that bewilderment of polymorphism lives.
But what is the same for everyone is that we wonder and ask questions of the type "what is it" (et al). And when we ask a genuine concrete question, we intend, but do not yet know, the answer.
Again, there is a moment of openness there. But polymorphism is an **inadequate ANSWER** (or set of answers) to the philosophical QUESTIONS that we stumble on informally as we grow up and, again, when we enter school and ask them in a more formal way (and then some professor gives you *another* inadequate answer). These are answers and not questions. The core is a set of intentions that turn into wonder and questions concretely.
So in that sense (that the core is a set of operative questions and not answers), again, polymorphism is clearly distinguished from that core.
From my own work in this, there IS a caveat to the above. That is, when we ask concrete questions (like: who is on the phone?), and unless we are involved in direct philosophical questioning, we commonly assume that we KNOW what a phone is; and we commonly ASSUME that it and the ringing are REAL. THOSE assumptions are not questions but are derived from the **habitual nature of our questioning CORE** as it regularly and over our lifetime operates for and in us concretely as a process--from intention to knowledge. It does so, and produces it's own set of assumptions insofar as we work within its parameters and raise no philosophical questions about those operations (like: is it a REAL phone and is it REALLY ringing? How do I KNOW it's REAL?)
The caveat then is that, in the sense that our core itself sets its own habits and assumptions POST-QUESTIONING, those habits and assumptions live in our interior as a part of the polymorphism that we become involved in--the correct part. Part of the "bewilderment" is because our habitual-correct assumptions then become all mixed up with our incorrect assumptions. Insofar as the correct assumptions are a part of our LEARNING, they live together with our ALSO-LEARNED incorrect assumptions. (Now we are talking confusion.)
But our core's **assumptions** flow from the core's built-up habit of operations as we go through life BEFORE we ask philosophical questions and BEFORE we impose our half-baked and incorrect assumptions on our interior life. Those bad assumptions then come into deeply-felt conflict with our core's habits and assumptions. Again, this is why a scientist can DO science (with their core intentions and its habitualized assumptions); but then THINK otherwise about what they are doing when they are doing it. The performative contradiction flows from this same interior conflict.
Also you say: "DB: Insights do not flow from oversights." First, insights can be mistaken. Here's an example: the question is: how do I know? the oversight of the nuances of all of one's own actual cognitional operations (as you suggest later in your note), coupled with the experienced quickness of some knowing, results in the inadequate/erred insight: Understanding is like looking. That's what I meant by "insights can flow from oversights." This also applies to your later paragraph about "false" knowledge. We can make wrong judgments, and so we can be wrong about what we think of as knowledge. But of course if it's not really true, then it's not truly knowledge. But our judgments can emerge from a set of badly formed or informed insights. Haven't you ever backtracked on anything you had insights about ("a dime a dozen"?). Galileo and Newton had many insights that were proven to be wrong later, but still they were insights. I think you are confusing insights with reflective insights (which is often where the backtracking comes from), and then the judgments that can follow from the whole erred process--as sometimes wrong. Knowing has an absolute aspect to it, but it's conditional, and those conditions can be badly set and interferred with via several issues (to much for here). But that's why collaboration is so essential, especially for important things.
You also say: "Polymorphism is undifferentiated potency. " First, I think there is a great difference between **normatively developing** consciousness and philosophical polymorphism, or any kind for that matter. Also, insofar as the core is our potency (our **intending** to understand and know [and BE involved with] meaning and intelligibility), it is not and cannot be "polymorphic," at least not in the sense that Lonergan is talking about in referring to all of the counter-positions. Being undeveloped (say, as a child) is not necessarily equate to being involved with a counter-position. In fact, insofar as our core is at work for us, we know reality when we do so, and we self-correct when we need to. (These activities are quite common for children, who can ALSO lie through their teeth and confuse what they want with what is real. But undifferentiated symbols can hold complete truth, but then keep revealing nuance as we are ready to understand it--as with the parables.
But it's the meaning and intelligibility post-intention that can be polymorphic (again as philosophical); and not the core as intentional (of All). In that sense, polymorphism, though rampant, is not a "native feature of the human mind." (I suspect the Christian idea of "born as sinful" going on here. If that's the case, I will not argue against it in a philosophical context.)
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
Jaray...@aol.com
) of today's overexposed
internet participants. The message is on communication:"Communication is key—the best ideas in the world don’t mean a thing if you can’t figure out a pithy way to get them across. That’s why the Sanders Institute is so important: it’s working in the tradition of the best explainer in contemporary American politics, a man who’s able to get across the essence of what needs to happen in language that sticks.
Consider “Medicare for all,” which is the perfect way of taking the word salad that surrounds health care policy and putting it in terms all of us viscerally get (including those, like me, who’ve been intimidated by the insurance industry’s endless efforts to “complexify” the problem behind an endless screen of words.” Or think about “Fight for $15.” Everyone who hears it immediately imagines what it would be like trying to live on less than that: it brings the idea of “living wage” into sharp focus." End quote.
The reality is that we have a loose canon in the WH: (I suspect he is not really the legitimate "president" due to the conspiracies now being investigated by former FBI chief Mueller).
My main point is that we here ARE touching on KEY issues. Math is at the base of contemporary science but what are its real foundations? Well David helped us get on that track, Catherine is specialized in pedagogy and I ask HOW can the scattered "GEM-FS community" help put it all together. The present exercise is a step in the right direction. (As a side issue, we are thinking of whether there is a way to "connect up with Phil's site now exploring BL's THIRD WAY!)
The genius BL had hte knack of addressing all relevant issues. E.G. I'm looking at Insight p. 168, CH 5 Space and Time, 2. 4 TRANSFORMATIONS, which pursues the discussion on REFERENCE FRAMES.
I find it challenging as we "inch on" toward answers that would invariably include BL's notions of heuristic structures, and e. g. pp. 718, 740 where he addresses the roles of heuristic structures in "Special Transcendent Knowledge" re the problem of EVIL,
John
Doug Mounce
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DavidB
Catherine Blanche King
Hello David:
I'm also off at my grandkids' soccer games this weekend--ALL weekend, so I'm taking a break from writing and responding. It's a good time to let things settle anyway. No hurry.
Catherine
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Jaray...@aol.com
Hi all,It's been a while since we've had the sustained type of discussion now occuring here which originally stemmed from David's probing questions on BL and math. Many peripheral issues arise as are being ably addressed below by Catherine and David. At the core of this probing discussion is the core of what I have come to call "GEM-FS" generalized empirical method functionally specialized.A key element in such ambitious discussion we are now attempting is FS8 which seems to be one of Catherine's key interests. For what it's worth, I'll share a couple of paragraphs from one of the so many emails I get each day (join the club"Communication is key—the best ideas in the world don’t mean a thing if you can’t figure out a pithy way to get them across. That’s why the Sanders Institute is so important: it’s working in the tradition of the best explainer in contemporary American politics, a man who’s able to get across the essence of what needs to happen in language that sticks.
Consider “Medicare for all,” which is the perfect way of taking the word salad that surrounds health care policy and putting it in terms all of us viscerally get (including those, like me, who’ve been intimidated by the insurance industry’s endless efforts to “complexify” the problem behind an endless screen of words.” Or think about “Fight for $15.” Everyone who hears it immediately imagines what it would be like trying to live on less than that: it brings the idea of “living wage” into sharp focus." End quote.
The reality is that we have a loose canon in the WH: (I suspect he is not really the legitimate "president" due to the conspiracies now being investigated by former FBI chief Mueller).
My main point is that we here ARE touching on KEY issues. Math is at the base of contemporary science but what are its real foundations? Well David helped us get on that track, Catherine is specialized in pedagogy and I ask HOW can the scattered "GEM-FS community" help put it all together. The present exercise is a step in the right direction. (As a side issue, we are thinking of whether there is a way to "connect up with Phil's site now exploring BL's THIRD WAY!)
The genius BL had hte knack of addressing all relevant issues. E.G. I'm looking at Insight p. 168, CH 5 Space and Time, 2. 4 TRANSFORMATIONS, which pursues the discussion on REFERENCE FRAMES.
I find it challenging as we "inch on" toward answers that would invariably include BL's notions of heuristic structures, and e. g. pp. 718, 740 where he addresses the roles of heuristic structures in "Special Transcendent Knowledge" re the problem of EVIL,
John
In a message dated 10/14/2017 1:21:40 AM Mitteleuropäische Sommerzei, cb-k...@live.com writes:
Jaray...@aol.com
BRINGING BERNARD LONERGAN DOWN TO EARTH AND
OUR HEARTS AND COMMUNITIES: THE ROLE OF THE KINGDOM OF GODAppendix 7 Linking Lonergan’s Notions of Cosmopolis, Emergent Probability, Economics
One can link Lonergan’s notion of cosmopolis with his own radically new, original thinking of economic process. While Marx opposed capitalism because it alienates humans from their true nature, for Lonergan, an economy should not primarily focus on profit but rather on sensible, equitable forms of production. Having read Feuerbach’s criticism of persons’ alienation within a society,[1] Marx concluded that alienation is due to the malfunctioning of the economy: “The philosophers have only interpreted the world; the point is to change it.”[2] Marx had already argued along this line in his Economic and Philosophical Manuscripts. (1844); alienation occurs when a worker is estranged from the products of his labor, from the forces of production, from himself and from the community.[3] Society is based on three elements: the relation of production, the force of production and the superstructure. Contrary to Hegel and Feuerbach who thought that men will be emancipated by enlightening their consciousness,[4] Marx argues that true emancipation will only occur by changing the material conditions of men—changing the mode of production. As to the practical side of Marx’s project, the superstructure[5] of religion, politics, science, education is determined by men’s concrete economic conditions. Marx asks whether man’s ideas, views and conceptions--his consciousness “changes with every change in the conditions of his material existence, in his social relations and in his social life?” He answers that the history of ideas proves “that intellectual production changes” to the extent that material production changes. In the Communist Manifesto, he and Engels fault the ruling classes for falsifying the problem.[6]
The Marxian claim that man’s economic condition is based on his anthropology which stressed that man is essentially a worker (homo faber). This idea can be traced back to Hegel’s Phenomenology of Spirit which Marx viewed as “the true birthplace and secret of the Hegelian philosophy.”[7][1] In his Essence of Religion (for Eng. Edition, Prometheus Books, 2004) wrote: "Man—this is the mystery of religion—projects his being into objectivity, and then again makes himself an object to this projected image of himself thus converted into a subject" (EC 29-30). He accuses Christianity of depriving man of his temporal life.
[2] Marx, “Theses on Feuerbach, XI” (1845), Early Writings, 423.
[3] Marx, Economic and Philosophical Manuscripts, Early Writings, 329-30, writes: “Estranged labor not only (1) estranges nature from man, it (2) estranges man from himself, from his own active function, from his vital activity; because of this, it also estranges man from his species. It turns his species-life into a means for his individual life. … (3) Estranged labor therefore turns man’s species-being – both nature and his intellectual species-power – into a being alien to himself... . estranged from his own body, from nature, … from his spiritual essence [Wesen], his human essence. (4) An immediate consequence of man’s estrangement from the product of his labor, his life activity, his species-being, is the estrangement of man from man. When man confronts himself, he also confronts other men. What is true of man’s relationship to his labor, to the product of his labor and himself, is also true of his relationship to other men, and to the labor and the object of the labor of other men.”
[4] In his “Theses on Feuerbach, “(1845) Marx writes: “Feuerbach wants sensuous objects, really distinct from the thought objects, but he does not conceive human activity itself as objective activity. …He regards the theoretical attitude as the only genuinely human attitude, while practice is conceived and fixed only in its dirty judaical manifestation. Hence, he does not grasp the significance of “revolutionary”, of “practical-critical”, of “activity.”
[5] As to Marx and Lonergan on production and the superstructure. See James Marsh, Lonergan in the World: Self-Absorption, Otherness, and Justice (Univ. of Toronto, 2014) 174-75. For Marx and Engels, superstructure refers to juridico-political institutions such as the law; infrastructure means the base for economic structure of society.
[6] Marx and Engels, The Communist Manifesto, 241.
[7] Marx, “Economic and Philosophical Manuscripts,” Early Writings, 382-83. (John)
Jaray...@aol.com
, and offer some
reflections I've had on Cusa and Franz Capra that in some ways parallel the
intricacies of the deeper implications of math and is possible deeper
connections with religious-mystical notions that you hint at in your own
note:"Mathematical Theologies
Nicholas of Cusa and the Legacy of Thierry of Chartres"
by David Albertson "Mathematization is usually regarded as the central element in the transition from medieval theology to modern science. David Albertsons genealogical study of the roots of Nicholas of Cusas thought in the Christian Neopythagoreanism of Thierry of Chartres demonstrates that theology and mathematics did not always go separate ways. What if, in our age of unprecedented quantification, Word and Number could be made to meet once again? That is the provocative question of this brilliant book." - Philipp W. Rosemann, University of Dallas
"This book is a brilliant example of how much the history of ideas can still add to the history of practices, especially scholarly practices." - Richard J. Oosterhoff, Isis
2) Or for what it's worth James Hollomon's review of Franz Capra's TAO of PHYSICS See https://www.goodreads.com/book/show/10238.The_Tao_of_Physics
"Don't
look to Capra for a highly disciplined discourse on particle physics or the
nature of cosmology. Nor is this book a deep exploration of Taoism or other
Eastern Religious Philosophy. Rather, it is a fascinating mental adventure
showing the ways the two schools of thought often developed in parallel and came
to similar conclusions from very different beginning points. The author's own
words in the epilogue sum it up nicely. "Science does not need mysticism and
mysticism does not need science, but man needs both."
That's what I said
before reading extensively in physics and cosmology and before watching so many
charlatans and the honest but misguided people duped by them try to sell Woo-Woo
in place of solid science. I wish I had not written the review above, but I'll
let it stand as mute warning to be careful of lay interpretations of science.
And a Medical Doctor like Dr. Robert Lanza or a New Age/Alternative Medicine
guru like Depak Chopra is not a particle physicist. Their pronouncements on
quantum mechanics are no more valid than mine would be if I suddenly set out to
perform delicate surgery.
It's very true that weird,
seemingly mystical things do go on at the tiny scale of the atom where quantum
physics operates. It is NOT true, however, that you can scale that quantum
weirdness up to the macro level where human beings, planets, galaxies and
universes operate, and draw realistic inferences on the parallels between the
macro world and Eastern mysticism.Here's a good
discussion of the Woo effect and why it should be avoided, provided by British
Physicist Dr. Phil Moriarty on the Sixty Symbols Channel on YouTube. END QUOTES
My point is that Lonergan's method offers possibilities of linking the deeper realities of life and knowledge hardly found in other thinkers, but at least explored by the ancients and by moderns hinted by the above 2 efforts and by your own efforts. Gauss' life work and the fundamental theorems of calculus, algebra etc are other building blocks for math-reality correlations John
I think what you guys might want is a quote from Rothendieck,"The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance."
On Fri, Oct 13, 2017 at 1:23 PM, 'DavidB' via Lonergan_L <loner...@googlegroups.com> wrote:
Hi John,Thanks, that's a lot to take in! I thought you added some comments at the end of the quote, but I can't find them now. Nevertheless, I can add a few thoughts below.What I was trying to do when talking about the Riemann hypothesis was to mirror Lonergan's argument by which he demonstrates the existence of God (Insight, chapter 19). I think that argument is instructive because many people say it can't be done, but if it is valid, then the implications are enormous. But the real way to put it to the test is by setting it on a mathematical footing.One of Lonergan's observations is that all ontological arguments for the existence of God must be false. I had an instinct that the same might be true of the Riemann Hypothesis, in which case, a clarification of the ontological nature of numbers would be a prerequisite for the proof. Of course, I might be mistaken, but the train of discovery this line of thought has led me on has demonstrated, at least to me, its efficacy. What I think is happening is that it is bringing to light the inner dynamics of consciousness, which is far more important and fundamental than the proofs and theorems of the formal systems of the old mathematics. And I think the expression of that discovery may be in terms of functional specialisation.When Andrew Wiles proved Fermat's Last Theorem, he said making the discovery was like being in a dark room, and then suddenly finding the switch. When he could see where everything was, he could find his proof. With the Riemann Hypothesis, we have been in the dark for around 150 years, but I think there is no light switch. Rather, the light will be like the rising of the sun at the dawn of day. When we can all see, and reflect, then we shall find a proof.As for those putative proofs on the web, I regret they do not interest me greatly. They might be true, but I would leave that to the reflection of the professional mathematical community. What is far more important is the dynamics of inquiry, the quest for understanding, the search for truth. Whether or not the Riemann Hypothesis is part of that now is a minor historical detail.
Best wishes,David
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Concrete mathematics : a foundation for computer science / Ronald
L. Graham, Donald E. Knuth, Oren Patashnik.
Hello again David:
Profound or not, I fear I have inadvertently misled you by using the term "unlearned." I do not mean anything even near being ignorant (or untutored) by the common meaning of those terms. What I mean is the condition for learning any content whatsoever, or, as you say: "the dynamic intentional core." We can learn ABOUT it but, when we do, we use it to do so. Whereas "untutored" implies a state of being in need of learning, like being obtuse, "unlearned" means (in my use of it) that about us which comes with being human--that core. It's not knowledge, but what we learn all knowledge with, including about itself. We come with a set of intentions and a structured-in set of questions (namely: What is it?, Is it so?)--we don't get those by learning--they are, then, "unlearned." And I WANTED you to disregard knowledge content.
Also, children have wonder long before they acquire language--they acquire language through the process of wondering and having insights. (Early pre-language insights produce images, on which we build our more formal language patterns.)
But the "unlearned" comment was an afterthought in my original note about your openness and willingness to say: I don't know. In my own writing, I'll find another way to express the "given" of consciousness, for sure.
Thanks--you need not respond again unless you wish. We've probably beaten this to death more than enough already!
Catherine
From: 'DavidB' via Lonergan_L <loner...@googlegroups.com>
Sent: Thursday, October 12, 2017 3:25 PM
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
Dear Catherine,
Thank you for your kind and detailed response.It is very helpful to me to get to grips with that dynamic intentional core that is unlearned ("given"), and the source of our wonder and inquiry. I never imagined the depths that might lie behind that innocent expression of "I don't know"!Firstly, a reply to clarify your first point.CK: Take out the "what" or the content of learning? I meant that our potential to learn any "what" is given to us or it is "UN-learned." We don't have to teach a child to wonder.DB: Agreed, a child does not need to be taught to ask questions. As soon as they acquire the use of language, the questions seem to flow spontaneously in an unending stream! Yet precisely for that reason, what is unlearned is also untutored. I did not mean to disregard the content of learning, nor to deny that our potential to learn is "given". I was merely paying attention to a different aspect of what I considered to be the same thing. Apologies for causing any confusion!All else I wish to say is that your remarks on consciousness are very profound. But I wish to draw attention to the dynamic intentional core that is in operation even in this very dialogue. Your interpretation: "I "perceived" your statement ("I don't know"); I use what I know of consciousness; and I generalize to point to its range of potential implications in the particular" is an example of how the intentional operators operate consciously, leading to your conclusion of an attitude of openness. Consciousness operates on three levels, the empirical (your perception of my statement), the intellectual (the use of your own understanding to generalise and reach a range of potential implications), and the rational (your evaluation of the evidence and judgement on a probable state of affairs.) These procedures are all very valid, and I am impressed with the way you showed me how you reached your conclusion.There is a lot here I need to assimilate, especially what you said about the "the basic structure as KNOWN is not merely ... a subjective or "my psychology" affair." Actually, that is what made me doubt that the statement "I don't know" could have revealed something about my "reaching back to the liveliness of unlearned consciousness". Is that a subjective or psychological affair? On the contrary, it is an objective expression of a general interpretation that is either true or false, depending on how honest I am in my spiritual confession.
Thanks, and best wishes,David
On Thursday, 12 October 2017 17:28:02 UTC+1, cb-king1 wrote:
Hello David:
Thank you again for your thoughtful response. I'll respond by copying your text first and responding at CK:
DB: "In my mind they (unlearned and untutored) were the same, because what one teaches, another learns, and there is no learning without teaching."
CK: Take out the "what" or the content of learning? I meant that our potential to learn any "what" is given to us or it is "UN-learned." We don't have to teach a child to wonder. It's "given" for humans to do so. And that aspect of our consciousness enables and conditions all learning-of-any-what, or content-x. (You'll find later that Lonergan connects this natural aspect of us to being itself. "The fundamental moment in the notion of being lies in the capacity to wonder and reflect; and that **as potency** we have from nature" [Col. 5/164/my emphasis].) All learned content depends on the basic structure and begins from there.DB: ". . . even when learning by oneself, there is the matter of tutoring one's own consciousness to do so."CK: Yes, indeed. FYI Emile Piscitelli develops this aspect of consciousness: internally, our speaking to ourselves about something--a subject-object-subject structure (the internal structure of speech/dialogue). He draws centrally from Lonergan's work but relates it to the movements of language (ala Ricoeur and others) that were going on as Lonergan was leaving the scene. Piscitelli's work (as far as I know) has been neglected; but I find it a powerful development and refinement of Lonergan's contributions, especially where language (EP's dissertation) and the dialectical attitudes are concerned (see: Lonergan Workshop 5).
DB: "I find your point about 'reaching back' very interesting, and that is certainly what I want to do. But I'm not sure the 'reaching back' resides in the 'I don't know' itself. If I ask the question, 'Am I a knower?' there is certainly a reaching involved, but the answer 'I don't know' is inconsistent, because if I do not know that I am a knower, I should not answer, preserving the silence of an animal that says nothing and offers no excuses for its silence. If nevertheless I answered 'I don't know,' then that would not reveal a reaching, but rather a lack of it."CK: If we leave behind the emphasis on the conceptual expression, there is an honesty in saying "I don't know". . . when one really doesn't know--regardless of content. It suggests, rather than empty silence, the dynamism of an attitude of openness to understanding which is not like an animal (because it's not an animal that can say it, but a human). That openness, though surrounded by content on all sides, so to speak--even the content of whatever question you are responding to (like your: am I a knower?), but shorn of that content--is identical with our dynamic intentional core from whence wonder (about any x) actually emerges.CK: Of course, we can ignore our own questions--perhaps they are not really ours but someone else's. But our intentional core doesn't go away; and if these particular questions ARE our own questions, they probably won't really go away either. They can dog the hell out of us for a very long time.CK: Also, and since we are in the context of Lonergan's work here, we can put that in a religious frame and say that the authentic "I don't know" is a kind of spiritual confession where, in humility, we neither pretend to know nor ignore our own questioning spirit, aka our desire to understand and know; and where hope resides in that openness-to as an attitude.CK: Also, that should double as a response to your next paragraph, except that the basic structure as KNOWN is not merely "the reaching back (that) occurs in (MY) own mind;" if that's what you mean (and I'm not sure it is). As a known, it's not merely a subjective or "my psychology" affair. I AM interpreting, and I AM assuming your honesty in saying "I don't know" in this case. But the general interpretation has a reality that supports one interpretation over another. A singular person is or is not "being honest."CK: But you are right that no one CAN know the state of honesty manifest in any one person and situation. On that, I don't think we are being "too general" but rather we need to keep that generality as key to our exchange and, I hope, in this case, along with my assumptions.CK: Nevertheless, I "perceived" your statement ("I don't know"); I use what I know of consciousness; and I generalize to point to its range of potential implications in the particular. That's my response also to your next paragraph:DB: ". . . I am also interested in the precise way this works because the same words may not have the same effect for another reader. 'I don't know' could also proceed from my ignorance, which is not very illuminating to anyone."CK: Yes, our ignorance, and then there's the question of the presence of our attitude of openness to understanding.I appreciate the dialogue,
Catherine
From: 'DavidB' via Lonergan_L <loner...@googlegroups.com>
Sent: Thursday, October 12, 2017 5:55 AM
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
Dear Catherine,
Thank you for your clarification, and apologies for confusing the distinction between "unlearned" and "untutored". In my mind they were the same, because what one teaches, another learns, and there is no learning without teaching. The latter is perhaps debatable, but even when learning by oneself, there is the matter of tutoring one's own consciousness to do so.I find your point about "reaching back" very interesting, and that is certainly what I want to do. But I'm not sure the "reaching back" resides in the "I don't know" itself. If I ask the question, "Am I a knower?" there is certainly a reaching involved, but the answer "I don't know" is inconsistent, because if I do not know that I am a knower, I should not answer, preserving the silence of an animal that says nothing and offers no excuses for its silence. If nevertheless I answered "I don't know", then that would not reveal a reaching, but rather a lack of it.
Maybe I am generalising too much, and if you perceived a reaching back in my answer "I don't know", then I should be pleased about it. But I would like to suggest that the reaching back occurs in your own mind. In interpretation, the proximate source of meaning resides in the interpreter's own mind, and "I don't know" may have been the phrase that broke your conscious flow and led you to advert to the open dynamism of intentional consciousness, prior to learning and experience, that Lonergan describes as "given". This would be experienced as a "reaching back". If that is the case then I am happy, but I am also interested in the precise way this works because the same words may not have the same effect for another reader. "I don't know" could also proceed from my ignorance, which is not very illuminating to anyone.Best wishes,David
On Thursday, 12 October 2017 11:37:13 UTC+1, cb-king1 wrote:
Hello David:
Speaking of interpretation, I need to clarify what I meant by "the liveliness of unlearned consciousness." That is, I didn't mean "untutored consciousness." (I never even thought that about your paper!)
What I meant, and was not very clear about, was that "I don't know" "reaches back," behind our experience and learning to the open dynamism of the basic structure of consciousness as intentional, which is not learned but natural to human intelligence or, to use Lonergan's term, it's "given."
Thanks,
Catherine
From: 'DavidB' via Lonergan_L <loner...@googlegroups.com>
Sent: Wednesday, October 11, 2017 5:47 AM
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
Dear Catherine,
Thank you for your kind remarks. I try to keep an open mind, I think it is a matter of being honest with oneself.What you say about the liveliness of untutored consciousness reminds me of Lonergan's account of the law of genuineness in his analysis of human development. When we speak of a simple and honest soul, we are not inclined to think of one that is given to self-introspection. However, there is a genuineness that has to be won back due to the ingrained habits that can be acquired over a lifetime. That is what we must reach to.Best wishes,David
On Wednesday, 11 October 2017 12:27:30 UTC+1, cb-king1 wrote:David:
I have read over the recent notes here, from you and John and Terry Quinn and, If I may offer just a brief comment: The remarkable openness of mind demonstrated in your writing is refreshing.
Though we all aim at knowing, your "I don't know," like Socrates, reaches back to the lively-ness of unlearned consciousness that is present before any knowledge accrues.
Catherine
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"The discoveries of practical intelligence, which once were an incidental addition to the spontaneous fabric of human living, now penetrate and overwhelm its every aspect. For just as technology and capital formation interpose their schemes of recurrence[1] between man and the rhythms of nature, so economics and politics are vast structures of interdependence invented by practical intelligence for the mastery not of nature but of man." (Insight, 238).
John
[1] “Schemes of Recurrence are conjoined dynamic activities where, in simplest form, each element generates the next action, which in turn generates the next, until the last dynamic regenerates the first one again, locking the whole scheme into long term stable equilibrium.” See Mike Bretz, “Emergent Probability: A Directed Scale-Free Network” https://arxiv.org/ftp/cond-mat/papers/0207/0207241.pdf
Catherine Blanche King
Hello David:
I cannot "delve" here, but I did have a recovered insight over the weekend about having incorrect insights.
That is, BEFORE heading into reflection and self-reflection, insights--though shown to be incorrect in a specific context--can also be the unexpected source of OTHER correct judgments (for actual knowledge) and for the open-ended creative process in general.
That process is not yet about knowing but about explorations of meaning and intelligibility, and the yet-unanswered questions of what we are to become in our living. That's not settled yet and, in that sense, cannot be knowledge in Lonergan's sense of the
conditioned whose conditions are fulfilled.
This week is full for me, but I did want to add that thought to our discussion.
Thanks,
Catherine
Sent: Friday, October 13, 2017 4:21 PM
To: loner...@googlegroups.com
DavidB
Dear Catherine,
I hope your grandchildren had a good time playing soccer. Yes, it's good to take a break.
Your comments are very helpful to me. However, I think as well as dealing with all the issues, we have to deal with them in the right order too. Lonergan's work operates on three levels, 1) a study of human understanding; 2) unfolding the philosophical implications of that understanding; 3) a campaign against the flight from understanding (cf. Insight, preface p6-7). We could briefly call these cognitional theory, philosophy and practicality, corresponding roughly to the three levels of empirical, intellectual and rational consciousness. So I would like to respond to your comments under those three headings.
1. Cognitional theory.
Is there such a thing as a mistaken insight?
I have tried in vain to find a reference in which Lonergan uses the term "mistaken insight". I think he does, but the fact it is not easy to find suggests to me that it is not fundamental to his theory. The question we should be asking is, what is an insight? Lonergan answers that question using over 700 pages, but I want to abstract and identify the significant features therein. Let me try to explain what I mean.
In his example of a dramatic instance of insight, Lonergan lists five characteristics. 1) Release of tension to inquiry, 2) occurring suddenly and spontaneously, 3) as a function of inner conditions, not outer circumstances, 4) pivoting between the abstract and the concrete, and 5) passing into the habitual texture of the mind.
Now a mistaken insight (such as "understanding is like seeing") could satisfy all these conditions except the first one. Precisely because it is mistaken, it will not put an end to all the further questions that could challenge its acceptance, and therefore the release of tension is incomplete, inviting the further insights that could correct and complement it. If other desires interfered with the pure intellectual desire then the incomplete release of tension might not be adverted to, but in Lonergan's philosophy, faithfulness to the pure desire is an earnest demand.
However I was mistaken when I said "every insight has a content of experience, a content of understanding and a content of judgement". That is not a definition of insight, but rather the heuristic structure of proportionate being. That mistake did not flow from an insight, but rather an oversight of the nature of reflective insight. If I had had the insight, then I could have backtracked and corrected myself. It is an example of failure of being attentive to my own cognitional processes, but I would not call it a mistaken insight. Using an inverse insight, you might grasp that there is no insight to grasp in my mistake, but simply a lack of it.
But if I deny such a thing as a "mistaken insight", then I have to concede that it arises in common sense speech, and you demonstrate very articulately how it arises within a context of judgements in which truth has an absolute objectivity. What I am trying to get at is an insight into insight. In Lonergan's example of the cartwheel, there is an image (hub, spokes, rim) and a set of concepts (points, lines, circle). Clearly it is nonsense to think of a line without breadth, or a point without magnitude, but that is what happens when we approach the definition of a circle. Still, I am trying to conceive of an insight while abstracting from the margin of error that accrues, to a greater or lesser extent, in any concrete instance. Instead of correct and mistaken insights, would it be possible to speak of adequate and inadequate insights, depending on whether all the relevant questions have been met?
As for reflective insights, there need not be any confusion. A direct insight may be an insight into some concrete situation. But a reflective insight may be an insight into some other insight, that determines whether or not the content of that insight agrees with the true state of affairs. And that insight will be a function of the habitual assumptions and beliefs we have built up into our inner core, which could lead to erroneous judgements. But that becomes a philosophical matter, which leads into our next topic.
2. Philosophy
Do scientists add "poly" to their knowing?
I think there is a danger for each of us of trying to talk about philosophical concepts in a common sense way. Common sense is simply not adequate to grapple with such complex issues as polymorphism, and the only way to handle it correctly is in a philosophical context.
"Understanding is like seeing."
If I thought that, then it might be based on an insight, because there is indeed a similarity between understanding and seeing. However, the error of the empiricists was to assume that "what is obvious in knowing is what knowing obviously is." (Insight p441). The fact that they did not bring their understanding to the level of critical reflection meant that their insights were due to be corrected and complemented by the further insights that would reveal the limitations of their outlook. (Perhaps this complementing and correcting is similar to what you mentioned in your latest email, about incorrect insights being the possible unexpected source of correct insights.)
Polymorphism.
To try and bring our discussion of polymorphism on a philosophical footing, I think we need to refer to Lonergan's notion of an explanatory interpretation (Insight p609-10). There are three elements, a) the genetic sequence of insights, b) the dialectical oppositions in which the insights may be formulated, c) the specialisation and differentiation of modes of expression. What I would like to draw attention to is that the dialectical oppositions exist within the formulations of insight, not necessarily the insight itself.
So the general pattern is Image -> Insight -> Formulation -> Reflection -> Judgement.
Moreover, this pattern is part of the inner dynamic structure of consciousness. But the formulations of insight may be either consistent or inconsistent with that basic dynamic structure. Moreover, the resulting dialectical oppositions will always be present at least theoretically, because simply changing one of the premises in a formulation may turn a position into a counterposition, and vice versa. That is why I say polymorphism is a native disposition of the human mind, although through culture and education it can be reduced to a minimum.
Please note that I am trying to abstract again. Formulations are not independent of insight, nor do the positions and counterpositions generally reside in individual formulations, but in overall orientations and outlooks. And rarely are they found in pure form, since most people live their lives in some blend of both. The point of making this distinction between insight and formulations is that it enables the fourth functional specialty, dialectic, to operate. If an insight were mistaken, how would we know if it were never formulated? But if it were formulated, then the consistency of the formulation with the dynamic structure resides in the formulation, not the insight.
I think a lot of your argument revolved around the core set of operative questions, noting that polymorphism resulted from "inadequate answers", not questions. Now I think we have to distinguish between different types of core. On an empirical level, the core is the inner dynamism of the pure desire, oriented towards the universe of being. On an intellectual level, the core is a set of operative questions, derived from a background context of habits and assumptions. On a rational level, the core is the latent integrated metaphysical knowledge derived from the sciences and common sense. Which of these cores were you "catching" yourself in when you asked yourself, who was on the phone? The point I wish to make is that there is an ambiguity here, and that is part of the polymorphism.
I just checked "polymorphism" in the index (Insight), and found this on page 452: "the polymorphism of human consciousness is the one and only key to philosophy." So whatever it is, it must be important!
3. Practicality
Having made all these remarks, I would like to return, with you, to the need for an open mind. I accept that anything I have written could be inadequate or mistaken, and as part of the campaign against the flight for understanding, I wish to submit to any valid reasons that can show that to be the case. The need is to reach the level of critical reflection, and the philosophy that not only explains itself but also all the other philosophies as well. The dialogue is helpful, but I think we all need to reflect, as we write.
Taking our time can sometimes be helpful with that. Some people can reflect spontaneously, others need to spend some time away and come back refreshed. So I invite you to reflect on who you are, your life, your joys, your grandchildren, your strengths, your experiences. Certainly you are skilled in grasping the inner dynamics of consciousness, and describing their subtle nuances. I feel I have learned a lot already. But Lonergan's vision is greater than any of us, and so we must grapple together to spiral along the inner dynamics of truth.
Something you said struck me as profound, but I can't get my head around it: "In the case of cognitional theory, the generalization of the theory becomes identical with the concreteness of my actually asking questions."
Has it got something to do with Insight p362? "What is the source of this peculiarity of cognitional theory? It is that other theory reaches its thing-itself by turning away from the thing as related to us by sense or by consciousness, but cognitional theory reaches its thing-itself by understanding itself and affirming itself as concrete unity in a process that is conscious empirically, intelligently, and rationally."
The difficulty I have with your statement is that the generalisation of a theory is simply more theory, so how can it become concrete?
I think I'll leave it at that. Feel free to reply (or not) as and when you wish.
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DavidB
DavidB
Thanks for that reference on mistaken insights. It's just what I needed.
The first reference says "the solution is to acknowledge the mistake and trace back to its original source in the mistaken or incomplete insight. In other words, it is a self-correcting process."
The origin was a mistaken generalisation! That will teach me to frame my generalisations better in future.
Best wishes,
David
Jaray...@aol.com
Catherine Blanche King
Hello David:
I'm not ignoring your posts--just swamped at present. I will respond, however, and appreciate your thoughtfulness.
Thanks,
Catherine
DavidB
That's fine, there is no rush. Respond whenever you are ready.
I thought I should add a note after John drew attention to my mistaken insight. What is significant here is not the mistaken insight itself, but rather the process whereby it is corrected. Very often mistaken insights can lead to dead ends, but that need not be the case if we follow through our rational thoughts to see where they lead, and trace the error back to its source, wherever that may be.
In my case, the source was the desire to have a theory about insights which conveniently assumed that they could not be mistaken. (That would be useful, wouldn't it, if our insights were always correct?) To save the theory, we could say that an insight has two components, a part which is correct and a part which is mistaken. Let's call them x and y. Then the correct part is the part that is verifiable in the realm of objective truth, so may be called real, while the mistaken part is not verifiable so is merely imaginary. So now we have a representation of insight as a complex number with real and imaginary parts, x + iy.
There are probably more mistaken insights going on here, but what I am trying to do is follow through the reasoning, correcting the mistakes as we go along. What really matters is not so much whether an insight is correct, but why. That is the reason mathematicians always focus on mathematical proofs, and why I think Lonergan's discovery of reflective insight is so important. It's not what I say or what anyone else says that goes, but that which is consistent with the dynamic structure of the operations of cognitional thought.
Best wishes,
David
Jaray...@aol.com
. I will reread your
present email--but you certainly got several of us thinking about Lonergan in
general and some of the needed RIGOROUS applications that are de rigeur in this
present complicated world, DavidB
Catherine Blanche King
Hello DavidB:
In the interim, and if you can, you might want to get Collection 5. (4 is excellent also.) In that text (5), Lonergan' goes much deeper into the occurrences, causes, and types of insights. Here's one quote that regards our prior conversation about erred insights and the shift of the insight's content-meaning from "what" for meaning/intelligibility, to "Is it so" for truth- reality.
"Insights of themselves are neither true nor false. All that is relevant to insights is that you
get them, and whether they are true or false is always a further
question" (265) .
Catherine
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
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Catherine Blanche King
Hello DavidB:
Yes--the content arises in the question first ("what?" is always about some content); but the question, and any new insights that occur, ALSO emerge "within a patterned context of other insights and judgments."
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics/Insights
Jaray...@aol.com
Jaray...@aol.com
the other hand, is pointed out implicitly by Shute in the quotation John
gives: "The standard model is neither a common understanding nor even a
common aspiration". The common aspiration was there in physics, but there is
no such aspiration in economics. The sad brutal fact re Lonergan's economics
is stated at the end of the eighth article in Divyadaan (2010), vol 22., no
2, the volume on "Do You Want A Sane Global Econony?" : "The spirit of
inquiry, the heart of serious science, is just not present either in
contemporary economics or in the range of views opposed to it".
As I think these days of the problem of dialogue with economists, and peruse
again their pretensions pseudo-scientific writings, I begin to glimpse
better a discomforting analogy, not with physics but with mathematics. I
think of Fermat.
Fermat's puzzle was that [read 'x squared' etc, if my symbolism is lost in
transmission] x2 + y2 = z2 has integral solutions [e.g. x=3, y=4, z=5] but
there is no such solution for x3 + y3 = z3 or higher powers.
Is the solution simple? It took Wiles 10 years, till 1995, to break through.
Reading over part 3 of FNPE yesterday it struck me that Lonergan's 90 page
solution is like Wiles 100 page solution to Fermat's Problem.
Let me push the parallel a little. At one stage in the struggle with
Fermat's Theorem - a struggle then already way beyond commonsense approaches
- the puzzle emerged: "what could modularity of elliptic curves possible
have to do with Fermat's Last Theorem? "(A.D.Aczel, Fermat's Last Theorem,
New York, 1996, 111) It emerged gradually that it had everything to do with
it. So, in the puzzles re government monetary policy one will get from
economists the simpler simple-minded greedy view [one must dig deeper, as
Frank Braio and Tony Russo note] "What could aggregated turnover structures
of surplus production flows have to do monetary policy?".
When the eighth functional specialty develops, so that GEM141 [the reference
is to Lonergan's mature view of it in 3rd Coll] is operative , the
triviality of all the destructive putterings [common nonsense with a veneer
of mathematics] of the likes of Friedman will be MANIFESTED. But there is
the problem . manifestation is a matter of an emergent probability of the
epiphany of genuine humanism. I suspect that the manifestation of GEM141 is
two generations away. But at least we should try to begin to sense - dig
deeper - that we need to somehow drive through and thrive through a
manifesting of the idiocy of e.g. monetary policy. But that manifestation
involves hard work - a beginning of the relevant work in the case of
monetary policy is the grim little climb through my appendix {Beyond
Establishment. or PastKeynes .] on "Trade Turnover and the Quantity Theory
of Money". The same can be said for an epiphany of the horror of Supermoney.
We need to plough into these zones to let loose the sick smelliness of these
interferences with the delicate task of monetary CONCOMITANCE in history's
global reach for human basic care and blossoming leisure. We need to hack
into the thorny hedge of hedge funding.
I have noted the absence of scientific spirit in economics. My hope in 2012
is to manifest the lack of that spirit in Lonergan Studies. At 80 I am not
looking for approval much less a job . indeed, I look hopefully for
condemnation for my extreme views. "What could Lindsay and Margenau possibly
have to do with Lonergan's Last Theorem?". "McShane, then is quite wrong [in
the biography, chapter 10] in his odd inclusion of it as a bridge to
Lonergan's world." END quote
David, as I thought a bit more about mistaken insights, I was reminded of his references to "oversights" and found the below at"Bernard Lonergan, S.J., has been called one of the most profound philosophers and theologians of the twentieth century, and his major work, Insight, has been favorably compared to David Hume’s An Enquiry Concerning Human Understanding (1748) and Immanuel Kant’sKritik der reinen Vernunft (1781; Critique of Pure Reason, 1838). With his grasp of modern science and philosophy, Lonergan was able to go well beyond these earlier philosophers in Insight, whose pivotal claim is that a general structure of inquiry exists in all thinking individuals, a structure that is operative in every endeavor from the simplest commonsense decisions to the most revolutionary ideas of scientific, artistic, and theological geniuses. The number of insights generated by humans is ungraspably immense and growing at an accelerated pace, but Lonergan is primarily concerned not with the known but the knowing. He has discovered that knowing has a recurrent structure of experiencing, pondering, judging, and deciding. He challenges readers to understand what it means when they themselves understand, and if they do this, then they not only will generally understand whatever needs to be comprehended but also will have an insight into the insight-making process itself. This understanding will promote intellectual progress in a variety of fields and also help humans to avoid false ideas (“oversights”) that lead to intellectual and social decline, unenlightened policies, and dangerous courses of action." John
In a message dated 10/16/2017 11:56:52 PM Mitteleuropäische Sommerze, loner...@googlegroups.com writes:
Dear John,
Thanks for that reference on mistaken insights. It's just what I needed.
The first reference says "the solution is to acknowledge the mistake and trace back to its original source in the mistaken or incomplete insight. In other words, it is a self-correcting process."
The origin was a mistaken generalisation! That will teach me to frame my generalisations better in future.
Best wishes,
David
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since Riemann is one
of the geniuses who helped turn geometry and math onto
new revolutionary paths as well as providing a base on which Einstein built
for his relativity theories,
To: loner...@googlegroups.com
Sent: 9/30/2017 1:05:52 PM Mitteleuropäische Sommerzeit
Subj: [lonergan_l] Phil vs Doran
where one reads, e. g.
Thoughts on Method
Catherine gives you a good reference below. My train of thought which you set in motion touches on for one thing, the ASSUMPTIONS that are made for instance in Eucledian and non-Euclidian geometries such as Riemann's. With Riemann, Euclid's axiom on two parallel lines NO LONGER applies. What is the role of such assumptions in various types of math as the commutative and associative laws of algebra? In a way we are working here on some aspects of functional specialization. You are more specialized than I in math but then,I do not to what extent your "Riemann-hypothesis proposal" meet Terry and Phil's criteria. In any case, in pursuit of this theme I googled:Bernard Lonergan mathematical assumptions Riemannand lo & behold the first hit was to some of endnotes of the book I co-authored 2 years ago with a Pakistani physicist, where I refer to such problems such as the above, quoting Phil and referring to chemistry among other subjects. I do NOT have enough answers but I do have LOTS of probing questions.
John
In a message dated 10/18/2017 12:09:09 PM Mitteleuropäische Sommerze, cb-k...@live.com writes:
Hello DavidB:
In the interim, and if you can, you might want to get Collection 5. (4 is excellent also.) In that text (5), Lonergan' goes much deeper into the occurrences, causes, and types of insights. Here's one quote that regards our prior conversation about erred insights and the shift of the insight's content-meaning from "what" for meaning/intelligibility, to "Is it so" for truth- reality.
"Insights of themselves are neither true nor false. All that is relevant to insights is that you
get them, and whether they are true or false is always a further question" (265) .
Catherine
From: 'DavidB' via Lonergan_L <loner...@googlegroups.com>
Sent: Tuesday, October 17, 2017 3:11 PM
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
Dear Catherine,
That's fine, there is no rush. Respond whenever you are ready.
I thought I should add a note after John drew attention to my mistaken insight. What is significant here is not the mistaken insight itself, but rather the process whereby it is corrected. Very often mistaken insights can lead to dead ends, but that need not be the case if we follow through our rational thoughts to see where they lead, and trace the error back to its source, wherever that may be.
In my case, the source was the desire to have a theory about insights which conveniently assumed that they could not be mistaken. (That would be useful, wouldn't it, if our insights were always correct?) To save the theory, we could say that an insight has two components, a part which is correct and a part which is mistaken. Let's call them x and y. Then the correct part is the part that is verifiable in the realm of objective truth, so may be called real, while the mistaken part is not verifiable so is merely imaginary. So now we have a representation of insight as a complex number with real and imaginary parts, x + iy.
There are probably more mistaken insights going on here, but what I am trying to do is follow through the reasoning, correcting the mistakes as we go along. What really matters is not so much whether an insight is correct, but why. That is the reason mathematicians always focus on mathematical proofs, and why I think Lonergan's discovery of reflective insight is so important. It's not what I say or what anyone else says that goes, but that which is consistent with the dynamic structure of the operations of cognitional thought.
Best wishes,
David
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Catherine Blanche King
Hello DavidB:
At your suggestion, I'll take these piecemeal and a little at a time. Two issues here, and then I'll respond later to others in your note (below).
First, we did discuss mistaken insights; then I think it was in a note to John, you referred only the first part of Lonergan's passage where he writes:
"Insights of themselves are neither true nor false. All that is relevant to insights is that you
get them, and whether they are true or false is always a further question" (Coll. 5/265).
Did you leave out "in themselves" and "whether they are true or false is always another question" in your note to John? (I'm going on memory here.) But I think the fuller context of that statement is essential to its meaning-- about the question of having mistaken insights. I think taking the first part out of context disregards their place in the concrete process and does a disservice to the cohesiveness of the theory? The point is that we can and often do have insights; and then (as concrete conscious process) we tend to bring the (Is-it-so?) truth/real question to those same insights; in which case we judge them to be true or false, plausible or not, or in need of more thought.
In that sense, the "in themselves" is an essential aspect of that passage as it shows that "insights are neither true nor false," TAKEN ALONE, becomes a cherry-picked distorting abstraction.
Second, you move to the question: "What is an insight?" and recount Lonergan's generalization of the insight event from "Insight," and refer to the first moment: "Release of the tension of inquiry." Then you say: (my **)
"Now a mistaken insight (such as 'understanding is like seeing') could satisfy all these conditions **except the first one.** Precisely because it is mistaken, it will not put an end to all the further questions that could challenge its acceptance, and therefore the release of tension is incomplete, inviting the further insights that could correct and complement it.
CBK: Again, I think you are wrongly abstracting and then judging on that abstraction rather than on the concrete movement of consciousness (or a theory of it).
First, the insight has content. Of course, we legitimately want to generalize and then develop our understanding of the theory, abstracting the moment of insight from its particular content, as you do in math and the cartwheel.
However, concretely the content and the insight are wedded. (In math the new content becomes the symbols.)
If so, then the content of the insight, AND the insight (we find later, as we ask: Is-it-so? of it) can be incorrectly drawn, missing significant aspects (oversights), or we can find that the question can be wrongly formed.
In THAT sense, both concretely AND in accordance with a theory that accounts for the relationship (wedding) of insight and content, we move into reflective understanding towards judgment. In doing so, we can and often do gather that we have made a "mistaken insight" or set of insights.
Yes, it's first descriptive; and as we move into theory development with other kinds of data, we leave the specific content behind--but not if we want to understand THIS kind of data. Here, we need to keep the generalization of the insight **as wedded to its content** in mind. This is so especially in the light of the great difference between other theory development and the process of self-appropriation and the "turn" back to the concrete that is essential, again, in THIS unique kind of inquiry (as your quoted Lonergan passage suggests later in your note).
As an aside, the whole post-modern "problem of knowledge" is based on a number of notably incorrectly- drawn insights that Lonergan exposes as false. So this is not a small issue.
If that's the case, and I think it is, then the first moment of having an insight DOES APPLY also; that is: the "release of the tension of inquiry." Lonergan doesn't say "it puts an end to all further questions" or that this insight won't be "challenged." In fact, the rest of the cognitional theory is about just that movement.
Also, the exceptional point that makes polymorphism so intractable is precisely because those erred insights "pass into the habitual texture" of our minds--big time. And in this case, they create their own underlying tension precisely because they conflict with the ACTUAL interior core and its operations. The core continues on, but now it does so as if it had an elephant sitting on its neck.
In that first moment in Insight, however, Lonergan is ONLY giving an account of a singular moment in the process. He's not even talking about reflection and judgment yet. Again, concretely, the tension of inquiry is about THIS question and its content, not yet further ones.
But you ARE right that other questions can emerge that can "challenge" that insight. However, that doesn't mean that the tension for this one insight (or set of insights) is not released in that moment. At that moment, other questions can follow quickly and the tension re-emerge--of course. But again, there is the several-centuries-old impasse that is based on some very old and recalcitrant erred insights where their content is about knowing and its relationship to reality.
Then you say:
"If other desires interfered with the pure intellectual desire then the incomplete release of tension might not be adverted to, but in Lonergan's philosophy, faithfulness to the pure desire is an earnest demand."
DavidB
Thanks for your thoughtful reply. I think we have found a point of agreement: faithfulness to the pure desire is an earnest demand. But where does it lead? Firstly, I wish to acknowledge my mistaken insight or generalisation on mistaken insights, and excuse myself for my limitations of self-expression. I didn't mean what I said! I will try to explain myself with a few strategic replies to your comments.
CK: "Insights of themselves are neither true nor false. All that is relevant to insights is that you
get them, and whether they are true or false is always a further question" (Coll. 5/265).
CK: Did you leave out "in themselves" and "whether they are true or false is always another question" in your note to John?
DB: yes, I probably did. But by abstraction, I intended those missing concepts to be implicitly present. If we are speaking of insights, then it is either an insight-for-us (descriptive), or an insight-in-itself (explanatory). Mathematics is an explanatory science, and therefore I intended the latter interpretation. As for the further question, whether it is true or false, yes that does arise, but I did not ask it. It is useful that you draw attention to these points, as you say the wider context is essential for the cohesiveness of the theory.
CK: Then you say: (my **)
"Now a mistaken insight (such as 'understanding is like seeing') could satisfy all these conditions **except the first one.** Precisely because it is mistaken, it will not put an end to all the further questions that could challenge its acceptance, and therefore the release of tension is incomplete, inviting the further insights that could correct and complement it."
CBK: Again, I think you are wrongly abstracting and then judging on that abstraction rather than on the concrete movement of consciousness (or a theory of it).
DB: I would like to add that my description of insight was taken from Lonergan's account of a dramatic instance. As dramatic, it is a clear illustration of an occurrence of insight, but does not answer all further relevant questions of what an insight is. Therefore I agree it was wrong of me to abstract and judge on that basis. But then this is itself an illustration of the incomplete release of tension of inquiry, that fails to answer all the questions and settle precisely what an insight is.
CK: concretely, the tension of inquiry is about THIS question and its content, not yet further ones.
DB: I appreciate where you are coming from when concrete questions are under discussion. But what are the concrete questions in a mathematical context? It could be that even the formulation of the question is part of the problem. What I am imagining is the height of tension required to solve a problem such as, say, the Riemann Hypothesis. The fact that I cannot communicate this adequately proves that I am not there yet. My ideas about mistaken insights etc. are really groping along to try and reach an adequate formulation.
Lonergan's formal definition of an insight is in the section that analyses the elements that lead to the genesis of the definition of a circle. I think they are instructive too: clue, concepts, image, question, genesis, primitive terms, implicit definition, higher viewpoints. I am trying to construct an image of mathematics with insight as one of the primitive terms. But the image is only approximate, it is an insight that mediates between the approximate image and the mathematical reality.
This may not be a satisfactory reply to your comment, but I wish to integrate your insights into cognitional theory with the directed dynamism of the pure desire that seeks to understand even simple mathematical statements, such as 1+1=2.
Long journey? The fact that we are on the road is what matters.
Best wishes,
David
Jaray...@aol.com
Complexifying Lonergan’s Account of Nature and Supernature
Mary Josephine McDonald
Doctor of Theology
Regis College and the University of Toronto
2014
Abstract
In the opening page of Method in Theology, Bernard Lonergan expresses a concern that theology would understand its role at this important juncture in history—a time when the modern world enters a new realm of meaning, one that represents a shift from classicism to interiority. In order to fulfill its task of mediating “between a cultural matrix and the significance and role of a religion in that matrix,”1 Lonergan states that theology must understand that it is no longer a “permanent achievement,” but rather “an ongoing process.”2 In proceeding, therefore, theology must become acquainted with the “framework for collaborative creativity” in the “ongoing process” that Lonergan calls method.3 In addition, Lonergan emphasizes that “a contemporary method would conceive those tasks in the context of modern science, modern scholarship, modern philosophy....”4
This thesis has sought to “collaborate creatively” with “modern science” in order that both theology and the cultural context might be mutually enriched. By drawing on
1 Bernard Lonergan, S.J., Method in Theology (Toronto: University of Toronto Press, 2003), xi.
2 Ibid.
3 Ibid.
4 Ibid.
iii
the insights of the science of neuroplasticity, this thesis undertakes the methodological task involved in developing an understanding of the bodily aspect of the human person in an interiority analysis. Within the eight functional specialties that Lonergan outlines in a contemporary method of theology, this work performs tasks within Foundations. While inclusive of Foundations, the primary goal of this work is the development of a theological anthropology. Development occurs by bringing to light the significance of the body in a theological anthropology.
Lonergan’s question, “What in terms of human consciousness is the transition from the natural to the supernatural?” in “Mission and the Spirit,”5 along with his articulation of the body-psyche-mind relations in his principle of correspondence in Insight,6 provide the framework for this development. A developed understanding of the body’s role in the transition from the natural to the supernatural furthers Doran’s work on psychic conversion by including “body data” in the self-appropriation of the unconscious. Such an integration of the organic and psychic spontaneities with conscious operations increases the probability of authentic agency in the unfolding of the Reign of God.
5 Bernard Lonergan, S.J., “Mission and the Spirit,” in A Third Collection, ed. Frederick E. Crowe (Mahwah, NJ: Paulist Press, 1985), 23.
6 Bernard Lonergan, S.J., Insight: A Study of Human Understanding, vol. 3, Collected Works
Catherine Blanche King
Hello DavidB:
First, you say:
DB: Long journey? The fact that we are on the road is what matters.
CK: Did you think I meant otherwise?
CK: Also, how many times have I written something that "sounded" perfectly coherent and then, upon reading later, didn't say what I wanted to say at all. Or I assumed but didn't want to write it out again. We could talk about that in terms of conscious operations, but let's get on with my questions about your note. It will make for a longer note, but I think more accessible if I copy your narrative at DB, then add my own at CK:
DB: If we are speaking of insights, then it is either an insight-for-us (descriptive), or an insight-in-itself (explanatory).
CK: First, your "insight for us" or "insight in itself" using (of course) L's distinction between commonsense (things described and as related to us) and theory (thing explained and as related to other things). Then you say:
DB: Mathematics is an explanatory science, and therefore I intended the latter interpretation.
CK: Well, there are insights explained theoretically where we don't leave theory to understand the insight's relationship to other aspects of human consciousness. And there is mathematics that, as you say, is an explanatory science where we abstract from concrete things, e.g., the mathematics abstracted from a cartwheel. Unlike mathematics, however, the study of insight-itself does get "sticky" because the field of verity is us and our experience of our interior selves. The point with insight, however, and our return to our own experience for verity, is that the theory provides (what L calls) the superstructure to understand the interior infrastructure (those terms are in Method somewhere-I'll find it if you want) rather than cartwheel roundness. The theory, then, provides CRITICAL access to the generalized data of consciousness as empirical.
CK: That being said, I'm wondering if you are confusing philosophical with mathematical theory? The first underpins and informs the latter, but still they remain completely different fields? For instance, though we apply mathematics in the concrete, there is no "mathematics for us" that suggests the relationship between theory and commonsense in Lonergan's **philosophical** distinction between knowledge fields--as knowledge in itself and not as any one specific field like mathematics; and as explained as CS and theory are related to one another. Mathematics, on the other hand, is a specific kind of theoretical knowledge field understood already as abstract-explanation. I probably haven't said this very well, but with Twain, I'd have written a shorter note if I had time.
DB: As for the further question, whether it is true or false, yes that does arise, but I did not ask it.
CK: Yes--that's the point that I think Lonergan was trying to get across in that passage.
DB: It is useful that you draw attention to these points, as you say the wider context is essential for the cohesiveness of the theory.
DB: I would like to add that my
description of insight was taken from Lonergan's account of a dramatic instance. As dramatic, it is a clear illustration of an occurrence of insight, but does not answer all further relevant questions of what an insight is. Therefore I agree it was wrong
of me to abstract and judge on that basis. But then this is itself an illustration of the incomplete release of tension of inquiry, that fails to answer all the questions and settle precisely what an insight is.
CK: Archimedes ran from the baths--clearly he understood and had a release of tension to his question about how to tell if the crown was really all gold--and so dramatically. Aha! If there is new or further tension, then it's from the movement itself, that is, the shifting to a new question with its own new tensions: Is it really so?
So from the point of view of absolution, and from already having answered all relevant questions for meaning AND for truth, then we can understand the release of tension as "incomplete." But beyond Archimedes as our controlling example, and from the point of view of having a direct insight (for meaning and intelligibility), and not yet for the refinements of reflection and judgments for truth, it's a satisfying release of the tension of inquiry about a particular question.
But in your sense of omniscience, there is NO insight and release of tension from having one that is "complete." So it's rather a moot point? Lonergan is only clarifying Archimedes' drama as an instance of insight. His pedagogical point is to "pay attention" to the occurrence of an insight, and then his theoretical point is to clarify some essential aspects of the progress of the insight which, as distinguished from other aspects, and as he develops the theory, will be related to the whole moement and to other questions given generally to conscious order, e.g., "Is it so?" I think you may be adverting to the general tension of conscious awareness itself, which is always with us so long as we are alive and conscious--"Insight comes as a release of the tension of inquiry." I really don't understand that there is a "completion" problem here? And in fact, it's "incomplete" from understanding the later movement in the same way that an insight can be in error--discovered from the later reflective movements of mind that are a part of our self-corrective process.
DB: B: I appreciate where you are coming from when concrete questions
are under discussion. But what are the concrete questions in a mathematical context? It could be that even the formulation of the question is part of the problem. What I am imagining is the height of tension required to solve a problem such as, say, the
Riemann Hypothesis. The fact that I cannot communicate this adequately proves that I am not there yet. My ideas about mistaken insights etc. are really groping along to try and reach an adequate formulation.
CK: I think I get what you mean, but I cannot answer your specific question, starting with: because I don't know what that is yet? If I might speculate, however, perhaps there is a confusion between the foundations of mathematics and mathematics as a specific science? In terms of imagery, philosophical foundations are "under" all other sciences, informing them "from below" so to speak. So that the tension of inquiry that you are dealing with in the RH, and though mathematics is a theoretical field, is basically the same tension that Archimedes was dealing with--both are examples of the same general philosophical point: the tension of inquiry about a particular problem--ANY particular problem.
I really hope that helps, and doesn't just add to the problem.
Long journey. . .
Catherine
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics--Piecemeal 1
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Catherine Blanche King
John:
Good questions. Philosophy IS a theoretical field; in the general sense like mathematics or physics. But AS philosophical, it is unique because it also concerns both (a) the object and content of our philosophical questions; AND, if our answers to those questions are correctly drawn, (b) its theory reflects the actual ground of that field, in each of us, as intelligent human beings--in which we can experiment to both verify the theory and initiate personal self-appropriation.
In that sense, philosophical method both objectifies our capacity to be reflexive, and it invites us to employ that reflexivity on our own foundational activities and functions, using the theory to remain critical. So it's "Lonergan theory" as superstructure; but OUR interior operations as philosophical infrastructure and as empirical methodological ground for the theory.
Further, philosophical method IS unique, (It's unique because it's data is unique). But it is not less critical (as is often thought). On the contrary, because it requires of the scientist to pre-condition their study on a critical study of their own philosophical foundations--that can be and often ARE (a) untutored and/or (b) polymorphic, it is MORE critical--it grounds the critical nature of the empirical tenets themselves.
Finally, because its function is to clear away the presence of all sorts of philosophical biases in scientists so that they can approach the mind sans their own mind's biases, its influence makes for enhancement of the critical nature of ALL of the other fields.
Presently, those fields can do well with their data up to a point; but ONLY up to that point.
Hence we see the fracturing of the fields and the emergence of both the existential gap where theory (as such) is concerned. But also that gap as the scientist's distorted and lesser philosophical horizon that comes into play when asked to entertain anything "mind," interior," or "merely subjective."
You had other questions, but that's the short of it . . . .
Catherine
Sent: Wednesday, October 25, 2017 10:27 AM
To: loner...@googlegroups.com
Subject: [lonergan_l] Lonergan and Mathematics
Catherine Blanche King
John:
Two other points:
First, what mathematicians actually DO is commonly different from what they SAY or think they are doing when doing math. So that has to be taken into consideration. They might be doing math really well; but when you ask them about their own operations and how they do what they are doing . . . . ? Those are philosophical and not mathematical questions.
Second, I earlier referred to Martos' note about "hardening" over time bad or insufficient insights and their judgments. Here is Lonergan on that same point from Insight. But also see his reflections on the scotoma. Let it be said that "unwanted insights" can be held away by old habits--judgments holding on to previously-learned but erred philosophical insights.
All quoted below, and so I'll sign off here:
Catherine
From INSIGHT
"Primarily, the censorship is constructive; it selects and arranges materials that emerge in consciousness in a perspective that gives rise to an insight; this positive activity has by implication a negative aspect, for other materials are left behind, and other perspectives are not brought to light; still, this negative aspect of positive activity does not introduce any arrangement or perspective into the unconscious demand functions of neural patterns and processes. In contrast, the aberration of the censorship is primarily repressive; its positive activity is to prevent the emergence into consciousness of perspectives that would give rise to unwanted insights; it introduces, so to speak, the exclusion of arrangements into the field of the unconscious; it dictates the manner in which neural demand functions are not to be met; and the negative aspect of its positive activity is the admission to consciousness of any materials in any other arrangement or perspective. Finally, both the censorship and its aberration differ from conscious advertence to a possible mode of behavior and conscious refusal to behave in that fashion. For the censorship and its aberration are operative prior to conscious advertence; and they regard directly not how we are to behave but what we are to understand" Coll. 4/216).
Sent: Wednesday, October 25, 2017 10:27 AM
To: loner...@googlegroups.com
Subject: [lonergan_l] Lonergan and Mathematics
DavidB
Catherine Blanche King
Hello DavidB:
Okay--briefly (ha!):
First, let's end the long-journey discussion?
Second, you say:
Ninth, you say about the tension in Archimedes being the same (generally) as your tension about the RH: (see my parens)
Jaray...@aol.com
An essay review and a summary by Gene B. Chase
“How can the history of mathematics shed light on philosophy and theology?” (81 et alia) In this project, he addresses this theme, but also the theme of how philosophy and theology shed light on mathematics, quite beyond the examples that I provided in (Chase, 1997).
Bovell says in his preface that Ideas is a collection of essays about Christian faith and mathematics. He cites a refreshing collection of authors who are not usually referenced in this JOURNAL. Despite his Reformed training at Westminster Theological Seminary and at Institute of Christian Studies, he draws freely on Catholic theologians. For example, he cites Bernard Lonergan’s use of mathematics. See (Manning, 1983) for more details than Bovell gives. For example, he cites Jean Luc Marion on infinity. As I was reading these essays, my list of things that I “must” read grew as Bovell whetted my appetite. You will find the same if you want to answer his big question.
Bovell approaches his big question primarily through phenomenology. The very title of this collection of essays is borrowed from “the father of phenomenology” Edmund Husserl’s Ideas. (Husserl, 1913) What is phenomenology? Without putting too fine a point on it, realism places reality “out there” and idealism places reality “in the mind.” As examples of “too fine a point,” I won’t ask whether it’s “my mind” (solipsism) or “human minds” collectively; I won’t ask whether “out there” is material or Platonic. Phenomenology places reality between those two loci: in perception, which of course needs both a perceiver and a perceived. Without “too fine a point,” perceptions include intuitions—insight as well as sight.
Some well-known mathematicians are phenomenologists, such as Gian-Carlo Rota, whose research spans a spectrum from linear operators on Hilbert spaces to Möbius inversion as a technique for solving combinatorial problems. See my review of Rota’s book Indiscrete Thoughts, where he makes his phenomenology explicit. (Chase, 1998) Conversely, some well-known phenomenologists are competent mathematicians, such as Husserl himself. See Dallas Willard’s definitive translation and commentary on some of Husserl’s mathematics. (Husserl, 2003) Yes, that Dallas Willard, author of The Divine Conspiracy. Some scholars whom Bovell cites are hard to classify. For example, he cites Charles Sanders Peirce multiple times—mathematical logician anticipating Cantor, Peano, and Zermelo; and a phenomenologist, although often he is usually called “the father of pragmatism.”
Yet in a typical course in philosophy of mathematics, phenomenology is omitted. The usual candidates to study are realism, intuitionism, formalism, and logicism, and if your text is the standard one by Stewart Shapiro, then you have to include structuralism, because Shapiro is a structuralist. (Shapiro, 2000) The present essays provide some remedy for this omission.
Bovell professes philosophy but has a strong background in mathematics. He even uses the generalized Stokes theorem as one of his examples! (If you’re searching his essays electronically for the example, search for “Spivak”.) Bovell probes further about things that you have probably thought about without probing them as much as he has. For example, in what sense is Aquinas’ Summa a “spiritual Euclid” as Morris Kline calls it? Or, in what sense does 1+1+1=1 model the Trinity as a variety of papers by Christian mathematicians point out?.... (John)
CK: I really hope that helps, and doesn't just add to the problem.DB: It has been a great help. But even if you added to the problem, by employing your dynamic conscious operations, whether correctly or mistakenly, you are revealing the truth about your inner structure.CK: Long journey. . .DB: “Long” is a comparative term. How do you know we aren’t there yet?Best wishes,David
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2) G'day Catherine, A couple of "things" bubbled up in my memory as I worked my way through your "far-reaching" paper. 1. Quidquid recipitur ad modum recipientis recipitur....if you get my "drift". So one participant couldn't get through the abstract and another deemed it "excellent" and then there were the varied "receptions" in LA. 2. The Parable of the Sower (for which I have a three page reflection--not exegesis--with which I will not "bother" you here) is about openness in giving, openness in receiving, and the various outcomes involved when a style of giving meets a style of receiving. 3. As for the short-term, there is Lonergan's functional collaboration... . Most conferences assemble conversationalists but do not differentiate conversational contexts: asking to whom am I talking? No wonder people get tired when everyone talks to a "general" audience made up of very specialised academics! 4. Incidentally, I find Lonergan's use of authenticity, especially when contextualised by conversion, to be more "provocative"--to borrow a phrase--than genuineness. My existential gap is "always with me"--again to borrow a phrase. And, I find horizon a more flexible image than silo. The better the phantasm, the more likely the insight! 5. Finally, I admire your courage in "finding the mind" even when "the odds--many minders--are against you"." Thanks, Tom Halloran.----
Catherine tells us that her paper was written in the audience-context of THEIR work on trying to find a way to integrate ethics with the neuro- and other sciences; "I was trying to meet a concrete and ongoing problem that others were trying to grapple with."
Good questions. Philosophy IS a theoretical field; in the general sense like mathematics or physics. But AS philosophical, it is unique because it also concerns both (a) the object and content of our philosophical questions; AND, if our answers to those questions are correctly drawn, (b) its theory reflects the actual ground of that field, in each of us, as intelligent human beings--in which we can experiment to both verify the theory and initiate personal self-appropriation.
In that sense, philosophical method both objectifies our capacity to be reflexive, and it invites us to employ that reflexivity on our own foundational activities and functions, using the theory to remain critical. So it's "Lonergan theory" as superstructure; but OUR interior operations as philosophical infrastructure and as empirical methodological ground for the theory.
Further, philosophical method IS unique, (It's unique because it's data is unique). But it is not less critical (as is often thought). On the contrary, because it requires of the scientist to pre-condition their study on a critical study of their own philosophical foundations--that can be and often ARE (a) untutored and/or (b) polymorphic, it is MORE critical--it grounds the critical nature of the empirical tenets themselves.
Finally, because its function is to clear away the presence of all sorts of philosophical biases in scientists so that they can approach the mind sans their own mind's biases, its influence makes for enhancement of the critical nature of ALL of the other fields.
Presently, those fields can do well with their data up to a point; but ONLY up to that point.
Hence we see the fracturing of the fields and the emergence of both the existential gap where theory (as such) is concerned. But also that gap as the scientist's distorted and lesser philosophical horizon that comes into play when asked to entertain anything "mind," interior," or "merely subjective."
You had other questions, but that's the short of it . . . .
Catherine
From: Jaraymaker via Lonergan_L <loner...@googlegroups.com>
Sent: Wednesday, October 25, 2017 10:27 AM
To: loner...@googlegroups.com
Subject: [lonergan_l] Lonergan and Mathematics
Hi,Just going back to the basics of L's method as stated e. g. MiT, 6, his method is derived from an understanding of the operations which exist within us and function spontaneously.Method is not a set of rules but a normative pattern from which the rules may be derived.Catherine and David are engaging in some precise refinements it seems, but my question is do not both math and philosophy--all disciplines for that matter follow (apply) this basic derivation L gives in MiT, 6? OK, we do have to clear many hurdles of false philosophical theories (which is Catherine's point).It seems to me, David would be well served if he comes to clearly understand how L's definition of operations fits with (relates to) how math defines its own valid and very successful operations in its ever increasing forms of specialization.My first question on this topic follows from how mathematicians describe a math operation as the process of carrying out rules of procedure such in addition, taking logarithms, making substitutions or transformations etc. The question is:how does what L say in MiT p. 6 in his general view of operations fit in with the immediately previous par. and with how great mathematicians such as Newton, Gauss, Riemann and others have applied it (REFINED it) in their own original ways. At issue are such questions as 1) are mathematicians taking some basics for granted? 2) how can GEM best serve the foundations of math (or any discipline) if the very top par. applies subordinating rules to our own INBUILT normative operations? 3) Is there confusion on this point? 4) if so how resolve the confusion to properly understand how GEM is a breakthrough?5) I would ask is that not a VERY CRUCIAL point to the GEM-FS enterprise which is now being addressed as to "L and math"? I bet e. g. Doug and David Oyler might have good insights on this,John
Hello DavidB:
First, you say:
DB: Long journey? The fact that we are on the road is what matters.
CK: Did you think I meant otherwise?
CK: Also, how many times have I written something that "sounded" perfectly coherent and then, upon reading later, didn't say what I wanted to say at all. Or I assumed but didn't want to write it out again. We could talk about that in terms of conscious operations, but let's get on with my questions about your note. It will make for a longer note, but I think more accessible if I copy your narrative at DB, then add my own at CK:
DB: If we are speaking of insights, then it is either an insight-for-us (descriptive), or an insight-in-itself (explanatory).
CK: First, your "insight for us" or "insight in itself" using (of course) L's distinction between commonsense (things described and as related to us) and theory (thing explained and as related to other things). Then you say:
DB: Mathematics is an explanatory science, and therefore I intended the latter interpretation.
CK: Well, there are insights explained theoretically where we don't leave theory to understand the insight's relationship to other aspects of human consciousness. And there is mathematics that, as you say, is an explanatory science where we abstract from concrete things, e.g., the mathematics abstracted from a cartwheel. Unlike mathematics, however, the study of insight-itself does get "sticky" because the field of verity is us and our experience of our interior selves. The point with insight, however, and our return to our own experience for verity, is that the theory provides (what L calls) the superstructure to understand the interior infrastructure (those terms are in Method somewhere-I'll find it if you want) rather than cartwheel roundness. The theory, then, provides CRITICAL access to the generalized data of consciousness as empirical.
CK: That being said, I'm wondering if you are confusing philosophical with mathematical theory? The first underpins and informs the latter, but still they remain completely different fields? For instance, though we apply mathematics in the concrete, there is no "mathematics for us" that suggests the relationship between theory and commonsense in Lonergan's **philosophical** distinction between knowledge fields--as knowledge in itself and not as any one specific field like mathematics; and as explained as CS and theory are related to one another. Mathematics, on the other hand, is a specific kind of theoretical knowledge field understood already as abstract-explanation. I probably haven't said this very well, but with Twain, I'd have written a shorter note if I had time.
DB: As for the further question, whether it is true or false, yes that does arise, but I did not ask it.
CK: Yes--that's the point that I think Lonergan was trying to get across in that passage.
DB: It is useful that you draw attention to these points, as you say the wider context is essential for the cohesiveness of the theory.
DB: I would like to add that my description of insight was taken from Lonergan's account of a dramatic instance. As dramatic, it is a clear illustration of an occurrence of insight, but does not answer all further relevant questions of what an insight is. Therefore I agree it was wrong of me to abstract and judge on that basis. But then this is itself an illustration of the incomplete release of tension of inquiry, that fails to answer all the questions and settle precisely what an insight is.
CK: Archimedes ran from the baths--clearly he understood and had a release of tension to his question about how to tell if the crown was really all gold--and so dramatically. Aha! If there is new or further tension, then it's from the movement itself, that is, the shifting to a new question with its own new tensions: Is it really so?
So from the point of view of absolution, and from already having answered all relevant questions for meaning AND for truth, then we can understand the release of tension as "incomplete." But beyond Archimedes as our controlling example, and from the point of view of having a direct insight (for meaning and intelligibility), and not yet for the refinements of reflection and judgments for truth, it's a satisfying release of the tension of inquiry about a particular question.
But in your sense of omniscience, there is NO insight and release of tension from having one that is "complete." So it's rather a moot point? Lonergan is only clarifying Archimedes' drama as an instance of insight. His pedagogical point is to "pay attention" to the occurrence of an insight, and then his theoretical point is to clarify some essential aspects of the progress of the insight which, as distinguished from other aspects, and as he develops the theory, will be related to the whole moement and to other questions given generally to conscious order, e.g., "Is it so?" I think you may be adverting to the general tension of conscious awareness itself, which is always with us so long as we are alive and conscious--"Insight comes as a release of the tension of inquiry." I really don't understand that there is a "completion" problem here? And in fact, it's "incomplete" from understanding the later movement in the same way that an insight can be in error--discovered from the later reflective movements of mind that are a part of our self-corrective process.
DB: B: I appreciate where you are coming from when concrete questions are under discussion. But what are the concrete questions in a mathematical context? It could be that even the formulation of the question is part of the problem. What I am imagining is the height of tension required to solve a problem such as, say, the Riemann Hypothesis. The fact that I cannot communicate this adequately proves that I am not there yet. My ideas about mistaken insights etc. are really groping along to try and reach an adequate formulation.
CK: I think I get what you mean, but I cannot answer your specific question, starting with: because I don't know what that is yet? If I might speculate, however, perhaps there is a confusion between the foundations of mathematics and mathematics as a specific science? In terms of imagery, philosophical foundations are "under" all other sciences, informing them "from below" so to speak. So that the tension of inquiry that you are dealing with in the RH, and though mathematics is a theoretical field, is basically the same tension that Archimedes was dealing with--both are examples of the same general philosophical point: the tension of inquiry about a particular problem--ANY particular problem.
I really hope that helps, and doesn't just add to the problem.
Long journey. . .
Catherine
From: 'DavidB' via Lonergan_L <loner...@googlegroups.com>
Sent: Tuesday, October 24, 2017 4:36 PM
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics--Piecemeal 1
Dear Catherine,
Thanks for your thoughtful reply. I think we have found a point of agreement: faithfulness to the pure desire is an earnest demand. But where does it lead? Firstly, I wish to acknowledge my mistaken insight or generalisation on mistaken insights, and excuse myself for my limitations of self-expression. I didn't mean what I said! I will try to explain myself with a few strategic replies to your comments.
CK: "Insights of themselves are neither true nor false. All that is relevant to insights is that you
get them, and whether they are true or false is always a further question" (Coll. 5/265).
CK: Did you leave out "in themselves" and "whether they are true or false is always another question" in your note to John?
DB: yes, I probably did. But by abstraction, I intended those missing concepts to be implicitly present. If we are speaking of insights, then it is either an insight-for-us (descriptive), or an insight-in-itself (explanatory). Mathematics is an explanatory science, and therefore I intended the latter interpretation. As for the further question, whether it is true or false, yes that does arise, but I did not ask it. It is useful that you draw attention to these points, as you say the wider context is essential for the cohesiveness of the theory.
CK: Then you say: (my **)
"Now a mistaken insight (such as 'understanding is like seeing') could satisfy all these conditions **except the first one.** Precisely because it is mistaken, it will not put an end to all the further questions that could challenge its acceptance, and therefore the release of tension is incomplete, inviting the further insights that could correct and complement it."
CBK: Again, I think you are wrongly abstracting and then judging on that abstraction rather than on the concrete movement of consciousness (or a theory of it).
DB: I would like to add that my description of insight was taken from Lonergan's account of a dramatic instance. As dramatic, it is a clear illustration of an occurrence of insight, but does not answer all further relevant questions of what an insight is. Therefore I agree it was wrong of me to abstract and judge on that basis. But then this is itself an illustration of the incomplete release of tension of inquiry, that fails to answer all the questions and settle precisely what an insight is.
CK: concretely, the tension of inquiry is about THIS question and its content, not yet further ones.
DB: I appreciate where you are coming from when concrete questions are under discussion. But what are the concrete questions in a mathematical context? It could be that even the formulation of the question is part of the problem. What I am imagining is the height of tension required to solve a problem such as, say, the Riemann Hypothesis. The fact that I cannot communicate this adequately proves that I am not there yet. My ideas about mistaken insights etc. are really groping along to try and reach an adequate formulation.
Lonergan's formal definition of an insight is in the section that analyses the elements that lead to the genesis of the definition of a circle. I think they are instructive too: clue, concepts, image, question, genesis, primitive terms, implicit definition, higher viewpoints. I am trying to construct an image of mathematics with insight as one of the primitive terms. But the image is only approximate, it is an insight that mediates between the approximate image and the mathematical reality.
This may not be a satisfactory reply to your comment, but I wish to integrate your insights into cognitional theory with the directed dynamism of the pure desire that seeks to understand even simple mathematical statements, such as 1+1=2.
Long journey? The fact that we are on the road is what matters.
Best wishes,
David
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Catherine Blanche King
Hello John:
Did you have a question?
Catherine
To: loner...@googlegroups.com
Subject: [lonergan_l] "Lonergan's theory" and Philosophical Method
Catherine Blanche King
Hello again John:
Your note did inspire some thoughts--so here they are FWIW:
I winced the first time I read Tom Halloran's note; and I winced again this time as you were so kind to bring it up again.
But Halloran's note had nothing to do with the content of the paper I gave, and everything to do with the delivery of it. On reflection, however, I appreciate any good critique I can get. And I have copied the "abstract" and "table of contents" below for anyone who wants to make their own judgment on it.
Also, about delivery and audience, I think I must be doing something right because I'm getting criticized from "both sides." That is, first, when I try to develop material for an audience of those new to Lonergan's work, I get critiqued in the vein that I am only "describing" and am probably seeing Lonergan's work only through commonsense lenses. While from others (like Halloran), I'm too technical and am not interpreting Lonergan to the "right" audience (of one: Tom Halloran?).
The audience for that paper BTW was at a Lonergan conference where (I assumed) most had SOME modicum of understanding of Lonergan's work. Even in that framework, as Halloran suggests, and as all here probably know, the range of understanding is wide, not to mention tall. The most anyone can expect is to raise a few probing questions.
Also about the existential gap: In our case [the conversation between myself and DavidB] that gap refers to two specific horizons: (1) the absence of theoretical understanding (or as Phil often refers to: a version of haute vulgarization) and (2) the absence of self-reflection that results in being both totally unaware of one's own mind, its activities and functions; and then further being in poly-error about same. Both have to do with a gap in one's horizon. As "existential," the gap relates more to (2) than to (1). Though in our time, one wonders even about that. Here is the "abstract" to the paper that Tom refers to, and I'll sign off: Catherine
Scrutinizing Our Philosophical Assumptions
Polymorphism: How is it that, “the subject’s reality lies beyond his own horizon”?
CONTEXT: Presidential Commission for the Study of Bioethical Issue
Presenter: Catherine Blanche King
KEY WORDS: philosophy, intentions, assumptions, horizon, genuineness, polymorphism, existential gap, education, bioethical, Lonergan
Abstract
At the center of our thesis is the empiricist’s assumption about knowing: “What is obvious in knowing is what knowing obviously is” (Lonergan 2000/441). Or: since knowing seems immediate and occurs simultaneously with looking or otherwise sensing, it must be or be LIKE sensing. From that erred epistemology flows a similarly erred ontology: Reality is visible or “already out there now;” images are vague replicas of it; and interiority is “already in here now,” but invisible; so it cannot be real or knowable. What, then, can ground invisible ethics as real?
We bring Lonergan’s notions of polymorphism, the existential gap, and philosophical genuineness[2] to President Obama’s Gray Matters Commission where scholars refer to “silo-thinking” and “obstinate resistance” to ethics and field integration as common in students of science. Our goals, then, are (1) to explain how scientists’ silo-thinking and obstinate resistance begin in deeply buried but wholly influential developmental errors in what are otherwise highly creative and intelligent thinkers; and (2) to reveal the “from the get-go” reeducation that is needed for philosophical genuineness to occur. Several insights emerge from our exploration:
1. Our knowing, with its self-corrective process and its assumed relationship with reality and being, continues on in us in its radiant way regardless of our thought-errors about it.
2. Our erred epistemology and ontology are the result of a set of erred insights; couched in a set of oversights; and encrusted in too-quick judgments about that radiant process.
3. Such judgments can occur quite early in a thinker’s learning life, often long before our critical capacities mature and before we begin our formal education. Too easily a young thinker can equate their speed of recall (an aspect of knowing) with “obvious” looking or otherwise sensing.
4. As with all learning, early-made and erred philosophical judgments tend to stay. But philosophical learning tends to shift its affective memory content to underpin “from below” and so to inform our reality-existence horizon. The result can be silo-thinking. Uncorrected, it remains remotely qualitative and selective and tends to poison authentic discourse, for instance, regarding ethical considerations and field integration.
5. Our study clarifies the distinction between (1) core philosophical intentions that already inform all spontaneous assumptions and concrete questions (latent metaphysics) and (2) reflectively established, insight-based philosophical assumptions which can be correctly drawn, or partly or wholly in error. Our core assumptions then come into conflict with our erred insight-based assumptions creating an existential gap and providing the ground for polymorphism (2000/500). Philosophical genuineness occurs when 1 and 2 become symmetrical, or when learning correlates with its object, and that learning as subject-constitutive.
6. Polymorphism emerges from those early oversights and errors, then, but still includes an operating radiant center: the core knowing-reality relationship fueling common, scientific, artistic, & spiritual knowing.
7. The errors’ effects are: (1) to reduce a thinker’s horizon re: the reality and, thus, the significance of human sciences, the arts and humanities, philosophy and ethics, and their professional fields through the presence of an existential gap; (2) to condition “resistance” to questions about our habits of erred thought and, thus, to philosophical study, self-reflection, and correction; and (3) to tacitly intrude on, confuse, distort and misguide otherwise insightful discourse via offering empiricist, subjectivist, or relativist red herrings; and overtly to use philosophical diversions to avoid unwanted truth.
8.
Despite but also because of resistance, the “obvious” need is for guided “questioning of
one’s own unconscious initiatives” or a reeducation of students of science that includes introspection and self-correction towards philosophical genuineness (2000/504). Such genuineness would flow into affording ethics a warranted significance for students’
life endeavors including excursions into scientific fields of study and application.
“Silo-thinking,” then, is a way to express what flows from that deep conflict at the level of foundations where our (a) “core” assumptions, and (b) our insight-based but flawed assumptions are “at cross-purposes” (2000/500). One outgrowth of the early-learned philosophical set of errors is that persons “get lost” somewhere between themselves as whole persons and as objectified and self-separated (an aspect of the existential gap). The logic flows from there so that subjects and fields become and remain isolated from one another, at least until a personal breakthrough occurs. We find the root of the isolation in the early-made conflictive subject-to-reality relationship error buried deep in the philosophical comportment of otherwise creative, intelligent and incisive thinkers. Problems of reeducation occur “from the get-go” because, by the time we take up philosophical self-reflection, we are already thinking WITH those errors as we approach those same errors, resulting initially in resistance.
Further, polymorphism and the existential gap are more likely to occur than not precisely because our knowing process is so complex and works so well for us. The empiricist “blunder” is almost unavoidable. What keeps us going and sane is our common spontaneous identity with critical consciousness which, though we may not be conscious of it, is operating in us and continues to be fueled by the radiance of our core philosophical assumptions. Also, in our formal education, our erred and/or correct but incomplete philosophical thinking often meets with educators and field professionals whose insight-based assumptions are also incomplete and/or in error. And so students’ early-made and now hidden philosophical judgments (incomplete, erred, or not) can easily become compounded and further confused. Today in the academy, it’s Frankenstein of Polymorphism meets the Werewolf of that same Polymorphism--a philosophical pox is afoot in both their houses. Presently, without adequate theoretical and personal guidance, students are left with the untenable, and often only partly conscious, choice between (a) abandoning the authentic resonances of their own critical intelligence and accepting any one of, or a conflicted complex of, poorly wrought philosophical views. Those views, in fact, are bifurcated away from their own radiant and spontaneous knowing; (b) rejecting out of hand most or all formal education; or (c) undertaking the unlikely task of recreating the wheel that Lonergan discovered, made conscious and theoretically clear, and started rolling. His is a finishing philosophical corrective of what started as the scientific revolution.
TO WCMI CONFERENCE ATTENDEES: This paper is drawn from a book-in-progress. Also, that book is written for a non-philosophical specialist audience. With that in mind, I have replaced philosophical with comprehensive or meta-mindset to reflect the difference between the spontaneous emergence of latent but yet-unnamed philosophical questioning and more formal philosophical inquiry in our thinker (the subject). I welcome questions and comments.
TO ONLINE READERS: I have edited and corrected some text here from the original paper given on April 2, 2016. Also, I have added the text boxes and appendixes drawn from the book to give some background to more summarized text herein.
Table of Contents
Abstract
Buried Problem with Far-Reaching Significance
Enter: The Existential Gap
A Brief Excursion into Authenticity (Genuineness)
Enter: Polymorphism
Intellectual Development and Informal and Formal Education
Interim Summary
Revisiting Education with Comprehensive Matters in Mind
Santa Claus Thinking (as Analogy)
Two Sources of Comprehensive Assumptions
Horizons and Their Expression, Genuine or Not
Meeting Polymorphism: The Inheritance Track in the Academy
Passing Down to Students (the Inheritance) or: Our Thinker in the Academy--OR the Academy’s Oversights and Errors in Our Thinker
The Pervasiveness of the Problem: the Broader Picture
Bibliography
Appendixes:
1. Cognitional Theory in a Philosophical Context
2. Brief supportive quotes
3. Excerpt from book in progress re: Resistance and Philosophical Restructuring
4. Integrative Approaches for Neuroscience, Ethics, and Society.” Presidential Commission for the Study of Bioethical Issues (vol. 1), Gray Matters: Topics at the Intersection of Neuroscience, Ethics, and Society (vol. 2).
[2] For polymorphism, see Insight, index. For the existential gap, see Collection 18 (280-, 302); for philosophical genuineness, see Insight (2000/500-04).
The rest of the paper is on www.academia.edu
Subject: Re: [lonergan_l] "Lonergan's theory" and Philosophical Method
DavidB
Many thanks for your reply, it is very helpful to clarify some misconceptions I had, especially the difference between philosophical and mathematical theory.
First, you say:
CK: You might want to reread that? There IS a movement from description to explanation.
DB: Did you mean I should re-read what I said? I was questioning that the explanatory understanding of insight was entirely on the theoretical level. I am trying to understand what this movement from description to explanation could be. As I read it, that movement has been described, but will it survive in a fully explanatory science? Or will it prove to be a mere nothing of contingence?
I try to read on what you say:
CK: That's clear in INSIGHT (DB: yes, descriptively). But initial description occurring under the critical questions of theory development is not merely what Lonergan means by a commonsense description. Badly-described content can set the stage for erred theory. And again, the explanation in this case depends on a distinction between the descriptive content of any particular insight, and insight itself as content (under the critical aim of scientific explanation); and as object of a theoretical explanation where relating generalized conscious activities and functions to one another is the further aim.
DB: so there is a three-fold distinction? a) the descriptive content of insight, b) the explanatory content of insight (under critical control), c) the theoretical account of that content. This is a three-fold movement from descriptive to theoretical formulation via the explanatory route. But this movement has the general structure of an insight, a) what insight presupposes (descriptive content), b) what the insight is in itself (explanatory content), c) the reflective insight (theoretical content). That is what I meant by the explanatory understanding of insight not being purely theoretical, because it itself rests on an insight.
In the second place, on the stickiness of studying mathematics,
CK: Of course, mathematicians can run into problems with math BECAUSE of the unknown (to the thinker) and wrongly-formed philosophical assumptions that reside in their interior arena of thought. However, and insofar as they do stem from philosophical issues, the problems are not fundamentally mathematical.
DB: But precisely because their mistaken assumptions can affect a mathematician's ability to do maths, it is a mathematical problem too. I refer to Lonergan's analysis of mathematicians as dealing with "the empirical residue of all data". (Insight p337) All data includes the philosophical problem of grappling with the polymorphism of human consciousness.
Third, on the superstructure and infrastructure. Thank you for drawing my attention to the critical word "critical"!
Fourth, on the realms of consciousness. I referred to a possible crossover between philosophical and mathematical theory. You have given a good philosophical explanation of the difference, but could there be a complementary mathematical one? Like the division of investigations into classical and statistical? The straight answer 'no' does not satisfy me, because when insight has occurred, what once seemed impossible suddenly becomes very feasible indeed.
Fifth, on the sense of mathematics being primitive. You asked if I was referring to a tautology. I'm not sure I understood exactly what you meant, but I accept that I have not been very clear either. I am digging into the idea that maths and philosophy are somehow complementary. I don't equate maths with logic, I accept that logic gives way to interiorty, therefore I don't think I have a tautology in mind.
Sixth, on the nature of mathematical theory. Thank you for a very clear explanation of what maths is (a specific field of theoretical knowledge) by contrast to philosophy (distinguishing and relating general fields of knowledge). By this token, mathematics and philosophy operate in completely different universes of discourse. I agree there is no competition between them, but the failure to recognise their complementarity could lead to conclusions drawn from a one-sided viewpoint. It is simply a matter of raising the further question, once we have identified mathematics as a theoretical knowledge field, what is mathematics? The answer to that will not be independent of the content of mathematics, within its theoretical subject domain. In general, unless we are professional mathematicians ourselves, the answer will rest on a belief, and even professional mathematicians have beliefs.
Seventh, on the need for an image. An image is necessary for insight to occur. It may not be perfect, but we have to get the general outlines correct for it to be of any use to theory.
Eighth, on the release of tension of inquiry. I like your critical-pedagogical approach. It is an important and necessary tool. But if we accept the use of this tool, then it leads even beyond the appropriation of rational self-consciousness, through the heightened tension of the dialectical succession of human situations to the objectification of the supernatural solution that Lonergan discusses in chapter 20 of Insight, until it reaches the point of insertion in human history. That is where the self-correction and re-orientation must lead.
Probably not long enough! But all I have time for, for now.
Best wishes,
David
Catherine Blanche King
DavidB:
I'll be away for 3 or 4 days, so I'll be quick here.
First, I meant for you to reread your note. Also, on the movement from description to explanation, see Insight--many places--the index should guide you, but if you have a problem with it, let me know and I'll check my reading notes.
Also, about "contingency," the shift from classical consciousness, it's method, and its expectations, to interiority calls for an understanding of how contingency related to what Lonergan refers to as the virtually unconditioned. So in that sense, and if I understand your meaning, there is no mere "nothing of contingency." Knowledge is a conditioned (contingency) whose conditions happen to be fulfilled. Also, I'm just referring you to Lonergan's work to understand that movement. I'm giving you a suggestion, not developing theory. In Insight, Lonergan does both: pedagogy and theoretical explanations. Once we understand the distinction, we can identify which he is doing ourselves in each passage, if and when that becomes an issue.
Also, in your last note you referred to a quote on page 356 of Insight--on that page in my text (coll. 4) bLonergan says: "The ultimate basis of our knowing is not necessity but contingent fact . . . " Also, on the next page there is a section called Description and Explanation, and on pages 368-9 there's another incisive narrative. If it's incisive theory, then it doesn't cut itself off from its descriptive beginning--as you seem to hold in your references to "pure"? It's not a mathematical 2+2=4. It's about a generalized movement of human mindedness beginning with an account of insight. I have trouble believing that you do not understand that and rather think that somehow it's not "pure" theory because it begins with a generalized description of what occurs when someone has an insight. Can someone else help out here?
Also, your "three fold distinction" has (1) as "the descriptive content of insight." First, it's a general description of an insight, not it's content. It's content is Archimedes' experience with the baths. Second, the critical control BEGINS there because that's the controlling context that the description is FOR, rather than for commonsense. That control isn't only in your #2 "the explanatory content of insight." And it's not "an explanatory content of insight." It's an general description of insight and its surrounding functions and activities.
Also, the activity of self-appropriation is an application of theory as we use it to experiment and even to identify with our own interior functions-in-operation. But of course, identifying our own questions and insights as they occur, while keeping the theory at hand, is certainly not merely a theoretical exercise, if that's what you mean. If you think that's really what self-appropriation needs to be in order to be authentic, then we really are in trouble here. But I suggest you spend some time with the above text?
In theses passages below, see my parens:
In
the second place, on the stickiness of studying mathematics,
DB: But precisely because their mistaken assumptions can affect a mathematician's ability to do maths, it is a mathematical problem too. (YES, of course--but if the root is a foundational problem, the math probably will only be "fixed" on a Procrustean bed, which is not fixed at all. )
DB: I refer to Lonergan's analysis of mathematicians as dealing with "the empirical residue of all data". (Insight p337) All data includes the philosophical problem of grappling with the polymorphism of human consciousness. (Okay . . .as part of a study, . . . but not in every case. )
CK: As you seem to understand the time problem here, I defer below to more brief parens throughout the rest of your note:
Third,
on the superstructure and infrastructure. Thank you for drawing my attention to the critical word "critical"! (You're welcome.)
Fourth, on the realms of consciousness. I referred to a possible
crossover between philosophical and mathematical theory. You have given a good philosophical explanation of the difference, but could there be a complementary mathematical one? (I'm still not sure what you mean here. But the whole point of Lonergan's work
is that, with polymorphism cleared away with a regime of self-correction, and with critical self-knowledge, there is a complementarity between actual conscious order and its dynamism and, by example, the foundations and then the movement of mathematics.)
DB: Like
the division of investigations into classical and statistical? The straight answer 'no' does not satisfy me, because when insight has occurred, what once seemed impossible suddenly becomes very feasible indeed. (I followed with a "why" I said no? Not enough?)
Fifth, on the sense of mathematics being primitive. You asked if
I was referring to a tautology. I'm not sure I understood exactly what you meant (your "chicken and the egg" reference, as if there were no ground to be had but only a series of self-references, or in logical terms, the logical fallacy of circular arguments
or begging the question), but I accept that I have not been very clear either. I am digging into the idea that maths and philosophy are somehow complementary. I don't equate maths with logic, I accept that logic gives way to interiority, therefore I don't
think I have a tautology in mind. (It sounded that way to me, but this is a conversation here where mistakes and misunderstandings (aka sxxt) happen
sometimes.)
Sixth, on the nature of mathematical theory. Thank you for a very
clear explanation of what maths is (a specific field of theoretical knowledge) by contrast to philosophy (distinguishing and relating general fields of knowledge). By this token, mathematics and philosophy operate in completely different (**but intimately
related**) universes of discourse. I agree there is no competition between them, but the failure to recognise their complementarity could lead to conclusions drawn from a one-sided viewpoint. (Yes, indeed.) It is simply a matter of raising the further question,
once we have identified mathematics as a theoretical knowledge field, what is mathematics? (I think we are not distinguishing enough, the different theoretical fields and THEIR relationship, e.g., between math and different aspects of physics, and besides
their underpinnings of philosophical assumptions. But I'm not a mathematician and so I refer you to others who are, and especially if you can find one whose foundations are [ahem] complementary with their own actual philosophical movements of mind.) The answer
to that will not be independent of the content of mathematics, within its theoretical subject domain. In general, unless we are professional mathematicians ourselves, the answer will rest on a belief, and even professional mathematicians have beliefs.
Seventh, on the need for an image. An image is necessary for insight
to occur. It may not be perfect, but we have to get the general outlines correct for it to be of any use to theory. (Yes. However, you implied in your note otherwise. But the above is why I initially suggested an image in the first place.)
Eighth, on the release of tension of inquiry. I like your critical-pedagogical
approach. It is an important and necessary tool. But if we accept the use of this tool, then it leads even beyond the appropriation of rational self-consciousness, through the heightened tension of the dialectical succession of human situations to the objectification
of the supernatural solution that Lonergan discusses in chapter 20 of Insight, until it reaches the point of insertion in human history. That is where the self-correction and re-orientation must lead. (okay . . . . that's down the road a bit, and there's
a lot in between, but okay.)
DB: Probably not long enough! But all I have time for, for now.
CK: Me, too. I'm away from my desk for a bit.
Catherine
To: Lonergan_L
Subject: Fw: [lonergan_l] Re: Lonergan and Mathematics 2.5
Best wishes,
David
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, and that I would think WILL
TAKE TIME.Dear Catherine,
Many thanks for your reply, it is very helpful to clarify some misconceptions I had, especially the difference between philosophical and mathematical theory.
First, you say:
CK: You might want to reread that? There IS a movement from description to explanation.
DB: Did you mean I should re-read what I said? I was questioning that the explanatory understanding of insight was entirely on the theoretical level. I am trying to understand what this movement from description to explanation could be. As I read it, that movement has been described, but will it survive in a fully explanatory science? Or will it prove to be a mere nothing of contingence?
I try to read on what you say:
CK: That's clear in INSIGHT (DB: yes, descriptively). But initial description occurring under the critical questions of theory development is not merely what Lonergan means by a commonsense description. Badly-described content can set the stage for erred theory. And again, the explanation in this case depends on a distinction between the descriptive content of any particular insight, and insight itself as content (under the critical aim of scientific explanation); and as object of a theoretical explanation where relating generalized conscious activities and functions to one another is the further aim.
DB: so there is a three-fold distinction? a) the descriptive content of insight, b) the explanatory content of insight (under critical control), c) the theoretical account of that content. This is a three-fold movement from descriptive to theoretical formulation via the explanatory route. But this movement has the general structure of an insight, a) what insight presupposes (descriptive content), b) what the insight is in itself (explanatory content), c) the reflective insight (theoretical content). That is what I meant by the explanatory understanding of insight not being purely theoretical, because it itself rests on an insight.
In the second place, on the stickiness of studying mathematics,
CK: Of course, mathematicians can run into problems with math BECAUSE of the unknown (to the thinker) and wrongly-formed philosophical assumptions that reside in their interior arena of thought. However, and insofar as they do stem from philosophical issues, the problems are not fundamentally mathematical.
DB: But precisely because their mistaken assumptions can affect a mathematician's ability to do maths, it is a mathematical problem too. I refer to Lonergan's analysis of mathematicians as dealing with "the empirical residue of all data". (Insight p337) All data includes the philosophical problem of grappling with the polymorphism of human consciousness.
Third, on the superstructure and infrastructure. Thank you for drawing my attention to the critical word "critical"!
Fourth, on the realms of consciousness. I referred to a possible crossover between philosophical and mathematical theory. You have given a good philosophical explanation of the difference, but could there be a complementary mathematical one? Like the division of investigations into classical and statistical? The straight answer 'no' does not satisfy me, because when insight has occurred, what once seemed impossible suddenly becomes very feasible indeed.
Fifth, on the sense of mathematics being primitive. You asked if I was referring to a tautology. I'm not sure I understood exactly what you meant, but I accept that I have not been very clear either. I am digging into the idea that maths and philosophy are somehow complementary. I don't equate maths with logic, I accept that logic gives way to interiorty, therefore I don't think I have a tautology in mind.
Sixth, on the nature of mathematical theory. Thank you for a very clear explanation of what maths is (a specific field of theoretical knowledge) by contrast to philosophy (distinguishing and relating general fields of knowledge). By this token, mathematics and philosophy operate in completely different universes of discourse. I agree there is no competition between them, but the failure to recognise their complementarity could lead to conclusions drawn from a one-sided viewpoint. It is simply a matter of raising the further question, once we have identified mathematics as a theoretical knowledge field, what is mathematics? The answer to that will not be independent of the content of mathematics, within its theoretical subject domain. In general, unless we are professional mathematicians ourselves, the answer will rest on a belief, and even professional mathematicians have beliefs.
Seventh, on the need for an image. An image is necessary for insight to occur. It may not be perfect, but we have to get the general outlines correct for it to be of any use to theory.
Eighth, on the release of tension of inquiry. I like your critical-pedagogical approach. It is an important and necessary tool. But if we accept the use of this tool, then it leads even beyond the appropriation of rational self-consciousness, through the heightened tension of the dialectical succession of human situations to the objectification of the supernatural solution that Lonergan discusses in chapter 20 of Insight, until it reaches the point of insertion in human history. That is where the self-correction and re-orientation must lead.
Probably not long enough! But all I have time for, for now.
Best wishes,
David
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Yet gravitational waves were not the merger’s only products. The event also emitted electromagnetic radiation—that is, light—marking the first time astronomers have managed to capture both gravitational waves and light from a single source. The first light from the merger was a brief, brilliant burst of gamma rays, a probable birth cry of the black hole picked up by NASA’s Fermi Gamma-Ray Space Telescope. Hours later astronomers using ground-based telescopes detected more light from the merger—a so-called “kilonova”—produced as debris from the merger expanded and cooled. For weeks much of the world’s astronomical community watched the kilonova as it slowly faded from view." End quote
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Dear Catherine,
Catherine
From: 'DavidB' via Lonergan_L <loner...@googlegroups.com>
Sent: Friday, October 13, 2017 12:52 PM
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics
Dear Catherine,I may be a little confused here, but I shall try to respond as best I can.CK: I'm not saying that, concretely, we don't or cannot have knowledge content, or that our reflection and self-reflection cannot and does not result in knowledge and self-knowledge. I'm just generalizing--distinguishing (a) the basic dynamic structure from (b) its content. Rather than confusing, differentiating often leads to its opposite.DB: That's fine. Distinguishing the dynamic structure from its content makes perfect sense, and is an efficacious path to self-knowledge. This is part of the process of clarification, not confusion. But there is a corollary, for if we make a distinction between the two, then we are abstracting each from the other. We cannot make the separation in fact, but we can do it mentally, and then our abstract conception of the dynamic structure is what we mean by the unlearned state of dynamic intentionality, which is without self-knowledge because we have made the differentiation between structure and content. Unless I have missed your point again?CK: But also in that paragraph, you refer to "the bewildering fact of polymorphism." ... In that (philosophical) context, I would consider that term refers also to learning or, in this case, to learning badly. So that polymorphism occurs **as a result** of the question-to-insight-to-understanding process.DB: On this, I would be inclined to disagree. My understanding of polymorphism is that it is prior to the self-knowledge that follows from the concrete subject becoming rationally aware and capable of issuing the transcendental precepts to him/herself. Confusion precedes clarification. The polymorphism is just as much a native feature of the human mind as the liveliness of its dynamic intentionality.DB: Polymorphism is undifferentiated potency. It represents the vast capabilities of the human mind, but without the directed dynamism that proceeds from an intellectual conversion. It is the capacity for insight, but also for failures of insight.CK: But as polymorphic, we can have insights that flow from oversights and we can have erred insightsDB: Insights do not flow from oversights. They issue from the dynamic intentional core, intellectual curiosity, the pure notion of being, whatever we want to call it. What happens however within polymorphic consciousness is that the insights can be formulated in such fashion that they are either consistent or inconsistent with the intentional operators of intelligence and reasonableness (Lonergan's definition of positions and counterpositions respectively). It is not the content of the insight that is at fault, but rather the orientation of concrete subject who failed to attend fully to the inner dynamics. That is the oversight, but the oversight does not yield insight.DB: Likewise, I would hold an erred insight to be a contradiction in terms. Every insight has a content of experience, a content of understanding and a content of judgement. The content of judgement is a virtually unconditioned yes. If there were such a thing as an erred insight, then the judgement making it would be false, which means it is not an insight at all. Rather, it proceeds from within the polymorphism of human consciousness by a subject that, by an oversight, mistakes the false judgement for a true one.CK: But the "many forms" of philosophical thought, ideas, and ideologies refer to what we have learned but where that learning does not correspond with the actual "what" that we asked about at some point in our learning career. Our present understanding, then, doesn't accurately reflect the actual philosophical (cognitional, epistemological, metaphysical) activities of our core consciousness and the assumptions that flow from it's actual activities. Those omissions and erred insights become a set of assumptions that, in turn and if not corrected, do not overcome the core and its activities, but rather continue to conflict with it. They become the source of much internal tension. They are the source of not only the philosophical mess we are in today but they extend themselves into all areas of thought.DB: Yes, our internal tension and philosophical mess. I do not dispute the facts, but if we wish to resolve the issues then we have to go back to the beginning of the argument and identify the inner dynamic structure that is the source of all our insights. Insights originate in the intentional core, dialectical oppositions from the polymorphism of consciousness, and our task is to critically distinguish between them so we can make some progress at overcoming the tension and ending the mess.CK: It's because our core still works, AND our polymorphism comes into play, that we can say with Einstein: do not listen to what scientists say about their knowing, but watch what they actually do.DB: This was certainly Lonergan's approach, in his analysis of empirical method. To be a successful scientist does not require being in possession of an articulate account of each and every conscious operation that scientists perform. But their success is grounded in being true to the precepts that issue from the inner, dynamic core.CK: The core continues to work; but what scientists think about it and about their own knowing adds the "poly" to the forms of philosophical knowing that are, with that bad learning still in place and influencing our further thought, "bewildering."DB: I am wondering how accurate the expression is that scientists add "poly" to their knowing. I would prefer to say that the "poly" is present even to the scientists who have not started wondering about their own conscious operations. When we speak of the pure state of the inner dynamic core, we are making an idealisation. The truth is that the positions and counterpositions of different philosophical outlooks are mixed in right from the start, and our task is to labour to reverse the counterpositions, while developing the positions.That is why I am finding this conversation so useful, it is helping me to understand and clarify my own polymorphism.
Thanks, and best wishes,David
DavidB
DavidB
Dear Catherine,
Thank you for your reply. It is very helpful to uncover some more of my oversights!
In the first place, on description and explanation. I followed up those references you gave me, thank you. I also checked the index and found another reference to p419, which I think is relevant to my particular question. “Metaphysics primarily regards being as explained, but secondarily it includes being as described.” Although the explanatory relations are discovered through a process of self-analysis and introspection that begin from descriptive relations, nonetheless, the descriptive relations are merely a subset of the explanatory relations. This is because the descriptive relations relate things to us, while the explanatory relations relate things among themselves, and since we are things, the descriptive relations are included in the explanatory ones. So the answer to my question, whether descriptive relations survive in fully explanatory science, is that “the inclusion of descriptive relations in metaphysics is implicit, general, mediated and intellectual.” Lonergan defines what he means by each of those terms.
Just to remind ourselves how we got on this topic, you said:
CK: Then you say: “Mathematics is an explanatory science, and therefore I intended the latter interpretation. [DB: on the distinction between the descriptive “insight-for-us” and the explanatory “insight-in-itself”].”
CK: Well, there are insights explained theoretically where we don't leave theory to understand the insight's relationship to other aspects of human consciousness.
Then I said:
DB: I would question what you mean by “we don’t leave theory”. If you mean that the explanatory understanding of the insight is entirely on the theoretical level that relates that insight to other aspects of human consciousness, then I would note that such an account presupposes an insight between the theory and its content, the insight-in-itself. Therefore the insight is not mere theory because there is an insight too, an insight into insight.
Perhaps I missed your point, but I’m still not sure what you meant by “we don’t leave theory”...
In the second place, on the three-fold distinction. I was not making this distinction myself, I was reading what you said below. I have added ** to indicate where I thought the distinctions lay.
CK: That's clear in INSIGHT. But initial description occurring under the critical questions of theory development is not merely what Lonergan means by a commonsense description. Badly-described content can set the stage for erred theory. And again, the explanation in this case depends on a distinction between **the descriptive content of any particular insight**, and **insight itself as content** (under the critical aim of scientific explanation); and **as object of a theoretical explanation** where relating generalized conscious activities and functions to one another is the further aim.
Perhaps I misinterpreted the exact meaning of the three elements in your last sentence, but there still appears to be this three-fold distinction. 1) A general description of an insight; 2) a general description of insight and its surrounding functions and activities; 3) an object of theoretical explanation. It doesn’t matter if these categories are not precisely defined, the point is that the distinction exists and it seems to satisfy the three-fold structure of insight.
In the third place, on self-appropriation. No, I don’t believe self-appropriation needs to be a merely theoretical enterprise to be authentic. I’m not quite sure what I said to suggest this, so apologies for any misunderstanding.
In the fourth place, on contingency. You are correct in drawing attention to the contingency of human knowledge, that it consists of matters of fact that merely happen to have their conditions fulfilled. But this means that we cannot have complete understanding of proportionate being without a corresponding discussion of transcendent being. By the nothing of contingency, I was referring to Insight page 675, when Lonergan says “If existence is mere matter of fact, it is nothing. If occurrence is mere matter of fact, it is nothing. If it is a mere matter of fact that we know and that there are to be known [various things], then both the knowing and the known are nothing.” I think I have been avoiding this topic because it is much easier to discuss things that we experience directly, but when it comes to mathematical foundations, even a simple expression like 1+1=2 is incomplete without a study of transcendence. Previously I did not advert to this fact, and it now suggests to me a theological interpretation of mathematics.
This leads on to the fifth place, foundations. We said:
DB: But precisely because their mistaken assumptions can affect a mathematician's ability to do maths, it is a mathematical problem too. (CK: YES, of course--but if the root is a foundational problem, the math probably will only be "fixed" on a Procrustean bed, which is not fixed at all.)
That’s a useful analogy, the Procrustean bed, and it indicates precisely the kind of reorientation required to fix the maths. The idea that there is some sort of “bed” which the maths needs to fit presupposes some sort of reference frame which specifies the dimensions of the bed. But Lonergan’s revolutionary idea of systematising Einstein is to remove the reference frames, and move to a statistical type of geometrical inquiry (cf. Insight p195). The Procrustean beds reappear on every return to the concrete, but the fix is on the foundational level, and this must be integrated into the field of mathematics, somehow.
In the sixth place, on the distinction between philosophy and mathematics. You suggested I was confusing the two. I was trying to grasp the distinction, and suggested a complementarity between them. Then you said:
CK: But the whole point of Lonergan's work is that, with polymorphism cleared away with a regime of self-correction, and with critical self-knowledge, there is a complementarity between actual conscious order and its dynamism and, by example, the foundations and then the movement of mathematics.
I like the idea of complementarity between actual conscious order and its dynamism, and I think I was mentally associating philosophy with the actual conscious order, and mathematics with its dynamism. There is a vast body of mathematical literature in libraries around the world, but maths in itself is not just theorems. It is about proof, and proof does not consist merely of a sequence of marks on paper. It is about the dynamism of the human mind that grasps the virtually unconditioned within those sequences of marks. This is what I believe Lonergan has to offer mathematics, but we have to precisely conceive what mathematics really is in order to make use of it.
If I might suggest, the weakness of Lonergan’s discussion of mathematics is that his examples are mainly for illustrative purposes only. That is because his primary intention was insight, not development of mathematics, which is entirely reasonable. But if we are to apply his critical approach to mathematics, then we have to go over the basics again. For example, Insight page 38, he says, “Let us suppose as too familiar to be defined the notions of ‘one’, ‘plus,’ and ‘equals’.” As a pedagogical tool, such an approach is fine, but in philosophy of mathematics, those definitions are critical.
You also said above “by example, the foundations and then the movement of mathematics.” Unfortunately, I don’t find this example very compelling for the reason above, that I want to know more about the foundations and movement of mathematics, and not simply use them as an illustrative example. I also doubt whether a complementarity exists here, because my suspicion is that the foundations of mathematics may be connected with its movement, so that the two may turn out to be exactly the same thing, in a similar way that philosophic method is coincident with philosophic work (Insight page 450).
This leads into the seventh place, the nature of mathematical theory. You said:
CK: I think we are not distinguishing enough, the different theoretical fields and THEIR relationship, e.g., between math and different aspects of physics, and besides their underpinnings of philosophical assumptions.
You are right that I have not mentioned much about other fields like physics. My answer to that is this is like asking the further questions which lead to other knowledge that, while desirable, do not directly pertain to the field of mathematics. As on Insight page 100, by asking different questions, the cartwheel can lead on to the fields of economics, forestry, mining, technology, sociology, psychology, none of which directly pertain to the question, why is it round?
Then you say:
CK: But I'm not a mathematician and so I refer you to others who are, and especially if you can find one whose foundations are [ahem] complementary with their own actual philosophical movements of mind.
I appreciate you are not a mathematician, and therefore I do not expect you to provide direct answers to all my questions. However, I might note that my aim is not to find a mathematician whose foundations are “complementary with their own actual philosophical movements of mind”, but rather to construct the foundations in such a sense that they are like this. I received some insights from Phil McShane on the nature of randomness (his doctoral thesis), and my idea is that randomness could be the empirical residue that connects the concrete with the abstract, through insight into the notion of emergent probability. Such a foundation based on randomness would be truly complementary to the philosophical movements of mind, because the latter is systematic while the former is non-systematic.
A lot more could be said I'm sure, but I’ll leave it there.
Best wishes,
David
Catherine Blanche King
DB: Perhaps I missed your point, but I’m still not sure what you meant by “we don’t leave theory”...
CK: I meant what I said in a note later--that when doing theory, descriptive beginnings are under the critical refinement of theoretical thinking, or "for" development of the theory, not "for us" in the same way that Lonergan means by "for us" in commonsense. In your L quote, "Metaphysics primarily regards being as explained, but secondarily it includes being as described,” in L's understanding of being, there is nothing that falls outside of being, so to speak; and so descriptions are included, but under different movements of thought: theory and commonsense. Perhaps you have the distinctions between (a) commonsense and theory, (b) things as related to us and things as related to other things, and (c) description and explanation as unrelenting conceptual divisions, rather than movements of mind? (That's a rhetorical question.) But descriptions can be "secondary" as falling under the critical-theoretical movement of mind (consciousness), just as we can "explain" what my dog is doing in the house, for instance, as a commonsense event. The same things and events can fall under the two different movements of consciousness (and more). To say that in another way, when we are in a theoretical "frame" of mind, all that we do with regard to our questions, including describing, falls under that frame. That's my reading of Lonergan's passages on this subject. It has to do with theoretical OR commonsense consciousness, and not with conceptual divisions between words like descriptions and explanations.
CK: Perhaps the above will help you also with that three-part distinction in that paragraph where you are talking about insights?
THEN YOU SAY:
DB: "I like the idea of complementarity between actual conscious order and its dynamism," . . .
CK: . . . and then you went on. But what I said was this (I include a and b here: ". . . with critical self-knowledge, there is a complementarity between (a) actual conscious order and its dynamism and, by example, (b) the foundations and then the movement of mathematics." I'll clarify: When a mathematician (for instance) has adequate and critical philosophical self-knowledge, the complementary is between (a) actual conscious order and its dynamism and, (b) the foundations and then the movement of mathematics. <--and you can put any subject/field name in place of "mathematics" there.
About contingence: The problem as I understand it is in the missing meaning in the context of your quotation. You quote: "If existence is mere matter of fact, it is nothing." But just before that, L writes: It follows that to talk about mere matters of fact **that admit no explanation** is to talk about nothing" (my emphases). I think the "that admit no explanation" is a key part to understanding what Lonergan means here since he is talking about the complete intelligibility of being?
CK: If you mean to usher in a discussion of theology at this point, I'm sure Lonergan has this in mind at some point and in some way, but I don't think in the way you imply here, because he has a high regard for facts that admit explanation? and this from an empirical point of view. On the other hand, many have critiqued Insight on just this issue of the movement from that empirical view into religion and theology; however, and ever-so-briefly, there is the important distinction that Lonergan himself makes in Collection 3 on Healing and Creating in History--that is, from below-upwards, and from above downwards. The movement and distinction between (a) critical-empirical philosophy and (b) religion, if not aspects of theology, is based on just this HUGE difference of vectoral movements. Perhaps you'll agree that this breaks open into a discussion for another time, however?
And when you say the below, it probably relates to the above:
DB: But this means that we cannot have complete understanding of proportionate being without a corresponding discussion of transcendent being.
About Lonergan's use of mathematics as merely an example of the movement of mind and how insights work: I think you are right in what you say. However, the point is no small issue for any field. And things get even more "sticky" because even mathematicians who are working from polymorphic philosophical foundations still have, as a part of those foundations, the basic structure which can work unimpeded by interior conflicts, at times, in some situations, and with some data. So that, if you are doing analysis, you have to take that into consideration also. Medical doctors, for instance, still cure patients with a huge background of excellently drawn knowledge. Enter: dialectic. But when you say:
DB: mathematics may be connected with its movement, so that the two may turn out to be exactly the same thing, in a similar way that philosophic method is coincident with philosophic work (Insight page 450). . .
CK: It's not the same thing, according to my above paragraph, and because mathematics has philosophical foundations; while philosophic work is ABOUT those same foundations and can add interior conflict that then has a come-and-go influence on ALL other work. But for philosophy, and when mathematicians do any philosophical work, polymorphism poisons the whole well, so to speak. We are inspecting philosophical issues WITH that polymorphic set of philosophical presuppositions already in place. We might be able to do math well without good foundations; however, we cannot do philosophy well because it's about those foundations, and not math. Hence, the need for self-appropriation as the basis for any critical-empirical beginning.
Lastly, you say at the end of a thoughtful paragraph:
DB: Such a foundation based on randomness would be truly complementary to the philosophical movements of mind, because the latter is systematic while the former is non-systematic.
CK: I think the stuff above about understanding different aspects of consciousness plays in here. But the window is closing. The sun has gone to bed, and so must I. Later.
Catherine
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics 2.6
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Catherine Blanche King
Hello DavidB and anyone who is reading this exchange:
A couple of additions to my last note:
First, a correction: "Collection 3" should be "Third Collection" where the Creating and Healing" essay appears.
Second, when I referred to two "frames" of consciousness, as commonsense and theoretical, I did not mean to exclude other "frames" or differentiations and conversions of consciousness of which there are many and where Lonergan expounds-on in several of his writings.
Third, I excerpted only the last line of your last paragraph about randomness, system, and non-system. I could comment more, but Phil McShane could probably give you a more comprehensive and satisfactory answer, particularly where the intersection of math and physics is concerned.
And lastly, the analogy of a Procrustean bed can probably also serve us in understanding why new-learning-about, and hard-won correction-of, our own (potentially undifferentiated and/or erred) philosophical foundations differs from doing so in relation to any other field or science, like mathematics.
If you want to bear with me, let us regard that we mean by "bed" the bed frame, and that frame as our actual philosophical method of mind. We don't learn that frame. Rather, it comes with being human; and it's that through which we do learn (it's "given").
From there, our philosophical foundations include (a) our actual Method, (b) its own set of presumptions we have developed from birth, and (c) our later philosophical learning.
That learning can become skewed quite early in our informal and formal learning career (the main oversight and its error is that knowing is looking, or like it).
Also, our erred learning can become supported and/or further skewed by commonsense cxxp and/or by academics in our later more formal training. And so, when we further consider philosophical issues, we do so, again, from within our already-built-on, habituated, but now erred and limited, philosophical horizon.
Math (et al) can go forward **in some regard** without being influenced by such problems, but not philosophy.
To use our Procrustean metaphor, because of our bad earlier learning, the "bed frame" of our own (given) ACTUAL Method of consciousness gets a thick layer of later erred learning--a mattress, so to speak, from which we begin to think as a "foundational" habit of mind--all mixed up now with our actual Method of mind which remains dynamic "beneath" the mattress. And so we become philosophically messed-up (polymorphic).
Further, most of the problematic exists pervasively, below, at the gate, and above the divisions of consciousness we refer to as un-, semi-, or fully conscious.
Then, when we get to new philosophical issues today--especially where self-reflection is anathema to our now-set ideas about objectivity--we are likely to actually think WITH that mattress of bad learning, rather than with the frame. We think WITH that mixed-up mattress in place, underneath our new thinking and informing it, RATHER than from (or with) the actual Method that actually structures the dynamism of our consciousness.
First, that bed frame-Method doesn't go away. It keeps operating, holding up whatever mattress we put on it. If it did go away, we wouldn't have to find ourselves explaining away the difference between (as Einstein regards) (a) what we actually do spontaneously with regard to knowledge , truth and reality (the bed frame), and (b) our now-powerful mattress, or what we THINK we do (so the many headed hydra of our performative contradictions emerges from this admixture of bed frame and mattress).
The mattress, then, rather than the bed frame, can become the pervasive and long-term habit of thought. And as habitual, it sinks to the level of philosophical presuppositions where it gets difficult to get at, even in the best of circumstances (again, as Joe Martos regards in his note). (You can see where guided self-reflection, with the aim of both development and self-correction, becomes imperative to philosophical learning?)
The mattress is our set of philosophical assumptions, (some or many as badly learned) that we carry around with us--as confused as they may be--and that are different for each of us.
Now, put a sheet and blankets on the mattress, and you have our new thinking about philosophical issues.
For math (et al), our history of good works (the history of knowledge development) can be set aside as still good while we go to the mathematician's (or the theologian's) philosophical foundations--to return to later with a new set of lenses with which to critique.
But for philosophy, there's no "good philosophy" that can be set aside in the same way as math or physics or other field/subject work can be set aside. Rather, we begin our philosophical thinking WITH bad foundations in place ABOUT philosophical issues. For instance, we stay at the level of comparing concepts (because self-reflection is "merely psychological" and so anathema to objectivity, for instance) rather than with even mentioning self-reflection, or deeper movements that are basically "the cure."
For instance, from those erred foundations, we MUST remain "objective"--which commonly means extroverted and conceptualist. Sigh . . . .
(Here, in my understanding of it, is the absence of and resistance to "the third way.")
Here, we enter philosophical dialogue **with that messy combination of now-impenetrable (<--on principle) habitual thought as our "philosophical lenses"** through which we try to understand philosophical issues (concepts). We think with THAT mattress of assumptions, INSTEAD of the actuality of the bed frame where, with proper learning, we might have a mattress of philosophical learning that happens to be well-developed. But if it's skewed, and from those "silo" foundations, we'll never get to it.
Thus, as we enter philosophical discourse, our new thinking about new philosophical issues can SEEM quite correlate with the ERRED mattress--rather than with the actual Method of mind, or with the bed frame and its own set of assumptions that still hold our spontaneous philosophical experience in place, even when our the mattress hangs over the side or has lumps and holes in it--and is otherwise totally ill-suited for its frame. Again, that Method still works, but now in come-and-go company with the erred mattress, struggling and creating various shades and degrees of internal tension as we try to find our natural place on that horrible mattress.
So math and philosophy have some similarities--that is, they are similar when the mathematician enters philosophical dialogue--where they will also have the same problematics as the philosopher whose work is in that arena of fields/sublects.
However, those problematics won't show up ALWAYS in OTHER fields/subjects as they will for philosophy-proper. This "showing up" is potentially a whole new "course" of study (perhaps someone's PhD thesis). But, from what I can tell, and though I have not thoroughly thought it out, problems do occur at the edges and intersections of fields/subjects where understanding relationships between different data and concepts are concerned. The big one of course, is between data that is commonly approached using Empirical Method and that of GENERAL Empirical Method.
I hope this night-time thinking helps. Anyway, I thought I should clear up a few of those absences in my prior note.
Catherine
Sent: Saturday, October 28, 2017 6:08 PM
To: loner...@googlegroups.com
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics 2.whatever
DavidB
CK: Well, there are insights explained theoretically where we don't leave theory to understand the insight's relationship to other aspects of human consciousness.
DB: Did you mean there are insights that are explained when we are in the theoretical "frame" of mind? c.f. Insight p319-320 on Lonergan's distinction between different universes of discourse: does the sun rise and set, or do the planets move in an elliptical orbit around the sun? I'll continue your quote to put it in its original context:
CK: And there is mathematics that, as you say, is an explanatory science where we abstract from concrete things, e.g., the mathematics abstracted from a cartwheel. Unlike mathematics, however, the study of insight-itself does get "sticky" because the field of verity is us and our experience of our interior selves. The point with insight, however, and our return to our own experience for verity, is that the theory provides (what L calls) the superstructure to understand the interior infrastructure (those terms are in Method somewhere-I'll find it if you want) rather than cartwheel roundness. The theory, then, provides CRITICAL access to the generalized data of consciousness as empirical.
DB: My issue is that I don't think mathematics can be understood by a simple contrast with the study of insight. I think the answer lies in the paragraph that spans pages 337-338 of Insight, in which Lonergan describes two complementary tendencies of mathematics. On the one hand, there is the movement from description to explanation, with the ideal goal of constructing systems of explanatory conjugates and ideal frequencies that cover all intelligible aspects of empirical data. On the other hand, there is the exploration of enriching abstraction with the empirical residue. We have discussed the former movement in some detail, but not really that much yet on the latter.
I'll add a couple more quotes from Insight to illustrate what Lonergan says about mathematics.
p338 "It follows that the mathematician is concerned to establish generally, completely and ideally the range of possible systems that include verifiable scientific systems as particular, fragmentary, or approximate cases."
p340 "Serially analytic principles [that is, mathematics] are the analytic propositions from which follow the ranges of systems of which some in some fashion exist."
My particular question is, does the theoretical account of insight you mentioned above fall under the "verifiable scientific systems" that the mathematician seeks to establish "generally, completely, and ideally", in some "particular, fragmentary, or approximate" way? In other words, could there be some mathematical system for insight? I don't mean that insight is like 1+1=2. Rather, it is the other way round, that 1+1=2 follows from a study of insight.
(I'll skip the confusion on our three-fold distinction).
In the second place, on contingence. Yes, Lonergan is talking about the complete intelligibility of being. But I think that is very relevant to our discussion, because mathematics is not about matters of fact that have no explanation. Even simple mathematical expressions have to be proved. And the only way to overcome contingence at the deepest level is through the reasonable choice of an unrestricted act of understanding that we name God. It is what Lonergan calls the "cause of causes", or the "ground of value" (Insight p679-680), and a complete mathematical system cannot be without it.
Then you said:
CK: The movement and distinction between (a) critical-empirical philosophy and (b) religion, if not aspects of theology, is based on just this HUGE difference of vectoral movements [that is, from below-upwards, and from above downwards] . Perhaps you'll agree that this breaks open into a discussion for another time, however?
DB: What I am suggesting is that mathematics is precisely about bringing together these two complementary movements. As for another discussion, another time, that goes back to the "long journey" - is it being on the road that matters, or when or where we discuss it?
In the third place, on philosophical foundations. You said:
CK: And things get even more "sticky" because even mathematicians who are working from polymorphic philosophical foundations still have, as a part of those foundations, the basic structure which can work unimpeded by interior conflicts, at times, in some situations, and with some data.
DB: The difficulty is present only if we fail to distinguish between different universes of discourse. Every mathematical statement is a theoretical abstraction, and should be preceded by the qualifying reservation "from the viewpoint of mathematical discourse ..." Philosophical polymorphism is irrelevant to mathematics, **as mathematical**. But from the viewpoint of philosophical discourse, polymorphism has every role to play.
Then I suggested in my last note, and you replied:
DB: mathematics may be connected with its movement, so that the two may turn out to be exactly the same thing, in a similar way that philosophic method is coincident with philosophic work (Insight page 450). . .
CK: It's not the same thing, according to my above paragraph, and because mathematics has philosophical foundations; while philosophic work is ABOUT those same foundations and can add interior conflict that then has a come-and-go influence on ALL other work. But for philosophy, and when mathematicians do any philosophical work, polymorphism poisons the whole well, so to speak. We are inspecting philosophical issues WITH that polymorphic set of philosophical presuppositions already in place.
DB: I accept that mathematics is not the same thing as philosophy. I was suggesting that mathematical foundations and mathematical movement may turn out to be the same thing. And I might be wrong. But until the mathematical foundations have been properly established, this seems to me an open question.
CK: We might be able to do math well without good foundations; however, we cannot do philosophy well because it's about those foundations, and not math.
DB: I beg to differ on being able to do maths well without good foundations. If that were the case, then the Riemann Hypothesis should have been proved by now. The fact that it has stymied even the best mathematicians for around 150 years suggests there is a foundational issue. I agree that philosophy has a foundational issue too.
In the fourth place, on movement. We have talked about movement in various ways (philosophical, mathematical, long journey etc.), but I think it is useful to see what Lonergan has to say about it. Insight p108 "It was obvious and excusable for Galileo and Kepler and Newton to conceive local movement in the two steps of determining a path or trajectory and then correlating points on the path with instants of time." Consciousness is a stream, and when we speak of inspecting the dynamic movements of mind, we must beware of making the same mistake as the Renaissance scientists, which is now less excusable than they. "What movement is, when movements are defined in terms of their relation to one another, is another question." I mention this to highlight the need of going beyond a view verified in subjective consciousness. As a pedagogical tool, it is indispensable, but it can only be a preliminary step for discovering the complete intelligibility of the concrete dynamics of the universe of being.
Time to go. Best wishes,
David
Catherine Blanche King
David B:
DB: Did you mean there are insights that are explained when we are in the theoretical "frame" of mind?
CK:
There are, but replace "explained" with "described" in your sentence, and you will have what I meant.
Catherine
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics 2.whatever
Catherine Blanche King
DavidB:
Your question:
DB: My particular question is, does the theoretical account of insight you mentioned above fall under the "verifiable scientific systems" that the mathematician seeks to establish "generally, completely,
and ideally", in some "particular, fragmentary, or approximate" way? In other words, could there be some mathematical system for insight? I don't mean that insight is like 1+1=2. Rather, it is the other way round, that 1+1=2 follows from a study of insight.
CK: If I understand you correctly, it's the other way around--except
to understand that 1+1=2 does not "follow from a study of insight," but from having not only one, but several of them--insights. The study of insight as such comes much later if at all. But my later "addendum" should shine some light on that?
And again, if I understand you correctly, intelligent consciousness differs as it's the empirical source of our understanding and development of all-things-system. In that sense, it underlies both the notions associated with system AND the openness that is
basic to, say, the fact that there are no systems that hold an account completely of themselves. In human affairs, there needs to always be a person's mind inserted between general system and its application for it to work well. The question "why" is a question
for the structure and dynamism of history itself.
The integral heuristic structure (aka Lonergan's metaphysics) is an albeit-grounded extrapolation that admits that openness. And again, this is where the from-below philosophical discourse meets up with the from-above-downward discourse where all can enter into a different frame of questioning and understanding.
The key, to me, is to keep them separate but to also understand how they are and might further be related. Concretely, I would advise against "jumping" from empirical method, or even general empirical method, to the language of theology or religion--in the presence of, for instance, a scientist or mathematician who isn't, in some respects, on the same page, so to speak.
Catherine
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics 2.whatever
DavidB
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Catherine Blanche King
DavidB:
DB: In the second place, on contingence. Yes, Lonergan is talking about the complete intelligibility of being. But I think that is very relevant to our discussion, because mathematics is not about matters of fact that have no explanation. Even simple mathematical expressions have to be proved. And the only way to overcome contingence at the deepest level is through the reasonable choice of an unrestricted act of understanding that we name God. It is what Lonergan calls the "cause of causes", or the "ground of value" (Insight p679-680), and a complete mathematical system cannot be without it.
CK: . . . and to your next two paragraphs in your note below: I think you changed the venue of the question, which makes it sound as a bit defensive and even contrarian rather than an open discussion?
I would continue to live in terms of my faith; but precisely because we are doing foundational/ philosophical work (I presume), I wouldn't talk about God yet. If you suspect that your philosophical foundations are still being formed and corrected (BIG IF: I'm not making that judgment), then you would have a Procrustean-bed situation already in the works--precisely because philosophical foundations influence, in many different ways, our understanding of theology and religion and the reading of those texts. (See Pierre's last Skipper note.)
CK: If so, then a person doing both at once will necessarily suffer from a probably-ongoing confusion based on the need (generally) to differentiate first, before making such relationships in a reflective discussion. It's too much like flying while fixing the plane? My aunt also used to have a saying: You've got "Two pounds of X in a one-pound bag."
CK: I will add this: in term of your questions about the relationship between math, philosophy, and God, I "get the feeling" that you MIGHT be looking for a confirmation (confirmation bias) of some preliminary ideas about those issues and their relationship, rather than coming at it with unadulterated openness and its (differentiated) questions? <--And THAT's merely a question raised for you, not necessarily answered HERE by you, or by me as I sit here in front of my computer. These are different fields with different questions and methods--again, not a competition about which is more important or "on top" of the other. You might want to see, again, in Third Collection, Lonergan's "Ongoing Genesis of Methods."
Ck: But again, about mathematics, Phil will probably be a better resource. I would add, however to go forward in Insight to the next page, last paragraph before 9/Summary in that section (p. 339). "The principal different in our approach . . . " I am glad to have re-read this section, especially about "mathesis" and the relationship of the empirical residue to math and to physics.
CK: As example of too-much/too soon, I find your comment below to be extremely troublesome:
DB: "And the only way to overcome contingence at the deepest level is through the reasonable choice of an unrestricted act of understanding that we name God."
CK: It's self-contradictory on the face of it. that is, we cannot "overcome contingence" by making a "reasonable choice." We rather fulfill the contingency that we happen to be in-question about. And it's where religious conversion comes in (from above downwards)--an entirely DIFFERENT foundational realm. I think there are many depth charges, so to speak, that come into play for such a comprehensive discussion to be fruitful.
CK: But reflecting on your L quotes in your below note, I don't see any conflict with what I have said in my other notes. But I'll read them again.
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics 2.whatever
Catherine Blanche King
DavidB:
I think the best you can do on that is a full understanding of what Lonergan means by integral heuristic structure. I presume mathematics is part of that--but again, I am not a mathematician--check this out with Phil? Or maybe
someone else (a scientist) in the Lonergan corpus of thought?
Catherine (signing off)
To: Lonergan_L
Subject: Re: [lonergan_l] Re: Lonergan and Mathematics 2.Systems
DavidB
To post to this group, send email to lone...@googlegroups.com.
Jaray...@aol.com
David, Catherine,
David caught my attention in that he writes "the only way to overcome contingence at the deepest level is through the reasonable choice of an unrestricted act of understanding that we name God. It is what Lonergan calls the "cause of causes", or the "ground of value" (Insight, 679-680), and a complete mathematical system cannot be without it."
In the middle of p. 679, L had also said: "Because being is intelligible, it also is good. As potentially intelligible, it is a manifold, and this manifold is good inasmuch as it it can stand under the formal good of order. But possible order are MANY......"
Since I have studied Buddhism, esp. Mahayana, I was led to ask myself, how would Buddhists react to the present topic
"L and mathematics"?
We probably WILL NOT be able to follow the subject "L, math, and Buddhism" but at least I'll forward 3 quickly googled references:
1) at http://rational-buddhism.blogspot.de/2012/09/buddhism-and-mathematics.html
Six aspects of mathematics which are relevant to Buddhist Philosophy
(i) The foundations of mathematics have parallels (and differences) with the Buddhist concept of emptiness (sunyata)
(ii) The bootstrapping of the integers out of the empty set provides a simple illustration of how causes and components can be expressed as algorithms and datastructures.
(iii) The further development of mathematics from its empty foundations creates computational algorithms and datastructures that can simulate all physical phenomena.
(iv) These simulations epitomize the 'unreasonable effectiveness' of mathematics in physics and engineering, which suggests that there may be aspects of the mind which are not explainable as the products of evolution.
(v) The concept of 'algorithmic compression', which is an aspect of the unreasonable effectiveness of mathematics, leads on to the Church-Turing-Deutsch principle, which gives us a workable philosophical demarcation between physical and non-physical phenomena, including physical and non-physical aspects of the mind.
(vi) The deep interconnection between the mind contemplating emptiness, and the workings of the physical world, suggests that mathematics may provide a bridge between ultimate and conventional truths.
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