Re: The Difference That Makes A Difference That Peirce Makes

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Jon Awbrey

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Sep 18, 2019, 4:20:55 AM9/18/19
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Cf: The Difference That Makes A Difference That Peirce Makes : 20
At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

Cross-paradigm communication, like cross-disciplinary and cross-cultural
communication, can be difficult. Sometimes people do not even recognize the
existence of other paradigms, disciplines, cultures, long before it comes to
the question of their value. Readers of Peirce know he often uses important
words in more primordial senses than later came into fashion. Other times his
usage embodies a distinct analysis of the concept in question. More than once
I've found myself remarking how Peirce "anticipates" some strikingly "modern"
idea in logic, mathematics, or science, only to find its roots lay deep in
the history of thought. Whether he anticipates a future sense or preserves
an ancient sense is not always easy to answer.

Regards,

Jon

John Bottoms

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Sep 18, 2019, 11:19:06 AM9/18/19
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JA: Interesting concepts, could you post a couple of references from his
work?

-John Bottoms

Jon Awbrey

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Sep 18, 2019, 4:44:56 PM9/18/19
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John, All ...

Re: The Difference That Makes A Difference That Peirce Makes : 20
At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/

That bit of blogging bubbled up from several weeks observing various discussions
around the web where people seemed to spending most of their effort talking past
each other and hardly ever getting any ideas or information out of one skull and
into another. It's not the first time I've noticed belief systems, comfort zones,
conceptual silos, paradigms, whatever we want to call them, operating a lot like
immune systems, insulating our mental metabolisms from any intellectual antigens.

Anyhow, it's a working hypothesis to prime future inquiry ...

As far as Peirce references go, the choices are legion, so I'll just link to
one place I have in mind at the moment, where he sets out a number of truly
radical ideas, ones I view as missed opportunities in that he did not fully
follow up on them in later years.

Peirce's 1870 Logic Of Relatives
================================
Overview : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
Part 1 : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1
Part 2 : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2
Part 3 : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_3
References : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_References
Resources : https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Resources

Regards,

Jon

On 9/18/2019 11:19 AM, John Bottoms wrote:> JA: Interesting concepts, could you post a couple of references from his work?
>
> -John Bottoms
>
> On 9/18/2019 4:20 AM, Jon Awbrey wrote:
>> Cf: The Difference That Makes A Difference That Peirce Makes : 20
>> At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/
>>
>> Cross-paradigm communication, like cross-disciplinary and cross-cultural
>> communication, can be difficult.?? Sometimes people do not even recognize the
>> existence of other paradigms, disciplines, cultures, long before it comes to
>> the question of their value.?? Readers of Peirce know he often uses important
>> words in more primordial senses than later came into fashion. Other times his
>> usage embodies a distinct analysis of the concept in question. More than once
>> I've found myself remarking how Peirce "anticipates" some strikingly "modern"
>> idea in logic, mathematics, or science, only to find its roots lay deep in
>> the history of thought.?? Whether he anticipates a future sense or preserves

joseph simpson

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Sep 18, 2019, 7:14:33 PM9/18/19
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Jon:

Interesting response and material. 

One of your referenced sections states:

"What strikes me about the initial installment this time around is its use of a certain pattern of argument that I can recognize as invoking a closure principle, and this is a figure of reasoning that Peirce uses in three other places: his discussion of continuous predicates, his definition of sign relations, and in the pragmatic maxim itself."

Due to the fact that you have a background in computer science and psychology, which kind of closure principle are you addressing?

Closure principle from psychology, closure principle from computer science or both?

Take care and have fun,

Joe




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Jon Awbrey

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Sep 19, 2019, 5:24:23 PM9/19/19
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Cf : The Difference That Makes A Difference That Peirce Makes : 22
At : http://inquiryintoinquiry.com/2019/09/19/the-difference-that-makes-a-difference-that-peirce-makes-22/

Re: Charles S. Peirce Society Facebook Page
At: https://www.facebook.com/groups/peircesociety/
Re: John Corcoran
At: https://www.facebook.com/groups/peircesociety/permalink/1688730107929641/
At: https://www.facebook.com/groups/peircesociety/permalink/1691535687649083/

A discussion -- well, more like a series of posts and counterposts --
arose on the Peirce Society Facebook Page last week, and I've been
going back over it this week because it seemed to invite a useful
re-examination of some old but important issues. There appears to
be some sort of disagreement, or maybe just failure to communicate,
but I'm still having trouble putting my finger on what the source
of the issue might be.

One factor seems to be different understandings of the relationship
between Peirce's brand of semiotics and standard first order logic.
One thing I've noticed before is that people who view Peirce's work
through the filter of first order logic are not likely to see what
many of us appreciate in his semiotic approach to logic. There are
commentators on Peirce's logical systems who treat them as nothing
more than first order logics in other syntaxes, but I am not one of
those. There is something more general and powerful going on with
Peirce's conception of "logic as formal semiotic", in other words,
a normative science of signs.

I still see that playing a role in the background of the animadversion
but I'm beginning to think there's probably a much simpler explanation.

Regards,

Jon

joseph simpson

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Sep 20, 2019, 6:34:36 PM9/20/19
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Jon:

As I work through the linked material, I find that there appears to be errors in Part 2 graphic displays when I use Firefox.

However, the errors are not present when I view the material using the Chrome browser.

This is just a note of information if anyone else has an issue reading the linked material.

The Boolean matrices are interesting, what software do you use to make these matrix calculations?

I use the Sage Math system for these types of Boolean matrix calculations, but I was wondering if there are other executable systems that preform the same type of operations.

My plan is to spin up an executable notebook and see if I can reproduce the presents material.

If I am successful, I will share the notebooks with the list.

Take care and have fun,

Joe
On Wed, Sep 18, 2019 at 1:44 PM Jon Awbrey <jaw...@att.net> wrote:
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Jon Awbrey

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Sep 21, 2019, 9:08:18 AM9/21/19
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Cf: The Difference That Makes A Difference That Peirce Makes : 23
At: https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/

Joe, All ...

A fundamental question in applications of mathematical logic is the threshold of
complexity between dyadic (binary) and triadic (ternary) relations, in particular,
whether 2-place relations are universally adequate or whether 3-place relations
are irreducible, minimally adequate, and even sufficient as a basis for all
higher dimensions.

One of Peirce's earliest arguments for the sufficiency of
triadic relative terms occurs at the top of his 1870
"Logic of Relatives".

Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1
Cf: At: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#Selection_1

<QUOTE>
The conjugative term involves the conception of "third", the relative that
of second or "other", the absolute term simply considers "an" object. No
fourth class of terms exists involving the conception of "fourth", because
when that of "third" is introduced, since it involves the conception of
bringing objects into relation, all higher numbers are given at once,
inasmuch as the conception of bringing objects into relation is independent
of the number of members of the relationship. Whether this "reason" for
the fact that there is no fourth class of terms fundamentally different
from the third is satisfactory or not, the fact itself is made perfectly
evident by the study of the logic of relatives. (Peirce, CP 3.63).
</QUOTE>

Peirce's argument invokes what is known as a "closure principle",
as I remarked in the following comment:

What strikes me about the initial installment this time around is
its use of a certain pattern of argument I can recognize as invoking
a "closure principle", and this is a figure of reasoning Peirce uses
in three other places: his discussion of "continuous predicates", his
definition of "sign relations", and in the "pragmatic maxim" itself.

* https://oeis.org/wiki/Continuous_predicate
* https://oeis.org/wiki/Sign_relation
* https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/

In mathematics, a "closure operator" is one whose repeated application
yields the same result as its first application.

If we take an arbitrary operator A, the result of applying A
to an operand x is Ax, the result of applying A again is AAx,
the result of applying A again is AAAx, and so on. In general,
it is perfectly possible each application yields a novel result,
distinct from all previous results.

But a closure operator C is defined by the property CC = C,
so nothing new results beyond the first application.

Regards,

Jon

joseph simpson

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Sep 22, 2019, 10:22:33 AM9/22/19
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Bob:

Interesting point of view. 

Jon wrote:

"What strikes me about the initial installment this time around is
its use of a certain pattern of argument I can recognize as invoking
a "closure principle","

It is still not clear to me what type of "closure principle."

The closure principle may be associated with the closure property of set theory (closed set operations) or

the closure principle may be associated with the concept of an idempotent executable operation.

An idempotent operation has the form f(f(x)) = f(x).

This form appears to be similar to the form provided by Jon:

"But a closure operator C is defined by the property CC = C,
so nothing new results beyond the first application."

Take care and have fun,

Joe


On Sun, Sep 22, 2019 at 5:14 AM Bob Kenley <ken...@purdue.edu> wrote:
I would not be surprised if someone has investigated the closure operator C using a variant of fixed point theory, which typically is stated using the operand rather than the operator as the fixed term in the relation, I.e., Ax=x for all x.

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Jon Awbrey

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Sep 22, 2019, 11:49:03 AM9/22/19
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Cf: The Difference That Makes A Difference That Peirce Makes : 24
At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/

The concepts of "closure" and "idempotence" are closely related.

We usually speak of a "closure operator" in contexts where the objects acted on are
the primary interest, as in topology, where the objects of interest are open sets,
boundaries, closed sets, etc. In contexts where we abstract away from the operand
space, as in algebra, we tend to say "idempotence" for the detached application
CC = C. (If I recall right, it was actually Charles Peirce's father Benjamin
who coined the term "idempotence".)

At any rate, I???ll have to mutate the principle a bit to cover the uses Peirce makes of it.

Regards,

Jon

joseph simpson

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Sep 23, 2019, 5:04:49 PM9/23/19
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Jon:

Thanks for the additional context.

I think we are closer to a common understanding of the terms use.

Also, it appears that Benjamin Peirce originated the term, idempotence.

Take care and have fun,

Joe


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Jon Awbrey

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Sep 25, 2019, 10:40:26 AM9/25/19
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Re: The Difference That Makes A Difference That Peirce Makes : 21
At: https://inquiryintoinquiry.com/2019/09/18/the-difference-that-makes-a-difference-that-peirce-makes-21/

Joe, John, All ...

I'm not seeing any errors from my Firefox, the only browser I use.

Cf: Peirce's 1870 Logic Of Relatives : Part 2
At: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_2

Is it a problem with the JPGs or the LaTeX generated images?
The JPGs were exported from LibreOffice Draw five years ago,
so I could try it again with a newer version of LibreOffice,
if that is where the problem lies.

At any rate, I serialized all this content to my blog a while back,
so folks could peruse that as an alternative. I'll post a link on
a separate thread.

Regards,

Jon

Jon Awbrey

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Oct 13, 2019, 10:05:57 AM10/13/19
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Cf: The Difference That Makes A Difference That Peirce Makes : 25
At: https://inquiryintoinquiry.com/2019/10/13/the-difference-that-makes-a-difference-that-peirce-makes-25/

I've been detecting something approaching a mini-zeitgeist lately.
Ideas and issues popping up in my recent discussions and readings
keep reminding me of themes I first encountered in Peirce's early
work, especially the Lectures on the Logic of Science (1865-1866)
and the 1870 Logic of Relatives. A number of Peirce's potentially
ground-breaking, paradigm-shifting ideas first saw the light of day
in these early ventures. I say "potentially" because what I regard
as his most revolutionary ideas never saw their full development in
Peirce's lifetime, only to arise again in the press of mathematical
and scientific advances later in the 20th Century.

Regards,

Jon

Jon Awbrey

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Oct 14, 2019, 1:10:35 PM10/14/19
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Cf : The Difference That Makes A Difference That Peirce Makes : 26
At : http://inquiryintoinquiry.com/2019/10/14/the-difference-that-makes-a-difference-that-peirce-makes-26/

Questions about Peirce's use of "formal" and "normative" in relation to logic
and semiotic have come up again on the Peirce List, but I have to run off to
another appointment, so for now I'll just post a link to a relevant previous
discussion.

* The Difference That Makes A Difference That Peirce Makes : 19
https://inquiryintoinquiry.com/2017/11/18/the-difference-that-makes-a-difference-that-peirce-makes-19/

In other recurring discussions, as far as my personal usage goes,
I've always suggested there is a place for descriptive semiotics,
whether of not that was Peirce's way of drawing the distinctions.

Regards,

Jon

Jon Awbrey

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Oct 15, 2019, 8:00:21 AM10/15/19
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Returning to the matter of form ...

Cf: The Difference That Makes A Difference That Peirce Makes : 27
At: https://inquiryintoinquiry.com/2019/10/14/the-difference-that-makes-a-difference-that-peirce-makes-27/

It's been my observation over many decades that people invoke
the "ethics of terminology" mainly to inveigh against everyone's
innovations but their own, so these days I've shifted more of my
attention to the "pragmatics of communication", the critical case
being communication across the boundaries and through the filters
of diverse communities of usage. In that spirit, I'll copy here
my last best attempt to devise a bridge between Peirce's special
sense of "formal" and the more generic brands we likely know.

Cf: Definition and Determination : 8
At: https://inquiryintoinquiry.com/2012/06/13/definition-and-determination-8/

<QUOTE>

The most general meaning of "formal" is "concerned with form",
but the Latin "forma" can mean "beauty" in addition to "form",
so perhaps a normative "goodness of form" enters at this root.

The Latin word "norma" literally means a "carpenter's square".
The Greek "gnomon" is a sundial pointer taking a similar form.
The most general meaning of "normative" is "having to do with
what a person ought to do", but a pragmatic interpretation of
ethical imperatives tends to treat that as "having to do with
what a person ought to do in order to achieve a given object",
so another formula might be "relating to the good that befits
a being of our kind, what must be done in order to bring that
good into being, and how to tell the signs that show the way".

Defining logic as formal or normative semiotic differentiates
logic from other species of semiotic under the general theory
of signs, leaving a niche open for descriptive semiotic, just
to mention the obvious branch. This brings us to the question:

How does a concern with form, or goodness of form, along with
the question of what is required to achieve an object, modify
our perspective on sign relations in a way that duly marks it
as a logical point of view?

</QUOTE>

Regards,

Jon

John F. Sowa

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Oct 15, 2019, 10:37:42 AM10/15/19
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Jon A, List,

I replaced the subject line with a very specific question.  That question is closely related to the question "How can we raise ethical children?"  The logical positivists destroyed philosophy by rejecting value judgments.  Carnap was the very intelligent, but emotionally stupid positivist whose most damning criticism of any mention of value judgments was "That's poetry!"  Wittgenstein refused to attend any meeting of the Vienna Circle if Carnap was present.  And I don't blame him.

Form alone cannot go beyond "is" to "ought".  It does not provide a basis for value judgments.  Beauty is the first of the emotional responses that provides a value judgement.  Beautiful actions are good.   Truth is both beautiful and good.

JA 1>  my last best attempt to devise a bridge between Peirce's special sense of "formal" and the more generic brands we likely know.

Peirce did not have a special sense of 'formal'.  His definition of formal logic was identical to De Morgan's, and he applied that term to the logic in Russell's 1903 book.  If you need more evidence, look at the 119 occurrences of 'formal logic' in CP.  As you examine them, note CP 1.672:  "the only hope of salvation lies in formal logic, which demonstrates in the clearest manner that reasoning itself testifies to its own ultimate subordination to sentiment."

That is the antithesis of Carnap:  Formal logic is the foundation for exact reasoning, but its goals must be determined by sentiment.   You can't derive "ought" from "is" by reason alone.  Poetry is essential.   So is music.  But the best poetry and the best music require elegant mathematical forms to elicit the most moving sentiments.

JA 2> How does a concern with form, or goodness of form, along with the question of what is required to achieve an object, modify our perspective on sign relations in a way that duly marks it as a logical point of view?

Form alone can't do that.  As Peirce said, form must be subordinate to sentiment.  But that leads to the next question:  How can we design our robots in a way that makes their formal reasoning subordinate to good, ethical sentiment?

Many good people haven't been very good at teaching their children to do that.  Is there any hope for designing our robots to do that?

John

John F. Sowa

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Oct 15, 2019, 10:57:31 AM10/15/19
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Jon A, List,

I replaced the subject line with a very specific question.

That question is closely related to the question "How can we raise ethical children?  he logical positivists destroyed philosophy by rejecting value judgments. Carnap was a very intelligent, but emotionally stupid positivist whose most damning criticism of any mention of value judgments was "That's poetry!"

Wittgenstein  refused to attend any meeting of the Vienna Circle if Carnap was present. An d I don't blame him.

Azamat Abdoullaev

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Oct 15, 2019, 11:11:02 AM10/15/19
to ontolog-forum
John wrote:
"Many good people haven't been very good at teaching their children to do that. Is there any hope for designing our robots to do that?"


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Jon Awbrey

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Oct 15, 2019, 12:08:15 PM10/15/19
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John,

I have another train of thought on the tracks,
so just the briefest observation before I get
back on board.

I think you are missing Peirce's deeper meanings
of ideas like Form (think Platonic Ideas and the
way Aristotle compounded Form and Matter). When
we come to Sentiment, by any other word, Feeling,
that is the medium of Aesthetics, which concerns
Beauty in no merely skin-deep sense but all that
embodies and manifests "the admirable in itself",
thus every form of life worth living. So Peirce
stands the normative science of Logic on grounds
within the pale of Ethics and fixes the sight of
Ethics on the prize Aesthetics picks to steer by.

Regards,

Jon

John F. Sowa

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Oct 15, 2019, 2:25:11 PM10/15/19
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Jon A, List,



Pure mathematics is the study of pure form (i.e., diagrammatic reasoning) without any admixture of emotion, sentiment, or value judgments about Beauty, Goodness. and Truth.  Boolean algebra computes the values 1 and 0.  But the assumption that 1 and 0 correspond to what we mean by truth and falsehood belongs to the *application* of Boolean algebra to an analysis of meaning (semiotic).

JA 1> I think you are missing Peirce's deeper meanings of ideas like Form (think Platonic Ideas and the way Aristotle compounded Form and Matter).

The Platonic forms are the purest of pure mathematics. Aristotle's theory of form and matter is an application of mathematics to physics. Plato's theory that the existence of the forms is prior to the physical combination is also an applied theory, but with different assumptions about the combination.

JA 2> Peirce stands the normative science of Logic on grounds within the pale of Ethics and fixes the sight of Ethics on the prize Aesthetics picks to steer by.

On this point, we are in complete agreement. For Peirce, formal logic is a branch of pure mathematics. And normative logic is the application of formal logic to semiotic, aesthetics, and ethics. See his 1903 classification of the sciences.

John

Jon Awbrey

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Oct 15, 2019, 4:16:21 PM10/15/19
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On 9/18/2019 4:20 AM, Jon Awbrey wrote:
> Cf: The Difference That Makes A Difference That Peirce Makes : 20
> At: https://inquiryintoinquiry.com/2019/09/17/the-difference-that-makes-a-difference-that-peirce-makes-20/
>
> Cross-paradigm communication, like cross-disciplinary and cross-cultural
> communication, can be difficult.?? Sometimes people do not even recognize the
> existence of other paradigms, disciplines, cultures, long before it comes to
> the question of their value.?? Readers of Peirce know he often uses important
> words in more primordial senses than later came into fashion.?? Other times his
> usage embodies a distinct analysis of the concept in question.?? More than once
> I've found myself remarking how Peirce "anticipates" some strikingly "modern"
> idea in logic, mathematics, or science, only to find its roots lay deep in
> the history of thought.?? Whether he anticipates a future sense or preserves
> an ancient sense is not always easy to answer.
>
> Regards,
>
> Jon
>

I had to go back a bit to remind myself why I restarted this thread,
but at least it supplies plenty of material for future study on the
difficulties of cross-paradigm communication.

At any rate, while I still have them in mind, I wanted to add to the record
a few exhibits on Peirce's definition of logic as "formal semiotic" and in
another place his description of logic as "semiotic, the quasi-necessary,
or formal, doctrine of signs".

Here's two variants of a paragraph where Peirce defines logic as "formal semiotic".

Selections from C.S. Peirce, "Carnegie Application" (1902)
==========================================================

Cf: C.S. Peirce : On the Definition of Logic
At: https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-%e2%80%a2-on-the-definition-of-logic/

<QUOTE>

No. 12. On the Definition of Logic

Logic will here be defined as formal semiotic. A definition
of a sign will be given which no more refers to human thought
than does the definition of a line as the place which a particle
occupies, part by part, during a lapse of time. Namely, a sign
is something, A, which brings something, B, its interpretant sign
determined or created by it, into the same sort of correspondence
with something, C, its object, as that in which itself stands to C.
It is from this definition, together with a definition of "formal",
that I deduce mathematically the principles of logic. I also make
a historical review of all the definitions and conceptions of logic,
and show, not merely that my definition is no novelty, but that my
non-psychological conception of logic has virtually been quite
generally held, though not generally recognized. (NEM 4, 20-21).

No. 12. On the Definition of Logic [Earlier Draft]

Logic is formal semiotic. A sign is something, A, which brings
something, B, its interpretant sign, determined or created by it,
into the same sort of correspondence (or a lower implied sort) with
something, C, its object, as that in which itself stands to C. This
definition no more involves any reference to human thought than does
the definition of a line as the place within which a particle lies
during a lapse of time. It is from this definition that I deduce the
principles of logic by mathematical reasoning, and by mathematical
reasoning that, I aver, will support criticism of Weierstrassian
severity, and that is perfectly evident. The word "formal" in
the definition is also defined. (NEM 4, 54).

</QUOTE>

Charles S. Peirce (1902), "Parts of Carnegie Application" (L 75), published in
Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce,
vol. 4, 13-73. http://www.iupui.edu/~arisbe/menu/library/bycsp/L75/l75.htm

Here's a passage where Peirce explains his sense of "formal" or "quasi-necessary".

Selection from C.S. Peirce, "Ground, Object, and Interpretant" (c. 1897)
========================================================================

Cf: C.S. Peirce : Logic as Semiotic
At: https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-%E2%80%A2-logic-as-semiotic/

<QUOTE>

Logic, in its general sense, is, as I believe I have shown,
only another name for semiotic (...), the quasi-necessary,
or formal, doctrine of signs. By describing the doctrine
as "quasi-necessary", or formal, I mean that we observe
the characters of such signs as we know, and from such an
observation, by a process which I will not object to naming
Abstraction, we are led to statements, eminently fallible,
and therefore in one sense by no means necessary, as to what
must be the characters of all signs used by a "scientific"
intelligence, that is to say, by an intelligence capable of
learning by experience. As to that process of abstraction,
it is itself a sort of observation.

The faculty which I call abstractive observation is one which
ordinary people perfectly recognize, but for which the theories
of philosophers sometimes hardly leave room. It is a familiar
experience to every human being to wish for something quite
beyond his present means, and to follow that wish by the question,
"Should I wish for that thing just the same, if I had ample means
to gratify it?" To answer that question, he searches his heart,
and in doing so makes what I term an abstractive observation.
He makes in his imagination a sort of skeleton diagram, or outline
sketch, of himself, considers what modifications the hypothetical
state of things would require to be made in that picture, and then
examines it, that is, observes what he has imagined, to see whether
the same ardent desire is there to be discerned. By such a process,
which is at bottom very much like mathematical reasoning, we can reach
conclusions as to what would be true of signs in all cases, so long as
the intelligence using them was scientific.

</QUOTE>

C.S. Peirce, Collected Papers, CP 2.227
From an unidentified fragment, c. 1897

Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1-6,
Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.),
Harvard University Press, Cambridge, MA, 1931-1935, 1958. Volume 2 :
Elements of Logic, 1932.

Nadin, Mihai

unread,
Oct 15, 2019, 4:27:25 PM10/15/19
to ontolo...@googlegroups.com
There is a bit more to Peirce:
The Logic of Vagueness and The Category of Synechism
https://academic.oup.com/monist/article-abstract/63/3/351/973996?redirectedFrom=fulltext

Mihai Nadin


-----Original Message-----
From: ontolo...@googlegroups.com <ontolo...@googlegroups.com> On Behalf Of Jon Awbrey
Sent: Tuesday, October 15, 2019 3:16 PM
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Subject: [ontolog-forum] Re: The Difference That Makes A Difference That Peirce Makes

On 9/18/2019 4:20 AM, Jon Awbrey wrote:
> Cf: The Difference That Makes A Difference That Peirce Makes : 20
> At:
> https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Finqu
> iryintoinquiry.com%2F2019%2F09%2F17%2Fthe-difference-that-makes-a-diff
> erence-that-peirce-makes-20%2F&amp;data=02%7C01%7Cnadin%40utdallas.edu
> %7C336633618ef04cb76fb708d751ac8b96%7C8d281d1d9c4d4bf7b16e032d15de9f6c
> %7C0%7C0%7C637067673837547838&amp;sdata=%2F7DpEnsBZhY3M5gacHweH%2BL2p3
> qG52uZKINRjKmXvUo%3D&amp;reserved=0
>
> Cross-paradigm communication, like cross-disciplinary and
> cross-cultural communication, can be difficult.?? Sometimes people do
> not even recognize the existence of other paradigms, disciplines,
> cultures, long before it comes to the question of their value.??
> Readers of Peirce know he often uses important words in more
> primordial senses than later came into fashion.?? Other times his
> usage embodies a distinct analysis of the concept in question.?? More than once I've found myself remarking how Peirce "anticipates" some strikingly "modern"
> idea in logic, mathematics, or science, only to find its roots lay
> deep in the history of thought.?? Whether he anticipates a future
> sense or preserves an ancient sense is not always easy to answer.
>
> Regards,
>
> Jon
>

I had to go back a bit to remind myself why I restarted this thread, but at least it supplies plenty of material for future study on the difficulties of cross-paradigm communication.

At any rate, while I still have them in mind, I wanted to add to the record a few exhibits on Peirce's definition of logic as "formal semiotic" and in another place his description of logic as "semiotic, the quasi-necessary, or formal, doctrine of signs".

Here's two variants of a paragraph where Peirce defines logic as "formal semiotic".

Selections from C.S. Peirce, "Carnegie Application" (1902) ==========================================================

Cf: C.S. Peirce : On the Definition of Logic
At: https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Finquiryintoinquiry.com%2F2012%2F06%2F01%2Fc-s-peirce-%25e2%2580%25a2-on-the-definition-of-logic%2F&amp;data=02%7C01%7Cnadin%40utdallas.edu%7C336633618ef04cb76fb708d751ac8b96%7C8d281d1d9c4d4bf7b16e032d15de9f6c%7C0%7C0%7C637067673837547838&amp;sdata=8kOfw2tZlRiOf1TjN%2B4omxBY84IBd%2F%2FFYHuZHA7DG8c%3D&amp;reserved=0

<QUOTE>

No. 12. On the Definition of Logic

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the same sort of correspondence with something, C, its object, as that in which itself stands to C.
It is from this definition, together with a definition of "formal", that I deduce mathematically the principles of logic. I also make a historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally recognized. (NEM 4, 20-21).

No. 12. On the Definition of Logic [Earlier Draft]

Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. The word "formal" in the definition is also defined. (NEM 4, 54).

</QUOTE>

Charles S. Peirce (1902), "Parts of Carnegie Application" (L 75), published in Carolyn Eisele (ed., 1976), The New Elements of Mathematics by Charles S. Peirce, vol. 4, 13-73. https://nam02.safelinks.protection.outlook.com/?url=http:%2F%2Fwww.iupui.edu%2F~arisbe%2Fmenu%2Flibrary%2Fbycsp%2FL75%2Fl75.htm&amp;data=02%7C01%7Cnadin%40utdallas.edu%7C336633618ef04cb76fb708d751ac8b96%7C8d281d1d9c4d4bf7b16e032d15de9f6c%7C0%7C0%7C637067673837547838&amp;sdata=vV1c20sF03YFTNQ2Les6EG980ZBiqFpXYBErDE8ysV4%3D&amp;reserved=0

Here's a passage where Peirce explains his sense of "formal" or "quasi-necessary".

Selection from C.S. Peirce, "Ground, Object, and Interpretant" (c. 1897) ========================================================================

Cf: C.S. Peirce : Logic as Semiotic
At: https://nam02.safelinks.protection.outlook.com/?url=https%3A%2F%2Finquiryintoinquiry.com%2F2012%2F06%2F04%2Fc-s-peirce-%25E2%2580%25A2-logic-as-semiotic%2F&amp;data=02%7C01%7Cnadin%40utdallas.edu%7C336633618ef04cb76fb708d751ac8b96%7C8d281d1d9c4d4bf7b16e032d15de9f6c%7C0%7C0%7C637067673837547838&amp;sdata=6aMylMIYVTHHXa0COwqToRNWtNyhTzn86EAJnUZeSNM%3D&amp;reserved=0

<QUOTE>

Logic, in its general sense, is, as I believe I have shown, only another name for semiotic (...), the quasi-necessary, or formal, doctrine of signs. By describing the doctrine as "quasi-necessary", or formal, I mean that we observe the characters of such signs as we know, and from such an observation, by a process which I will not object to naming Abstraction, we are led to statements, eminently fallible, and therefore in one sense by no means necessary, as to what must be the characters of all signs used by a "scientific"
intelligence, that is to say, by an intelligence capable of learning by experience. As to that process of abstraction, it is itself a sort of observation.

The faculty which I call abstractive observation is one which ordinary people perfectly recognize, but for which the theories of philosophers sometimes hardly leave room. It is a familiar experience to every human being to wish for something quite beyond his present means, and to follow that wish by the question, "Should I wish for that thing just the same, if I had ample means to gratify it?" To answer that question, he searches his heart, and in doing so makes what I term an abstractive observation.
He makes in his imagination a sort of skeleton diagram, or outline sketch, of himself, considers what modifications the hypothetical state of things would require to be made in that picture, and then examines it, that is, observes what he has imagined, to see whether the same ardent desire is there to be discerned. By such a process, which is at bottom very much like mathematical reasoning, we can reach conclusions as to what would be true of signs in all cases, so long as the intelligence using them was scientific.

</QUOTE>

C.S. Peirce, Collected Papers, CP 2.227
From an unidentified fragment, c. 1897

Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1-6, Charles Hartshorne and Paul Weiss (eds.), vols. 7-8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931-1935, 1958. Volume 2 :
Elements of Logic, 1932.

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Jon Awbrey

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Oct 16, 2019, 2:15:20 PM10/16/19
to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List
Dear Mihai,

Thanks for your paper, "The Logic of Vagueness and The Category of Synechism".
There is much subtlety there. In my applied life these days I'd be satisfied,
or at least satisficed, just to make my ideas clear about the applications of
triadic sign relations to simple logic, along with getting my programs up and
running far enough again to finally get plain vanilla propositional logic out
of first gear, where our chop-logic school books have kept it for many a year.

But fuzzy logic and fuzzy sets were something I explored way back during my
first foundational crisis when I was exploring all the alternatives I could
find to standard set theory. As I got to know Peirce's theory of relations
better I saw a way to understand fuzzy sets within the framework of certain
triadic relations. I think I posted some comments about that somewhere, so
I'll try to dig them up ...

Regards,

Jon

Jon Awbrey

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Oct 18, 2019, 10:45:19 AM10/18/19
to Helmut Raulien, Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List
Helmut, Mihai, All ...

Peirce's take on the twin topics of generality and vagueness
does bear a relationship to what I've been posting lately on
the Precursors of Category Theory and the Logic of Relatives,
so it may be worth the candle to throw better light on those
connections. Looks like it'll be next week before I can get
back to it, though. Meanwhile, here's a good entry point --

Peirce (CP 5.447)
https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Excerpt_5._Peirce_.28CP_5.447.29

<QUOTE>

Accurate writers have apparently made a distinction between
the definite and the determinate. A subject is determinate in
respect to any character which inheres in it or is (universally
and affirmatively) predicated of it, as well as in respect to
the negative of such character, these being the very same respect.
In all other respects it is indeterminate. The definite shall be
defined presently.

A sign (under which designation I place every kind of thought,
and not alone external signs), that is in any respect objectively
indeterminate (i.e., whose object is undetermined by the sign itself)
is objectively 'general' in so far as it extends to the interpreter
the privilege of carrying its determination further.

Example: "Man is mortal." To the question, What man? the reply is
that the proposition explicitly leaves it to you to apply its assertion
to what man or men you will.

A sign that is objectively indeterminate in any respect is objectively
vague in so far as it reserves further determination to be made in some
other conceivable sign, or at least does not appoint the interpreter as
its deputy in this office.

Example: "A man whom I could mention seems to be a little conceited."
The suggestion here is that the man in view is the person addressed;
but the utterer does not authorize such an interpretation or any other
application of what she says. She can still say, if she likes, that
she does not mean the person addressed.

Every utterance naturally leaves the right of further exposition
in the utterer; and therefore, in so far as a sign is indeterminate,
it is vague, unless it is expressly or by a well-understood convention
rendered general.

C.S. Peirce, Collected Papers, CP 5.447

</QUOTE>

On 10/16/2019 8:41 PM, Helmut Raulien wrote:
> Jon, Mihai, List,
> the unity of vagueness and continuum seems very reasonable to me. So vagueness
> is not (merely) a matter of inexact language, but of nature. Inexact language
> problems are not (always) vagueness, but instead e.g. ambiguity or misdenotation
> (so I understand the text). I guess, whether two elements are separated by a
> clear or fuzzy border depends on scales. Example: On a normal taxonomic scale,
> horse and donkey are two different species, because they cannot interbreed
> fertile offspring (in case this would be the definition for species). But on a
> smaller scale, maybe it is impossible to identify an exact time or a single
> genetic mutation, from which on the species have separated, and separation has
> been continuous, making it gradually more and more unlikely to interbreed
> fertile offspring. (?)
> To say, that scales are only a matter of observation however would lead back to
> language and representation, and away from naturalistic or realistic
> interpretation. To solve this problem, I guess that scale differences work
> together in nature, recreating a continuum even of discreteness: A single gene
> mutation is discrete, but for species separation, other influences on other
> scales may play a role too, such as epigenetics, culture, individual preference.
> Best,
> Helmut

Jon Awbrey

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Oct 19, 2019, 9:16:37 AM10/19/19
to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List
Cf: The Difference That Makes A Difference That Peirce Makes : 30
At: https://inquiryintoinquiry.com/2019/10/18/the-difference-that-makes-a-difference-that-peirce-makes-30/

Peirce on "General" & "Vague" ...

I added a remark by way of context and corrected a typo.
(See the linked blog post for a better formatted copy.)

***

I first encountered Peirce's dimensions of generality and vagueness --
two measures of determinacy on sign relations telling how well objects
are determined by signs and interpretant signs -- while exploring the
closely related subjects of definition and determination.

* https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Definition
* https://oeis.org/wiki/User:Jon_Awbrey/Peircean_Pragmata#Determination_2

Lately I've noticed Peirce's treatment of objectively indeterminate signs has
a bearing on my approach to Category Theory through the Logic of Relatives --

* https://inquiryintoinquiry.com/2015/05/15/survey-of-precursors-of-category-theory-%E2%80%A2-1/
* https://inquiryintoinquiry.com/2019/09/24/peirces-1870-logic-of-relatives-%e2%80%a2-overview/

so it looks worth paying attention to their potential relationships.
To get things rolling, here's a good entry point:
C.S. Peirce, Collected Papers, CP 5.447

</QUOTE>

Regards,

Jon

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
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Jon Awbrey

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Oct 21, 2019, 7:54:17 AM10/21/19
to Arisbe List, SysSciWG, Structural Modeling, Ontolog Forum, Laws Of Form Group, Cybernetic Communications, Peirce List
All,

One of the more disconcerting developments, I might even say "devolutions",
I've observed over the last 20 years has been the general slippage back to
absolutist and dyadic ways of thinking, all of it due to the stubborn pull
of unchecked reductionism, a failure to comprehend the relational paradigm,
especially triadic relations, their irreducibility, and its consequences.

With all that in mind, I'll return to a point in our earlier discussions,
add a bit more on the concept of closure, and continue from there to its
bearing on the pragmatic maxim.

> Cf: The Difference That Makes A Difference That Peirce Makes : 23
> At: https://inquiryintoinquiry.com/2019/09/20/the-difference-that-makes-a-difference-that-peirce-makes-23/
>
> A fundamental question in applications of mathematical logic
> is the threshold of complexity between dyadic (binary) and
> triadic (ternary) relations, in particular, whether 2-place
> relations are universally adequate or whether 3-place relations
> are irreducible, minimally adequate, and even sufficient as
> a basis for all higher dimensions.
>
> One of Peirce's earliest arguments for the sufficiency
> of triadic relative terms occurs at the top of his
> 1870 "Logic of Relatives".
>
> Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview
> Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1
> Cf: https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1#Selection_1
>
> <QUOTE>
>
> The conjugative term involves the conception of "third",
> the relative that of second or "other", the absolute term
> simply considers "an" object. No fourth class of terms exists
> involving the conception of "fourth", because when that of "third"
> is introduced, since it involves the conception of bringing objects
> into relation, all higher numbers are given at once, inasmuch as the
> conception of bringing objects into relation is independent of the
> number of members of the relationship. Whether this "reason" for the
> fact that there is no fourth class of terms fundamentally different
> from the third is satisfactory or not, the fact itself is made
> perfectly evident by the study of the logic of relatives.
> (Peirce, CP 3.63).
>
> </QUOTE>
>
> Peirce's argument invokes what is known as a "closure principle",
> as I remarked in the following comment:
>
> What strikes me about the initial installment this time around is
> its use of a certain pattern of argument I can recognize as invoking
> a "closure principle", and this is a figure of reasoning Peirce uses
> in three other places: his discussion of "continuous predicates", his
> definition of "sign relations", and in the "pragmatic maxim" itself.
>
> * https://oeis.org/wiki/Continuous_predicate
> * https://oeis.org/wiki/Sign_relation
> * https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/
>
> In mathematics, a "closure operator" is one whose repeated application
> yields the same result as its first application.
>
> If we take an arbitrary operator A, the result of applying A
> to an operand x is Ax, the result of applying A again is AAx,
> the result of applying A again is AAAx, and so on. In general,
> it is perfectly possible each application yields a novel result,
> distinct from all previous results.
>
> But a closure operator C is defined by the property CC = C,
> so nothing new results beyond the first application.
>

Cf: The Difference That Makes A Difference That Peirce Makes : 24
At: https://inquiryintoinquiry.com/2019/09/22/the-difference-that-makes-a-difference-that-peirce-makes-24/

The concepts of "closure" and "idempotence" are closely related.

We usually speak of a "closure operator" in contexts where the
objects acted on are the primary interest, as in topology, where
the objects of interest are open sets, boundaries, closed sets,
etc. In contexts where we abstract away from the operand space,
as in algebra, we tend to say "idempotence" for the detached
application CC = C. (If I recall right, it was actually Charles
Peirce's father Benjamin who coined the term "idempotence".)

At any rate, I'll have to mutate the principle a bit

Jon Awbrey

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Oct 27, 2019, 2:00:50 PM10/27/19
to Peirce List, SysSciWG, Structural Modeling, Ontolog Forum, Cybernetic Communications
Cf : The Difference That Makes A Difference That Peirce Makes : 32
At : http://inquiryintoinquiry.com/2019/10/27/the-difference-that-makes-a-difference-that-peirce-makes-32/

Re: FB | Foundations of Mathematics
At: https://www.facebook.com/groups/563574553770077/

Re: John Corcoran
At: https://www.facebook.com/groups/563574553770077/permalink/2383887155072132/ )

There was a huge -- and of course ultimately futile -- discussion
of truth theories back in 2005 when the Wikipediot article on Truth
was under development. Pragmatists of one stripe or another from
the Peirce List ventured in vain to explain the difference between
(1) "classical" correspondence theories, (2) consensus or "social"
theories, and (3) Peircean pragmatic -- I'm guessing what Tarski
meant by "utilitarian" -- theories of truth. I'll dig up some
links and forks when I get a chance.

Regards,

Jon

Jon Awbrey

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Oct 20, 2021, 11:20:26 AM (7 days ago) Oct 20
to Peirce List, Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG
Cf: The Difference That Makes A Difference That Peirce Makes • 33
https://inquiryintoinquiry.com/2021/10/20/the-difference-that-makes-a-difference-that-peirce-makes-33/

Re: Ontolog Forum
https://groups.google.com/g/ontolog-forum/c/IRa-uP9FUow
::: William Frank
https://groups.google.com/g/ontolog-forum/c/IRa-uP9FUow/m/4WiZr44hAgAJ

William Frank asked a question about propositional attitudes and presuppositions.

<QUOTE WF:>
Are there any formal languages, such as Common Logic,
that adequately represent statements about propositions —
statements from which, in natural reasoning, one can draw
conclusions about the elements of the embedded proposition?
</QUOTE>

Dear William,

Propositional attitudes and presuppositions were hot topics in the 80s —
scanning an old bib I see:

• Salmon, N.U., and Soames, S. (eds., 1988), Propositions and Attitudes,
Oxford University Press, New York, NY.

And everyone was reading:

• Barwise and Perry, Situations and Attitudes
https://web.stanford.edu/group/cslipublications/cslipublications/site/1575861933.shtml

But the roots of the problem go way back, and of course it can't be
rooted out till more people read and comprehend and apply Peirce's
theory of triadic sign relations.

At this point in time, however, the gravitational pull
of Russell's Planet and its inconstant satellite Quine
continue to weigh against any real progress being made.

But even Russell almost, barely, just not completely broke orbit
at one of those critical branch points of intellectual history —
it appears it was only Wittgenstein who pulled him back from the
brink of 3-adicity and back to the two-folds of dyadic relations.

I discussed all these issues in some detail in the
old Standard Upper Ontology (SUO) group and its kin.
Here's a few pertinent fragments I archived at my
current haunts:

• Russell's Theory Of Knowledge
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK._Russell.27s_Theory_Of_Knowledge

• Russell's Philosophy Of Logical Atomism
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA._Philosophy_Of_Logical_Atomism
• Note 25
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA._Note_25

Regards,

Jon
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