Inquiry Into Inquiry • Understanding

[Jon Awbrey]

Cf: Inquiry Into Inquiry • Understanding 1
http://inquiryintoinquiry.com/2022/07/26/inquiry-into-inquiry-understanding-1/

All,

Another passage from Russell further illustrates what I see as a critical
juncture in his thought. The graph-theoretic figure he uses in analyzing
a complex of logical relationships brings him to the edge of seeing the
limits of dyadic analysis — but he veers off and does not make the leap.
At any rate, that's how it looks from a perspective informed by Peirce.

Here's the first part of the passage.

Excerpt from Bertrand Russell • “Theory of Knowledge” (The 1913 Manuscript)
===========================================================================

<QUOTE BR:>

Part 2. Atomic Propositional Thought

Chapter 1. The Understanding of Propositions

(4). We come now to the last problem which has to be treated in
this chapter, namely: What is the logical structure of the fact
which consists in a given subject understanding a given proposition?
The structure of an understanding varies according to the proposition
understood. At present, we are only concerned with the understanding
of atomic propositions; the understanding of molecular propositions
will be dealt with in Part 3.

Let us again take the proposition “A and B are similar”.

It is plain, to begin with, that the complex “A and B being similar”,
even if it exists, does not enter in, for if it did, we could not
understand false propositions, because in their case there is no
such complex.

It is plain, also, from what has been said, that we cannot understand
the proposition unless we are acquainted with A and B and similarity
and the form “something and something have some relation”. Apart from
these four objects, there does not appear, so far as we can see, to be
any object with which we need be acquainted in order to understand the
proposition.

It seems to follow that these four objects, and these only, must be
united with the subject in one complex when the subject understands the
proposition. It cannot be any complex composed of them that enters in,
since they need not form any complex, and if they do, we need not be
acquainted with it. But they themselves must all enter in, since if
they did not, it would be at least theoretically possible to understand
the proposition without being acquainted with them.

In this argument, I appeal to the principle that, when we understand,
those objects with which we must be acquainted when we understand,
and those only, are object-constituents (i.e. constituents other than
understanding itself and the subject) of the understanding-complex.
(Russell, TOK, 116–117).

</QUOTE>

Reference
=========

Bertrand Russell, “Theory of Knowledge : The 1913 Manuscript”,
edited by Elizabeth Ramsden Eames in collaboration with
Kenneth Blackwell, Routledge, London, UK, 1992.
First published, George Allen and Unwin, 1984.

Resources
=========

Notes on Russell's “Theory of Knowledge” • Note 1
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK_1

Regards,

Jon

[John F Sowa]

Jon,

 

That's a good example where Bertie R. ran into a dyadic relation "A is similar to B", which cannot be fully understood without a third argument that explains in what way A is similar to B.

 

For example, if I say "Your dog is similar to my cat",  you or anybody else who happens to hear or read that claim might ask, "In what way?"

 

Possible answers:  (1) They're friendly with visitors.  (2) They're both black.  (3) They tend to bite anybody who pets them.  (3) They're playful. (4) They run and hide from visitors,

 

You have obviously read quite a bit of Peirce's writings.  For anybody else who might need a review, see http://jfsowa.com/pubs/signs.pdf.

 

John

 

---

From: "Jon Awbrey" <jaw...@att.net>

[Jon Awbrey]

Cf: Inquiry Into Inquiry • Understanding 2
http://inquiryintoinquiry.com/2022/07/28/inquiry-into-inquiry-understanding-2/

All,

We continue with the example Bertrand Russell uses to
illustrate his way of analyzing the following question.

“What is the logical structure of the fact which consists
in a given subject understanding a given proposition?”

Excerpt from Bertrand Russell • “Theory of Knowledge” (1913)

============================================================

<QUOTE BR:>

Part 2. Atomic Propositional Thought
Chapter 1. The Understanding of Propositions

(4). [cont.] It follows that, when a subject S understands
“A and B are similar”, “understanding” is the relating relation,
and the terms are S and A and B and “similarity” and R(x, y), where
R(x, y) stands for the form “something and something have some relation”.
Thus a first symbol for the complex will be

• U{S, A, B, similarity, R(x, y)} .

This symbol, however, by no means exhausts the analysis of the form of
the understanding-complex. There are many kinds of five-term complexes,
and we have to decide what the kind is.

It is obvious, in the first place, that S is related to the four other
terms in a way different from that in which any of the four other terms
are related to each other.

(It is to be observed that we can derive from our five-term complex
a complex having any smaller number of terms by replacing any one or
more of the terms by “something”. If S is replaced by “something”,
the resulting complex is of a different form from that which results
from replacing any other term by “something”. This explains what
is meant by saying that S enters in a different way from the other
constituents.)

It is obvious, in the second place, that R(x, y) enters in a different
way from the other three objects, and that “similarity” has a different
relation to R(x, y) from that which A and B have, while A and B have the
same relation to R(x, y). Also, because we are dealing with a proposition
asserting a symmetrical relation between A and B, A and B have each the same
relation to “similarity”, whereas, if we had been dealing with an asymmetrical
relation, they would have had different relations to it. Thus we are led to the
following map of our five-term complex.

[Display] Russell • Understanding (S, A, B, Similarity, Rxy)
https://inquiryintoinquiry.files.wordpress.com/2022/07/russell-e280a2-understanding-s-a-b-similarity-rxy.png

In this figure, one relation goes from S to the four objects; one relation
goes from R(x, y) to similarity, and another to A and B, while one relation
goes from similarity to A and B.

This figure, I hope, will help to make clearer the map of our five-term complex.
But to explain in detail the exact abstract meaning of the various items in the
figure would demand a lengthy formal logical discussion. Meanwhile the above
attempt must suffice, for the present, as an analysis of what is meant by
“understanding a proposition”. (Russell, TOK, 117–118).

</QUOTE>

Reference
=========

Bertrand Russell, “Theory of Knowledge : The 1913 Manuscript”,
edited by Elizabeth Ramsden Eames in collaboration with
Kenneth Blackwell, Routledge, London, UK, 1992.
First published, George Allen and Unwin, 1984.

Resources
=========

Notes on Russell's “Theory of Knowledge” • Note 2
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#RTOK_2

Regards,

Jon

[Jon Awbrey]

Cf: Inquiry Into Inquiry • Discussion 4
http://inquiryintoinquiry.com/2022/08/05/inquiry-into-inquiry-discussion-4/

Re: Inquiry Into Inquiry • Flashback
https://inquiryintoinquiry.com/2022/07/23/inquiry-into-inquiry-flash-back/
Re: FB Comment • Daniel Everett

Russell's Figure. Othello Believes Desdemona Loves Cassio
https://inquiryintoinquiry.files.wordpress.com/2022/07/o-believes-d-loves-c-1.0.png

<QUOTE DE:>
The most interesting aspect of such constructions from my perspective
is that embedding is unnecessary for the reading. In Piraha you can
get independent clauses expressing the same thing. Or even in English.
Othello believes something. That something is that Desdemona loves Cassio.
So the advantage of Peircean graphs (and later of Discourse Representation
Theory) is that the syntactic feature of embedding is not crucial. Just as
in larger discourse of multiple independent sentences.
</QUOTE>

All,

Russell asks, “How shall we describe the logical form of a belief?”
The question is a good onen, maybe too good, loaded with a surplus of
meanings for “logical form”. Read in the spectrum of interpretive lights
traditional schools of thought have brought to bear on it, “logical form”
hovers between the poles of objective form and syntactic form without ever
settling down. A more stable fix on its practical sense can be gained from
the standpoint staked out by Peirce on the basis of the pragmatic maxim
( https://inquiryintoinquiry.com/2008/08/07/pragmatic-maxim/ ), aiming at
objective structure and seeing syntactic structure as accessory to that aim.

To be continued …

Reference
=========

Bertrand Russell, “The Philosophy of Logical Atomism”, pp. 35–155
in The Philosophy of Logical Atomism, edited with an introduction by
David Pears, Open Court, La Salle, IL, 1985. First published 1918.

Resources
=========

Notes on Russell’s “Philosophy of Logical Atomism” • Note 25
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA
https://oeis.org/wiki/User:Jon_Awbrey/Philosophical_Notes#POLA_25

[Jon Awbrey]

Cf: Inquiry Into Inquiry • Discussion 5
http://inquiryintoinquiry.com/2022/08/11/nquiry-into-inquiry-discussion-5/

All,

A quick review of the highlights so far, and then I'll continue from
the standpoint I indicated last time. As you recall, Dan Everett
opened with the following problem.

<QUOTE DE:>
I am trying to represent two readings of the three juxtaposed sentences
in English. The first reading is that the judge and the jury both know
that Malcolm is guilty. The second is that the judge knows that the
jury thinks that Malcolm is guilty.

Figure 1. The judge and the jury both know that Malcolm is guilty
https://inquiryintoinquiry.files.wordpress.com/2022/07/daniel-everett-e280a2-judge-jury-malcolm-guilty-graph-1.png&h=233

Figure 2. The judge knows that the jury thinks that Malcolm is guilty
https://inquiryintoinquiry.files.wordpress.com/2022/07/daniel-everett-e280a2-judge-jury-malcolm-guilty-graph-2.png&h=117

Do these purported EGs of mine seem correct to you?
</QUOTE>

Dan's initial question about logical graphs sent me further down memory lane
than I usually go, to my first encounters with extensions vs. intensions in
logic, intentional contexts, propositional attitudes, referential opacity,
truth-functionality, and triadicity, puzzles about which my first logic prof
sent me off to read Quine's “Ways of Paradox” and a host of others.

I had been studying Peirce on my own through all my undergrad years
and was fortunate at long last to find an advisor who was a fund of
knowledge about Peirce and Pragmatism, not to mention the Ancients
and philosophy in general. In several of our discussions from those
days I can remember expressing my hunch the problems of intentionality
were not due to a distinct modality or quality of propositions but
a different quantity or dimension of relations. I did not get to
Russell's monographs of 1918 and 1913 until much later but when
I did I was struck immediately by his use of graphs to represent
relations, so like Peirce's graphs for the logic of relatives.

Figure 3. Othello Believes Desdemona Loves Cassio
https://inquiryintoinquiry.files.wordpress.com/2022/07/o-believes-d-loves-c-1.0.png

To be continued …

Regards,

Jon