Relations & Their Relatives • Discussion

[Jon Awbrey]

Relations & Their Relatives • Discussion 24
• https://inquiryintoinquiry.com/2024/07/28/relations-their-relatives-discussion-24/

Re: Daniel Everett • June 20, 2024
•
https://www.facebook.com/permalink.php?story_fbid=pfbid02oCRz4EYHAtbrJeAzzoAaRS6yu48GTo9HddLxaQmyrhSDCDbxuR57TpwBLLNyrvZZl&id=100093271525294

Daniel Everett remarks:

❝Among the several ideas Peirce and Frege came up with was the idea
of a predicate before and after it is linked to its arguments. Frege
called the unlinked predicate unsaturated. But Peirce built this into
a theory of valency. An unsaturated predicate in Frege's system is a
generic term, a rheme, in Peirce's system. So in Peirce's theory all
languages need generic terms (rhemes) to exist. Additionally, through
his reduction thesis (a theorem proved separately by various logicians)
Peirce set both the upper and lower bounds on valency which — even to
this day — no other theory has done.❞

Dear Daniel,

In using words like “predicate” or “relation” some people mean an item of
syntax, say, a verbal form with blanks substituted for a number of subject
terms, and other people mean a mathematical object, say, a function f from
a set X to a set B = {0, 1} or a subset L of a cartesian product X₁ × … × Xₖ.

It would be a great service to understanding if we had a way to negotiate
the gap between the above two interpretations.

To be continued …

Resources —

Relation Theory
• https://oeis.org/wiki/Relation_theory

Survey of Relation Theory
• https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-8/

Regards,

Jon

cc: https://www.academia.edu/community/lzAqAe

[Jon Awbrey]

Relations & Their Relatives • Discussion 25
• https://inquiryintoinquiry.com/2024/07/30/relations-their-relatives-discussion-25/

Re: Relations & Their Relatives • Discussion 24
• https://inquiryintoinquiry.com/2024/07/28/relations-their-relatives-discussion-24/

Dear Daniel,

I've been meaning to get back to this as it keeps coming up and
it's kind of important but it took me a while to find the thread
again. Just by way of jumping in and hitting the ground running
I found a record of a previous discussion from the heydays and
fraydays of the old Peirce List — I'll plunder that for what it's
worth and see if I can render the main ideas any clearer this time
around.

Cf: The Difference That Makes A Difference That Peirce Makes • 9
• https://inquiryintoinquiry.com/2017/06/13/the-difference-that-makes-a-difference-that-peirce-makes-9/

Re: Peirce List | Rheme and Reason • Jon Awbrey • Gary Fuhrman • John Sowa
• https://list.iupui.edu/sympa/arc/peirce-l/2017-06/thrd2.html#00036

The just-so-story that relative terms got their meanings by blanking out
pieces of clauses and phrases, plus the analogies to poly-unsaturated
chemical bonds, supply a stock of engaging ways to introduce the logic
of relative terms and the mathematics of relations but they both run
into cul-de-sacs when taken too literally, and for the same reason.
They tempt one to confuse the syntactic accidents used to suggest
formal objects with the essential forms of the objects themselves.
That is the sort of confusion that leads to syntacticism and on
to its kindred nominalism.

Here's a short note I wrote the last time questions about
rhemes or rhemata came up.

I wanted to check out some impressions I formed many years ago —
this would have been the late 1960s and mainly from CP 3 and 4 —
about Peirce's use of the words rhema, rheme, rhemata, etc.

Rhema, Rheme —

• CP 2.95, 250-265, 272, 317, 322, 379, 409n
• CP 3.420-422, 465, 636
• CP 4.327, 354, 395n, 403, 404, 411, 438, 439, 441,
446, 453, 461, 465, 470, 474, 504, 538n, 560, 621

Reviewing the variations and vacillations in Peirce's usage
over the years, I've decided to avoid the whole complex of
rhematic terms for now. As I've come to realize more and
more in recent years, analyzing and classifying signs as
a substitute for analyzing and classifying objects is the
first slip of a slide into nominalism, in effect, thinking
the essence or reality of objects is contained in the signs
we use to describe them.

Resources —

Logic Syllabus • Relational Concepts
• https://oeis.org/wiki/Logic_Syllabus#Relational_concepts

Relation Theory
• https://oeis.org/wiki/Relation_theory

Relative Term
• https://oeis.org/wiki/Relative_term

Survey of Relation Theory
• https://inquiryintoinquiry.com/2024/03/23/survey-of-relation-theory-8/

Regards,

Jon

cc: https://www.academia.edu/community/LpDGve