John, List:
JFS: I have no idea how Peirce would respond to your note ... Nobody knows
what Peirce would say.
I sincerely appreciate this acknowledgment. For me, it usually goes
without saying that we are expressing our own opinions here, including our
peculiar interpretations of Peirce's writings. We can and should provide
verbatim quotations to substantiate such views, but it would be needlessly
cumbersome to abstain completely from offering abbreviated summaries and
paraphrases. I find Lane's book to be an excellent example of maintaining
the proper balance, and will continue striving to do likewise.
JAS: As helpfully diagrammed by Existential Graphs, every assertion is the
attribution of general concepts (Spots) by means of continuous predicates
(Pegs) to indefinite individuals (Lines of Identity).
JFS: Anybody who had translated Peirce's EGs to and from his algebra of
1885 would not write the above sentence. Any feature of either notation
that is lost in translation is a syntactic item that has no semantic
meaning.
There is nothing "lost in translation" here, since syntax necessarily
conveys part of the meaning in both cases. In modern notation, every
proposition is likewise the attribution of general concepts (capital
letters) by means of continuous predicates (sequence of letters) to
indefinite individuals (lowercase letters).
As I have pointed out before, Peirce gave "Cain killed Abel" as an example
of a sentence in which all of the words are subjects, such that the syntax
alone embodies the continuous predicate ("_____ stands in the relation of
_____ to _____") in accordance with "the flow of causation" (R 664:9-13;
1910 Nov 26-27). The corresponding EG (Cain---killing---Abel) can be
analyzed as having five subjects--three general concepts, two indefinite
individuals--and the same is true of the corresponding modern expression
(Ǝx)(Ǝy)(Cx ∧ Ay ∧ Kxy). In addition, the surface on which the EG is
scribed represents the relation of *coexistence*, which appears in the
modern expression as the connectives.
"Cx" and "Ay" are usually translated as "x is Cain" and "y is Abel,"
respectively; but further analysis of the copula yields "x possesses the
identity of Cain" and "y possesses the identity of Abel." These both
denote what Lane calls *concrete* individuals, which "can be but in one
place at one time," as distinguished from *strict* individuals, which are
"absolutely determinate in all respects" (CP 5.299; 1868 and cf. CP 3.93;
1870). In other words, concrete individuals are *indeterminate*, and
therefore *general*, to some degree--which is why there is always room to
attach even more Spots to any Line of Identity. "Kxy" is usually
translated as "x kills y," but further analysis of the *discrete* predicate
yields another subject (general concept) and a *continuous* predicate--"x
stands in the relation of killing to y."
JFS: As I had pointed out, you took the word 'proper' out of context in a
single passage. There he was talking about what was proper for just one
step in a syllogism.
I strongly disagree with your narrow interpretation of that passage (NEM
3:885-886; 1908 Dec 5), but it is not *necessary* for my purposes to insist
that throwing everything possible into the subject is "the proper way in
logic." It is *sufficient *simply to recognize that "A proposition can be
separated into a predicate and subjects in more ways than one," and this is
one of the valid ways to do so. In fact, Peirce wrote a few days later
that "when we have carried analysis so far as to leave only a continuous
predicate, we have carried it to its ultimate elements" (SS 72; 1908 Dec
14). That is how an English sentence with only *three* words can be
analyzed as having *five* logical subjects. Such flexibility is due to the
fact that *definite* propositions--as well as their constituent subjects
and predicates--are artificial "creations of thought" (cf. NEM 3:917-918;
1904 Nov 21) that we invent for the purpose of describing the *continuous*
inferential process of semeiosis (cf. R 295:117-118[102-103]; 1906).
JFS: You have never found, and I'm sure that you never will find any
example where he showed a larger EG with all its polyadic relations
eliminated.
Of course not; why would I even bother looking for such an example? The
point is not to *eliminate* polyadic relations, but rather to analyze them
more thoroughly. It is not a matter of how we *scribe* EGs--remember, I
eventually realized that it was not necessary to propose any such
adjustments--but of how we *interpret* them.
JFS: Logicians have discovered a wide range of methods that go far beyond
anything that was known in Peirce's day. The method you suggested is not
one of them.
Indeed, it seems to have been almost completely overlooked in the interim,
which is one reason why I am so interested in exploring it. After all, one
of Peirce's stated purposes for EGs was to represent propositions "as
analytically as possible" (CP 4.561n; 1908, recalling CP 4.533; 1906).
JFS: A 20th century logician would say that Peirce was talking about two
different ways of being indefinite: by the referent of a quantifier or by
the modality of a predicate. Modern logicians don't apply the word 'vague'
to either method.
That is presumably the basis for Lane's comment that Peirce's "idea of
vagueness is quite different from the contemporary one" (p. 139), hence my
suggestion that we consider using "indefinite" for Peirce's conception
instead. It strikes me as an important insight on his part that although
continuity itself is *generality* (3ns), the parts of a true continuum are
*indefinite* (1ns) unless and until they are "marked off" (R S30 [Copy
T:6-7]; c. 1906), which is what makes them *actual* (2ns)--i.e., both
individual and definite.
Regards,
Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt
On Mon, Jul 22, 2019 at 10:04 PM John F Sowa <s...@bestweb.net> wrote:
> Jon,
>
> At the age of 12, Peirce acquired a knowledge of logic at the level
> of a freshman at Harvard. Over the next 60 years, he developed
> ideas that are at the forefront of today's research in logic,
> artificial intelligence, and cognitive science. Please read
> the article "Peirce's contributions to the 21st century":
> http://jfsowa.com/pubs/csp21st.pdf
>
> > JFS: Since Peirce is no longer with us, somebody has to pick the nits.
> >
> > JAS: No, since Peirce is no longer with us, /no one/ can presume
> > to speak for him; at least, that is what you have been persistently
> > maintaining.
>
> I have no idea how Peirce would respond to your note. The question
> I'm addressing is what Peirce's ideas mean for us: How are they
> related to ongoing research in logic and cognitive science?
>
> > JAS: As helpfully diagrammed by Existential Graphs, every assertion
> > is the attribution of general concepts (Spots) by means of continuous
> > predicates (Pegs) to indefinite individuals (Lines of Identity).
> >
> > JFS: Peirce would not agree with Jon's sentence above.
> >
> > JAS: There you go again.
>
> I'll rephrase my point: Anybody who had translated Peirce's EGs
> to and from his algebra of 1885 would not write the above sentence.
> Any feature of either notation that is lost in translation is a
> syntactic item that has no semantic meaning.
>
> JAS
> > Every EG asserts a proposition, claiming it to be true in the
> > Universe of Discourse, and thus is accurately characterized as
> > an assertion. That is why Peirce called the surface on which EGs
> > are scribed the "Sheet of Assertion," not the "Sheet of Proposition."
>
> No. As early as 1898 (RLT, p. 151) Peirce showed how to use EGs
> without asserting them. The idea is as old as Aristotle, and
> Ockham developed it in detail. Peirce studied both, lectured on
> both, and incorporated the distinction in his logics.
>
> Clarence Irving Lewis and Arthur Prior are two 20th. c logicians
> who learned that idea from Peirce and incorporated it in their
> versions of logic. I discuss their innovations in the article
> http://jfsowa.com/pubs/5qelogic.pdf
>
> JAS
> > I do [use the word 'spot'] and I suspect that there are other
> > Peirce scholars who do.
>
> When you're doing textual criticism, it's essential to be precise
> about the exact words of the MSS. But when you're trying to reach
> a 21st c audience, it's essential to use current terminology.
>
> I've attended Peirce sessions at various APA meetings, and it's
> frustrating to see Peirce's magnificent vision isolated from
> the broader field. I also attended other APA sessions, where
> professional philosophers are making mistakes that Peirce had
> criticized and moved beyond.
>
> > JFS: He never said nor implied that a peg is a continuous predicate.
> >
> > JAS: Indeed, and I have never claimed that he did; rather, it is
> > my own interpretation of EGs in accordance with Peirce's late 1908
> > analysis of propositions that throws everything possible into the
> > subject.
>
> As I had pointed out, you took the word 'proper' out of context in
> a single passage. There he was talking about what was proper for
> just one step in a syllogism. You have never found, and I'm sure
> that you never will find any example where he showed a larger EG
> with all its polyadic relations eliminated.
>
> This is another reason why it's important to look at developments
> in logic during the 20th and 21st c. Logicians have discovered
> a wide range of methods that go far beyond anything that was known
> in Peirce's day. The method you suggested is not one of them.
>
> > JFS: The sentence "A cat is on a mat" is indefinite about the
> > referents of the two subjects, but neither Peirce nor any modern
> > logician would say that it's vague.
> >
> > JAS: Lane's (and Peirce's) point is that "a cat" is indefinite/vague,
> > such that the principle of contradiction does not apply, because both
> > "a cat is black" and "a cat is not-black" might be (and, in fact, are)
> > true; likewise for "a mat."
>
> Your previous example was about the existential quantifier, which
> is indefinite about its referent. This point is about predicates
> without attached indexes. They are indefinite about what might or
> might not be. That is a way of being indefinite because of modality.
>
> A 20th century logician would say that Peirce was talking about
> two different ways of being indefinite: by the referent of a
> quantifier or by the modality of a predicate. Modern logicians
> don't apply the word 'vague' to either method.
>
> In summary, I'm talking about the way a modern logician would
> interpret these issues. Nobody knows what Peirce would say.
>
> John
>
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