ONT Re: Effective Logical Formalism
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ELF. Discussion Note 5
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JA = Jon Awbrey
JS = John Sowa
John,
As interesting as this is to me, I really am trying
to stay focussed on Murray's request to read through
the LBase document in a comparative light, the chain
of relevance in command being: LBase -> S/CL -> SUO,
as I have been given to understand. However, as late
as he stays up during the week, I can see that Murray
is no weekend warrior, which tells me that he retains
far more sanity than all the rest of us put together,
and so I am tempted to follow his, Galadriel's, and
Voltaire's lead in this matter, to diminish and go
into the West, and to cultivate my own garden.
Mulch!
Back Tomorrow, But Don't Bet On It,
Jon Awbrey
P.S. By the by, there were some questions that you
left unanswered about the S/CL reading of relations:
http://suo.ieee.org/email/msg11301.html
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JS: Actually, Peirce was continuing the tradition from
Aristotle to the scholastics to Boole to Tarski
to today's model-theoretic proponents.
JA: At any rate, it wasn't blame so much I had in mind,
but a very fuzzy memory from a long time ago that
this is one of those curious things that Peirce
had in common with Frege.
JS: Not really. Frege made a major break with the
tradition with his claim that truth was too vague
a notion to serve as the foundation for logic.
Following is a quotation from 'Der Gedanke' (1918):
GF: But could we not maintain that there is truth
when there is a correspondence in a certain
respect? But in what respect? For in that case
what ought we do to do so as to decide whether
something is true? We should have to inquire
whether it is _true_ that an idea and reality,
say, correspond in the specified respect.
And then we would be confronted by a question
of the same kind, and the game could begin again.
So it seems likely that the content of the word
'true' is _sui generis_ and indefinable.
JS: Frege denounced Husserl's "psychologism", but he
was guilty of the same sins himself. From his
1879 'Begriffsschrift' to his 1918 'Gedanke',
Frege kept mixing psychological notions with
his discussions of the foundations of logic.
JS: In that respect, Frege was more guilty of psychologism
than the medieval scholastics, who introduced the word
"proposition" as a formal notion that was independent
of the mind. But Frege was skating on thin ice by using
the word Gedanke. He should have adopted the scholastic
term to make a clear distinction.
JS: By contrast, following is a quotation from Peirce, MS 75, 1902:
CSP: I define a sign as something, A, which brings something, B,
its interpretant, into the same sort of correspondence with
something, C, its object, as that in which itself stands to C.
In this definition I make no more reference to anything like
the human mind than I do when I define a line as the place
within which a particle lies during a lapse of time.
JS: Note that Frege (1918) was still struggling with the notion of
correspondence and getting mired in an endless regress. Peirce
had long ago analyzed that notion and come to the conclusion that
there are an open-ended number of possible correspondences. He
emphasized the point that "symbols grow" -- the number and kinds
of correspondences can change. But Frege was terrified by that
idea. He wanted to freeze the meaning of his symbols for all
time. Carnap and the Vienna circlers pushed that goal to an
extreme in logical positivism.
JS: When Tarski introduced his model theory in the 1930s, he had
to fight an uphill battle against Carnap, one of Frege's very
few students, to get his truth-based approach accepted. Peirce
and Tarski were working in the same tradition (and by the way,
Tarski used Peirce's notation for his early publications, and
Polish logic still uses Peirce's Pi and Sigma notation for
the quantifiers).
JS: Carnap was Quine's mentor and close friend for many years,
and neither Quine nor Carnap ever did any serious work
with model theory. They never mentioned it in their
publications, except for a few criticicms by Quine.
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