Pat H and Chris P, (01)
(This thread had no subject line, so I added the one above.) (02)
Among modern logicians, there are two attitudes toward the
tradition from Aristotle to the 19th century: (03)
1. The Frege-Russell view that mathematical logic is a total
break with the past and nothing useful can be learned
from the old dusty tomes. (04)
2. The view espoused by many modern logicians (including
Peirce, Whitehead, Lukasiewicz, Tarski, and others) that
modern logic is an extension and formalization of ideas
that had been developed in detail by many dozens of
brilliant logicians over a period of two millennia. (05)
PH> And aren't we, in this forum, talking about logics (in a
> broad sense, ie formalisms for description) and KR, rather
> than statistics or metaphysics? (06)
The study of ontology is usually considered a subset of and
sometimes nearly identical to metaphysics, and logic is quite
capable of representing any kind of mathematical statement,
including statistical statements. (07)
CP> I think John was espousing in an earlier set of emails (in
> relation to Aristotelian syllogisms), which is that logic is
> a formalism for describing the way the world is – or more
> grandly, what exists. And that in some way the form of the
> logic reflects the structure/nature of the world. (08)
I didn't claim that logic reflects the structure of the world,
but that logic in combination with an ontology can be used to
describe someone's conception of the structure of the world. (09)
I think that many descriptions are fairly accurate for limited
domains, but I don't believe that any known unified attempt is
adequate to capture the full structure. (010)
CP> A colleague pointed out to me something you may be familiar
> with, "ARISTOTLE'S LOGIC: A COMPARISON OF LUKASIEWICZ'S AND
> CORCORAN-SMILEY'S RECONSTRUCTIONS". (011)
Thanks for that reference. See the excerpt copied below. (012)
For the record, Lukasiewicz is the logician who developed Polish
notation. (It's called "Polish notation" because people had
trouble spelling or pronouncing 'Lukasiewicz'.) (013)
And John Corcoran is the editor of Tarski's collected papers.
In his famous paper that introduced model theory, Tarski said
that his approach was a formalization of Aristotle's theory
of correspondence. (014)
The following excerpt illustrates how a study of the tradition
can clarify contemporary debates, including those in this forum.
For the record, I prefer the view of "formal epistemology" as
described by Corcoran and Smiley. (015)
John Sowa
__________________________________________________________________ (016)
http://www.nfillion.com/images/stories/docs/aristotelian-logic.pdf (017)
From the concluding section, p. 33: (018)
It has long been noticed that there are two qualitatively
distinct traditions in contemporary logic. In his famous paper,
van Heijenoort (1967) calls them “logic as calculus” and “logic
as language”. Shapiro (2005) calls the former “the algebraic
perspective”, while Hintikka (1997) calls the latter “logic as
universal medium”. Peckhaus (2004) calls them, respectively,
“logic as lingua characterica” and “logic as calculus rationcinator”,
after Leibniz famous distinction. However, I think Corcoran (1994)
makes the most precise characterization of the two traditions, by
calling them, respectively, “formal ontology” and “formal epistemology”. (019)
If both groups of logicians call themselves “formal logicians”, it
should be emphasized that it is for very different reasons. The
formal ontologists justify their use of the adjective ‘formal’ by
the contention that the propositions they deal with are expressed
“exclusively in general logical terms, without the use of names
denoting particular objects, particular properties, etc.” (Corcoran,
1994, p. 19) This point appears to be Lukasiewicz’s real motivation
for the claim that concrete terms do not pertain to logic. On the
other hand, the formal epistemologists justify their use of the
adjective ‘formal’ by the contention that they deal not with the
content of the scientific discourse, but with its form... (020)
The question that seems to animate the debate between the proponents
of the Lukasiewiczian view and the Corcoran-Smiley view concerns where
Aristotle stands. If Lukasiewicz is right to claim that Aristotle’s
logic is a formal ontology, then we can take Aristotle to be presenting
a system of propositions organized deductively. On the other hand,
if Corcoran and Smiley are right, then we can take Aristotle to be
presenting a system of deductions, organized epistemically... (021)
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