John Corcoran corcoran at buffalo.edu
Sat Oct 28 15:10:56 EDT 2006

QUOTE OF THE MONTH:  LEIBNIZ ON CERTITUDE: People have known something
of the road leading to certitude: the logic of Aristotle and the Stoics
is proof of it, but above all is the example set by the mathematicians.
– Leibniz 1685.

Friday, November 3, 2006	4:00-6:00 P.M.	141 Park Hall
SPEAKER: Kevin Tracy, Classics, Washington and Lee University.
COMMENTATOR: David Hitchcock, Philosophy, McMaster University.

TITLE: Rationales for the Five Stoic Rules.
ABSTRACT: The five rules of Chrysippus’ undemonstrated syllogisms
(anapodeiktoi sullogismoi), like the four rules of the first-figure
syllogisms of Prior Analytics, can be cast either as sentential rules or
as argumental rules (Corcoran 1974, “Remarks on Stoic Deduction”;
Bobzien 1996, “Stoic Syllogistic”). In his 1953 book Stoic Logic, Mates
presents the text evidence for these rules in a handy table. No matter
which way they are cast, when compared with modern deduction systems for
propositional logic, the five appear to be entirely arbitrary.
Scholarship on Stoic logic has sought ways to account for them.  One
suggestion is that the system was designed to allow derivations only for
certain kinds of arguments in propositional logic (Bobzien, “Stoic
Syllogistic”; Hitchcock 2005, “The Peculiarities of Stoic Propositional
Logic”). I will present an alternative rationale which indicates that
the system was designed to produce derivations for categorical
arguments. If this rationale is correct, our present understanding of
the system must be emended: scholars generally assume that the Stoic
system did not extend beyond the bounds of propositional logic into
categorical logic. I will also briefly discuss a possible Stoic claim of
“completeness” for their system in light of the suggestions I have made
concerning the five rules.
Bobzien, Suzanne.  “Stoic Syllogistic.” Oxford Studies in Ancient
Philosophy. 14 (1996): 133-92.
Corcoran, John.  “Remarks on Stoic Deduction.” in Corcoran, ed.  Ancient
Logic and its Modern Interpretations. Dordrecht: D. Reidel, 1974.
Hitchcock, David. "The peculiarities of Stoic propositional logic". In
Kent A. Peacock and Andrew D. Irvine (eds.), Mistakes of Reason: Essays
in Honour of John Woods (Toronto/ Buffalo/ London: U of Toronto Press,
2005), 224-242.
http://www.humanities.mcmaster.ca/~hitchckd/peculiarities.pdf .
Mates, Benson. Stoic Logic. Berkeley: U of California Press, 1953.

Dutch treat supper follows.
Seguirà una cena alla romana.

Friday, November 10, 2006	4:00-6:00 P.M.	141 Park Hall

SPEAKER: Daniel Merrill, Philosophy, Oberlin College.
COMMENTATOR: John Corcoran, Philosophy, University of Buffalo.

TITLE: De Morgan’s Ways of Construing the Syllogism.

ABSTRACT: Augustus De Morgan's logical work seems to have been
constrained by a fixation on tinkering with the traditional syllogism.
Nevertheless, he introduced three logical innovations which go far
beyond the syllogism. What is notable is that the syllogism emerges as a
special case of each approach and that each ends up construing the
syllogism in a different way. The three innovations are: the logic of
complex terms (Boolean algebra), the numerically definite syllogism, and
the logic of relations. All are found in his FORMAL LOGIC (1847), though
the logic of relations is only developed fully later on. This talk will
outline the innovations, and discuss critically the ways in which De
Morgan embeds the traditional syllogism within them.

Dutch treat supper follows.

Future Speakers: George Boger (Canisius College), William Demopoulos
(University of Western Ontario and UC-Irvine), William Rapaport
(University of Buffalo), José Miguel Sagüillo (University of Santiago de
Compostella), Stewart Shapiro (Ohio State University), Barry Smith
(University of Buffalo).
Sponsors: Some meetings of the Buffalo Logic Colloquium are sponsored in
part by the C. S. Peirce Professorship in American Philosophy and by
other institutions.

All are welcome.
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