John Corcoran corcoran at buffalo.edu
Tue Sep 19 09:07:41 EDT 2006

denied that the laws established by induction are not enough. New
propositions must be derived from them which are not contained in any
one of them by itself. No doubt these propositions are in a way
contained covertly in the whole set taken together, but this does not
absolve us from the labour of actually extracting them and setting them
out in their own right. – Frege 1884 §17.

Program note: The ancient Greek thinkers produced two very different
logics. The Peripatetic “Categorical Syllogistic” due to Aristotle has
been compared to Boole’s Class Logic, which it is known to have
inspired. The Stoic “Hypothetical Logic” due to Chrysippus has been
compared to Boole’s Propositional Logic, which it might have inspired
indirectly. Modern propositional logic was established after being
introduced by Boole (in 1847 and 1854) and completely axiomatized by
Frege in 1879.  In the 1920s Lukasiewicz, the great Polish logician,
Tarski’s teacher, “discovered” that ancient Stoic logic was the world’s
first try at solving the problems now thought to be solved by modern
propositional logic. After years of uncritical acceptance, in the 1970s
the Lukasiewicz thesis began to be questioned. The first two meetings
concern alternatives to the Lukasiewicz thesis. David Hitchcock, an
internationally recognized authority in this field, will be commentator
on both presentations.
Friday, September 22, 2006
4:00-6:00 P.M.
141 Park Hall

SPEAKER: Mauro Nasti De Vincenti,	Communication Sciences,
University of Salerno.

COMMENTATOR: David Hitchcock, Department of Philosophy, McMaster

TOPIC: Stoic Logic and Modern Consequential Logic.

ABSTRACT: The received view of the Stoic conditional (Chrysippean
implication) is that it is an ancient counterpart of modern strict
implication, i.e. of a standard necessary material implication.
Nevertheless, widely unnoticed testimonial evidence (notably in Sextus
Empiricus, Apollonius Dyscolus, Themistius and Boethius) suggests that
that Chrysippus' logic is an ancestor of a more sophisticated kind of
modern modal-connexive (non-classical) logic, namely the logic of
analytic consequential implication. This interpretation of Stoic logic
throws new light on many difficult questions, but is not without
Dutch treat supper follows.
Seguirà una cena alla romana.

Friday, October 13, 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. For 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 3, 2006
4:00-6:00 P.M.
141 Park Hall

TENTATIVE SPEAKER: John Corcoran, Philosophy, University of Buffalo.


TENTATIVE TITLE: Ambiguity in Logic.
ABSTRACT: This talk returns to the themes of my previous presentation
“Varieties of Ambiguity”, but it focuses entirely on ambiguities in the
literature of logic – notably logic textbooks and articles – and in
discourses that have traditionally been subject to logical analysis. In
particular, I will discuss ambiguities of metalogical expressions such
as the following and their cognates: imply, infer, deduce, expression,
proposition, tautology, instance, independent, consistent, occurrence,
variable, argument, proof.  No familiarity with my previous lectures and
publications on related subjects is presupposed. 

Dutch treat supper follows.

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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