[FOM] FOM: BLC 1ST FALL 20078
John Corcoran
corcoran at buffalo.edu
Mon Sep 10 17:31:10 EDT 2007
BUFFALO LOGIC COLLOQUIUM
http://www.philosophy.buffalo.edu/EVENTS/blc.htm
20078 THIRTYEIGHTH YEAR
FIRST FALL ANNOUNCEMENT
QUOTE OF THE MONTH: DEMORGAN ON LIMITING LOGIC: I cannot find that Aristotle
either limits his reader in this way or that he anywhere implies that he has
exhausted all possible modes of reasoning. Anyone is at liberty to limit the
inferences he will use in any manner he pleases. But he may err if he
declare his own arbitrary boundary to be a natural limit imposed by the laws
of thought. A. De Morgan, 1847, 127.
FIRST MEETING
Thursday, September 13, 2007
4:006:00 P.M.
141 Park Hall
SPEAKERS: George Boger, Canisius College, and John Corcoran, University of
Buffalo.
TITLE: Aristotle’s Independence Proofs: a Workshop.
ABSTRACT: This meeting is a workshoptype discussion of Aristotle’s methods
of establishing that given conclusions are independent of (do not follow
from) given premises. The focus is mainly on two methods: the method of
counterarguments MCA and the method of contrasted instances MCI. In each
application, MCA uses one counterinterpretation and deals with one
conclusion. In contrast, each application of MCI uses two
counterinterpretations and deals with four conclusions. One issue is whether
the method of contrasted instances was regarded by Aristotle as a compact
combination of four applications of the method of counterarguments or
whether he regarded it as a separate and independent method. Both methods
were ignored for centuries, both have been criticized as logically
inadequate, and both have been praised as clear foreshadowings of modern
modeltheoretic procedures. Corcoran will open the meeting with a short
introduction to modern metamathematical results about Aristotle’s methods
including some rather striking discrepancies between Aristotle’s statements
and what would be expected metamathematically. Most of the meeting will
consist of Boger’s workshop presentation of the relevant Aristotelian text.
Boger will raise problems of translation and interpretation and he will
suggest his own original solutions. Audience participation is welcome at any
point.
References.
Aristotle. Prior Analytics. Book A, Ch 16.
Boger, G. 2004. Aristotle’s Underlying Logic. In Gabbay, D. and J. Woods,
Eds, Handbook of the History of Logic. Amsterdam: Elsevier. Reviewed by
Klaus Glashof. The Bulletin of Symbolic Logic. 10 (2004) 57983.
Corcoran, J. 2003. Aristotle's Prior Analytics and Boole's Laws of Thought.
History and Philosophy of Logic. 24 , 261288. Reviewed by M. Guillaume.
Mathematical Reviews 2033867 (2004m: 03006). Reviewed by R. Vilkko. The
Bulletin of Symbolic Logic. 11(2005) 8991.
Smith, R. (Trans) 1989. Aristotle’s Prior Analytics. Indianapolis: Hackett.
Reviewed by J. Gasser. History and Philosophy of Logic.12 (1991) 235–240.
SECOND MEETING: JOINT MEETING WITH THE UB PHILOSOPHY COLLOQUIUM
Thursday, September 20, 2007
3:305:00 P.M.
141 Park Hall
SPEAKER: John Corcoran, Philosophy, University of Buffalo.
TITLE: Aristotle’s Demonstrative Logic.
ABSTRACT: This elementary expository paper on Aristotle’s demonstrative
logic is intended for a broad audience that includes nonspecialists.
Demonstrative logic is the study of demonstration as opposed to persuasion.
Every demonstration produces (or confirms) knowledge of (the truth of) its
conclusion for every person who comprehends the demonstration. Persuasion
merely produces opinion. Aristotle presented a general truthandconsequence
conception of demonstration meant to apply to all demonstrations. According
to him, a demonstration is an extended argumentation that (1) begins with
premises known to be truths and (2) involves a chain of reasoning showing by
deductively evident steps that its conclusion is a consequence of its
premises. Aristotle’s general theory of demonstration required a prior
general theory of deduction presented in the Prior Analytics. His general
immediatedeductionchaining conception of deduction was meant to apply to
all deductions. According to him, any deduction that is not immediately
evident is an extended argumentation consisting of a chaining of immediately
evident steps showing its final conclusion to follow logically from its
premises. Advance copies are available by email request
[corcoran at buffalo.edu].
THIRD MEETING: JOINT MEETING WITH THE UB PHILOSOPHY COLLOQUIUM
Thursday, September 27, 2007
TBA
141 Park Hall
SPEAKER: Dale Jacquette, Philosophy, Pennsylvania State University.
TITLE: Intensional Truth Functions.
ABSTRACT: TBA
FOURTH MEETING: JOINT MEETING WITH THE UB PHILOSOPHY COLLOQUIUM
Thursday, October 11, 2007
TBA
141 Park Hall
SPEAKER: Emily Grosholz, Philosophy, Pennsylvania State University.
TITLE: Leibnizian Analysis, Canonical Objects, and Generalization
ABSTRACT: Mathematics stands at the crossroads of history and logic:
essential as logic is to the articulation of relations among mathematical
items, the very constitution of a problem in mathematics is historical,
since problems constitute the boundary between the known and the yet to be
discovered. We cannot explain the articulation of mathematical knowledge
into problems and theorems without reference to both logic and history. The
outcome of mathematical progress is not always, and perhaps only rarely, an
axiomatized system, where solved problems recast as theorems that follow
deductively from a set of special axioms, logical principles, and
definitions. Careful study of the history of mathematics, even twentieth
century mathematics, may discover that mathematicians pursue generality as
often as they pursue abstraction, and sometimes prefer deeper understanding
to formal proof. An axiomatic system is not the only model of theoretical
unity, and deduction from first principles is not the only model for the
location and justification of mathematical results. In this essay, I claim
that Leibniz’s notion of analysis can be understood as an art of both
discovery and justification in a mathematics that aims for generalization
rather than abstraction, and explanation rather than formal proof. (This may
seem odd, since Leibniz has been heralded as the champion of formal proof
ever since the days of Russell and Couturat.) I will review some of
Leibniz’s pronouncements on analysis as the search for conditions of
intelligibility, and then review aspects of his investigation of
transcendental curves, focusing on the catenary. That is, I will show that
both his philosophical ideas and his mathematical practice support my claim.
FIFTH MEETING
Friday, October 12, 2007
4:006:00 P.M.
141 Park Hall
SPEAKER: Stewart Shapiro, Philosophy, Ohio State University.
TITLE: Frege’s Holistic Rationalism.
ABSTRACT: TBA
SIXTH MEETING
Friday, November 2, 2007
4:006:00 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: William Demopoulos (University of Western Ontario and
UCIrvine), John Kearns (University of Buffalo), Kevin Tracy (Lawrence
University), William Rapaport (University of Buffalo), Thomas Reber
(Canisius College), José Miguel Sagüillo (University of Santiago de
Compostella), Barry Smith (University of Buffalo), John Zeis (Canisius
College).
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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John Corcoran. For further information, to report glitches, suggest a talk,
unsubscribe or make other suggestions, please email: John Corcoran:
corcoran at buffalo.edu

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