[FOM] FOM BUFFALO LOGIC COLLOQUIUM 2007 FIRST SUMMER ANNOUNCEMENT
corcoran at buffalo.edu
Wed Jun 6 17:56:32 EDT 2007
BUFFALO LOGIC COLLOQUIUM
2007-8 THIRTY-EIGHTH YEAR
FIRST SUMMER ANNOUNCEMENT
QUOTE OF THE MONTH: FEFERMAN ON STUDYING LOGIC: Logical thinking in
mathematics can be learned only by observation and experience. In fact, the
ability to reason correctly and to understand correct reasoning is itself a
prerequisite to the study of formal logic. - Solomon Feferman, The Number
Tuesday, June 19, 2007 12:00-1:30 P.M. 141 Park Hall
SPEAKER: John Corcoran Philosophy, University of Buffalo.
TITLE: Aristotle's Demonstrative Logic: A Preview.
ABSTRACT: This unfinished expository paper on Aristotle's demonstrative
logic is intended for a broad audience including non-specialists.
Demonstrative logic is the study of demonstration as opposed to persuasion.
It presupposes the Socratic knowledge/belief distinction - between beliefs
that are known (or that have been cognitively established) and those that
are not known (or that have not been cognitively established even though
perhaps true). Demonstrative logic is the subject of Aristotle's two-volume
Analytics, as he said in the first sentence. Every demonstration produces
[or confirms] knowledge of (the truth of) its conclusion for every person
who can comprehend the demonstration. Persuasion merely produces belief.
Aristotle presented his general truth-and-consequence conception of
demonstration, meant to apply to all demonstrations. According to him, a
demonstration is an extended argumentation that begins with premises known
to be truths and that involves a chain of reasoning showing by deductively
evident steps that its conclusion is a consequence of its premises. In
short, a demonstration is a deduction whose premises are known to be true.
For Aristotle, starting with premises known to be true, the knower
demonstrates a conclusion by deducing it from the premises. His general
theory of demonstration required a prior general theory of deduction
presented in the Prior Analytics. To illustrate his general theory of
deduction, he presented an overly simplified special case known as
categorical syllogistic. With reference only to categorical propositions, a
narrowly circumscribed class, he painstakingly worked out exactly what those
evident deductive steps are. In his specialized theory, Aristotle explained
how to deduce from a given categorical premise set, no matter how large, any
categorical conclusion implied by the given set. He did not extend this
treatment to all deductions. He treated only categorical deductions whose
intermediate steps involve only categorical propositions, although he
discussed non-categorical intermediate steps.
ADVANCE PDF COPIES AVAILABLE BY EMAIL REQUEST.
Wednesday, June 20, 2007 12:00-1:30 P.M. 141 Park Hall
SPEAKER: Amanda Hicks, Philosophy, University of Buffalo.
TITLE: Motivations for Studying Independence of Axiom Sets.
ABSTRACT: Historically, different conceptions of the role of axioms have
contributed to different motivations for studying their independence. This
paper discusses four conceptions of the role of axioms as found in certain
works by Husserl, Hilbert, Huntington, and Tarski. The conceptions
discussed are of axioms as (1) propositions known with certainty on
non-deductive grounds, (2) expressions of laws that unify facts about the
domain of investigation, (3) propositions that characterize a particular
subject matter, and (4) propositions taken arbitrarily as premises for
deductions. It then relates each of these conceptions to different
motivations for studying independence. The second conception can be
understood as providing residual motivation even for mathematicians and
philosophers who do not explicitly regard axioms in this light.
Thursday, June 21, 2007 12:00-1:30 P.M. 141 Park Hall
TENTATIVE SPEAKER: John Corcoran, Philosophy, University of Buffalo.
TITLE: Theories of Proportion.
ABSTRACT: This paper discusses first-order theories of [pure] proportion in
which the only primitive non-logical concept is the four-place relation of
proportionality. In the simplest one-sorted or homogeneous case, four
magnitudes of the same kind a, b, c, and d [in that order] are proportional
if a is to b as c is to d, or a : b :: c : d (to use the traditional
notation). In an important special case, arithmetic takes the magnitudes to
be natural numbers (positive integers). 1 : 2 :: 3 : 6. In another special
case, linear geometry takes the magnitudes to be [finite] lines (line
segments). Proportion propositions are often heterogeneous, i. e., involve
more than one sort of magnitude. Given any two numbers a, b, there are two
lines c, d such that, as a is to b, c is to d, or c : d :: a : b. In the
simplest heterogeneous case, we have a two-sorted theory. Two magnitudes of
one kind a, b, and two of another c, d [all in that order] are proportional
if a : b :: c : d. The oldest extant treatment of this subject is Book V of
Euclid's Elements, which was regarded as "containing the general theory of
proportion equally applicable to geometry, arithmetic, music, and all
mathematical sciences". This paper reconstructs a general one-sorted theory,
whose theorems are generic principles, i. e., apply equally to any given
sort of magnitude. It also reconstructs three specific theories having
theorems that apply to some but not all sorts of magnitudes. Two are
one-sorted; one applies to numbers but not to lines and the other applies to
lines but not to numbers. The remaining theory is two-sorted and applies at
once to both, to numbers as one sort and to lines as the other.
ADVANCE PDF COPIES AVAILABLE BY EMAIL REQUEST.
Wednesday, July 25, 2007 12:00-1:30 P.M. 141 Park Hall
TENTATIVE PANEL: John Corcoran, John Kearns, Leonard Jacuzzo, John Zeis, and
TITLE: Teaching Logic.
ABSTRACT: This is the third in a series of panels on the teaching of logic.
Each member of a panel of logic teachers will give a ten-minute presentation
of a message about teaching logic followed by ten minutes of open
discussion. Among the topics that are under consideration are: the goals of
logic, what to say the first day, the role of paradigm cases, the role of
fallacies, the role of history, the best non-logical content to use in
introductory courses, number theory, alternative logics, existential import,
identity logic, logic textbooks, which system of logic should be taught
first. All logic teachers are invited to volunteer to be on a future panel.
As soon as there are two volunteers, a panel will be scheduled.
Future Colloquium Speakers: George Boger (Canisius College), Leonard Jacuzzo
(Fredonia State University), Daniel Merrill (Oberlin College) November 2,
Thomas Reber (Canisius College), Stewart Shapiro (Ohio State University)
October 13, Barry Smith (University of Buffalo), John Zeis (Canisius
Future Colloquium Dates: August 1, September 14, October 5, 13, and 19,
THESE BROWN-BAG MEETINGS WILL CONTINUE ON VARIOUS DAYS AT NOON THROUGH JULY,
POSSIBLY INTO AUGUST. COME WHEN YOU ARE FREE. BRING LUNCH. LEAVE WHEN YOU
HAVE TO. ALL ARE WELCOME.
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