# [FOM] FOM: BLC 3RD FALL

John Corcoran corcoran at buffalo.edu
Sun Sep 23 21:52:36 EDT 2007

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BUFFALO LOGIC COLLOQUIUM
http://www.philosophy.buffalo.edu/EVENTS/blc.htm
2007-8 THIRTY-EIGHTH YEAR
THIRD FALL ANNOUNCEMENT
QUOTE OF THE MONTH: CHURCH 1956 ON TRUTH-FUNCTIONS: By a function –or, more
explicitly, a one-valued singulary function –we shall understand an
operation which, when applied to something as argument, yields a certain
thing as the value of the function for that argument (page 15). A function
whose range of values consists exclusively of truth-values
is a
propositional function (page 28). We shall use the term truth-function for a
propositional function of truth-values which has as its range [of
arguments], if it is n-ary, all ordered systems of n truth-values (page 39).

THIRD MEETING: JOINT MEETING WITH THE UB PHILOSOPHY COLLOQUIUM
Thursday, September 27, 2007
4:00-6:00 P.M.
141 Park Hall

SPEAKER: Dale Jacquette, Philosophy, Pennsylvania State University.

TITLE: Intensional Truth Functions.
ABSTRACT: The extensionality thesis for truth functions holds that all (weak
version) or all and only (strong) truth functions are extensional.  A
sentence function is any function that has only sentences in its domain.  A
truth function is a sentence function defined by means of a truth table,
relating truth values in the function's domain to truth values in its
range.  An extensional sentence function is any sentence function that
supports the uniform intersubstitution of coreferential terms or logically
equivalent sentences salva veritate.  Many commentators have endorsed the
extensionality thesis in this form, which indeed is widely held and seldom
questioned.  Recently, Stephen Neale maintains in Facing Facts (OUP 2001):
"the class of extensional connectives is the same thing as the class of
truth-functional connectives" (147).  If the extensionality thesis is true,
then there can be no intensional truth functions.  Unfortunately for
extensionalism, there is a large family of intensional truth functions that
have not been properly recognized in philosophical logic.  It is possible to
provide truth table definitions of sententially dedicated constant truth
functions that fail to satisfy the substitution salva veritate criterion of
extensionality, and that are consequently intensional.  Intensional truth
functions constitute counterexamples to the extensionality thesis and raise
difficulties for efforts to provide formal criteria of truth functionality
and non-truth-functionality.

FOURTH MEETING: JOINT MEETING WITH THE UB PHILOSOPHY COLLOQUIUM
Thursday, October 11, 2007
4:00-6:00 P.M.
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
4:00-6:00 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
4:00-6:00 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. It will also ask what to make of the fact that the traditional
syllogism is a special case of such different logical frameworks.

Dutch treat supper follows.

Future Speakers: William Demopoulos (University of Western Ontario and
UC-Irvine), Leonard Jacuzzo (Fredonia University), 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).
part by the C. S. Peirce Professorship in American Philosophy and by other
institutions.
Institutional Representatives: George Boger, Canisius College; Leonard
Jacuzzo, Fredonia University.

All are welcome.
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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