John Corcoran corcoran at buffalo.edu
Sun Nov 9 09:32:24 EST 2008


PLATONIC AXIOMATICS: It is probably due to Plato that subsequent
mathematicians began [presentations of] the subject with a carefully
compiled series of definitions, postulates, and axioms. —W. W. Rouse Ball
1908, 43. Contrary to widely held opinion, Euclid was not the originator of
the axiomatic method. Plato was dead when Euclid wrote and it is likely that
there were axiomatizations long before Plato. Heath’s 1908 translation of
Euclid has a section on axiomatizations preceding Euclid’s (vol. I, ch.IX, §
2).—Saci Pererê 2001

HENKIN ON ARITHMETIC VS. ALGEBRA: In arithmetic we learn how to add,
subtract, multiply, and divide numbers. In algebra we learn how to add,
subtract, multiply, and divide letters. —Leon Henkin 1964.

Monday, November 10, 2008	4:00-6:00 P.M.	141 Park Hall

SPEAKER: John Corcoran, Professor of Philosophy, University of Buffalo

TITLE: 2nd-Order Logic, 1st-Order Logic, and Basic Logic 

Abstract: This expository article focuses on the fundamental differences
between second- order logic and first-order logic. It employs second-order
propositions and second-order reasoning in a natural way to illustrate the
fact that second-order logic is actually a familiar part of our traditional
intuitive logical framework and that it is not an artificial formalism
created by specialists for technical purposes. To illustrate some of the
main relationships between second-order logic and first-order logic, this
paper introduces basic logic, a kind of zero-order logic, which is more
rudimentary than first-order and which is transcended by first-order in the
same way that first-order is transcended by second-order. The heuristic
effectiveness and the historical importance of second-order logic are
reviewed in the context of the contemporary debate over the legitimacy of
second-order logic. Rejection of second-order logic is viewed as an
incipient paradigm shift involving radical repudiation of a part of our
scientific tradition that is defended by traditionalists. But it is also
viewed as analogous to the reactionary repudiation of symbolic logic by
supporters of “Aristotelian” traditional logic. But even if “genuine” logic
comes to be regarded as excluding second-order reasoning, which seems less
likely today than fifty years ago, its effectiveness as a heuristic
instrument will remain and its importance for understanding the history of
logic and mathematics will not be diminished. Second-order logic may some
day be gone, but it should never be forgotten. Technical formalisms have
been avoided entirely in an effort to reach a wide audience, but every
effort has been made to limit the inevitable sacrifice of rigor. This paper
is a kind of sequel to my “Second-order Logic” in Anderson, C.A. and Zeleny,
M., Eds.  Logic, Meaning, and Computation: Essays in Memory of Alonzo
Church. Dordrecht: Kluwer, 1998. 

For a PDF preprint, email corcoran at buffalo.edu with SOL in the subject line.

Dutch treat supper follows.

Friday, November 14, 2008	3:30-5:00 P.M.	Talbot College TBA
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 non-specialists.
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 truth-and-consequence
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
immediate-deduction-chaining 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. The talk is based on a paper to appear in the journal History and
Philosophy of Logic 30 (2009) 1-20.

Advance PDF preprints are available by email request with ADL in the subject
line [corcoran at buffalo.edu].

Buffalo Logic Classics Project

The Buffalo Logic Classics Project is a series of meetings devoted to close
reading and careful discussion of short classic “papers” in logic. We have
already had one session on Tarski’s “Truth and Proof” and two on Frege’s
“Thoughts”. Future sessions are planned on the following: passages from
Aristotle’s Organon, passages from Boole’s two books,  Frege’s “Sense and
Denotation”, Padoa’s paper on deductive method, Russell’s “On Denoting”,
Church’s papers on existential import and on sentences and propositions,
passages from Church’s Chapter 0, Tarski’s paper’s on truth, on consequence,
and on the deductive method, passages from Quine’s paper on Peano. Please
let me know of papers that have meant a lot to your thinking about logic and
that are suitable for close reading and discussion by a diverse
interdisciplinary audience. Also let me know if you are available to chair
or co-chair a session.

Future Speakers: George Boger (Canisius College), Julian Cole (Buffalo State
University), William Demopoulos (University of Western Ontario), Randall
Dipert (University of Buffalo), David DeVidi (University of Waterloo), David
Hitchcock (McMaster University) , John Kearns (University of Buffalo),
Stewart Shapiro (Ohio State University), Barry Smith (University of
Buffalo), Leonard Jacuzzo (Canisius College and Fredonia University), Frango
Nabrasa (Manatee Institute), Thomas Reber (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

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