John Corcoran corcoran at buffalo.edu
Fri Nov 7 07:17:06 EST 2008

falsity of the particular premisses and conclusions is of no concern to
logicians. They want to know only whether the premisses imply the
conclusion.-Mendelson. Introduction to Mathematical Logic. p. 1. [Logic is]
not concerned with how propositions follow from propositions without regard
to truth-value...truth is the goal of logic.-Frege. Posthumous Writings.
p.122. Evert Beth said that Aristotle's most important discovery was that
the same processes of reasoning used to infer new truths from propositions
previously known to be true are also used to deduce consequences from
premises not known to be true and even from premises known to be false;
something Frege never noticed, as least not in print.-Frango Nabrasa.
  Friday, November 7, 2008	4:00-6:00 P.M.	141 Park Hall
SPEAKER: David Braun, Romanell Professor of Philosophy, University of
TITLE: The Logic of Complex Demonstratives
ABSTRACT: The expressions 'this', 'that', 'he', and 'she' are simple
demonstratives.  Many theorists hold that these expressions refer to
individuals, with respect to contexts, and that their semantic (or
propositional) contents, in contexts, are simply the individuals to which
they refer, in those contexts.  There is much less agreement about the
semantics of complex demonstratives.  Examples include 'this table', 'that
blue chair', and 'that tall man standing next to the door'. Direct-reference
theorists emphasize the similarity between simple and complex
demonstratives.  They hold that complex demonstratives refer to individuals,
in contexts, and that their semantic contents, in contexts, are also just
individuals.  On their view, the semantic content of 'blue' (in a context)
is not a constituent of the semantic content of 'that blue chair' (in that
context).  By contrast, quantificational theorists emphasize the apparent
similarities between complex demonstratives and quantifier phrases (such as
'all blue chairs' and 'the largest blue chair', on Russellian views of
definite descriptions).  Quantificational theorists hold that complex
demonstratives do not refer to individuals (in contexts) and that the
property of being blue is a constituent of the semantic content of 'that
blue chair' (in a given context).  In this talk, I will outline a
direct-reference theory of complex demonstratives and defend it from
objections that say that direct-reference theories get the logic of complex
demonstratives wrong. See: Braun, David.  2007.  "Indexicals."  Stanford
Encyclopedia of Philosophy. http://plato.stanford.edu/entries/indexicals/
Dutch treat supper follows.

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.

Future Speakers: George Boger (Canisius College),), 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)


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