John Corcoran corcoran at buffalo.edu
Thu Nov 10 14:18:00 EST 2005

Alonzo Church (1956, 6) wrote: "We shall say that a name denotes or
names its denotation and expresses its sense. Or less explicitly we may
speak of a name just as having a certain denotation and having a certain
sense.  Of the sense we say that it determines its denotation, or is a
concept of the denotation."
I would modify this as follows [the changes are bracketed]: "We shall
say that a name denotes or names its denotation [or denotations, if any]
and expresses its sense [or senses]. Or less explicitly we may speak of
a name just as having a certain [entity or certain entities as its]
denotation [or denotations] and having a certain [concept or certain
concepts as its sense or senses].  Of [each] sense we say that it
determines or is a concept of the [entity or entities denoted by the
name or names that express it]." The only changes made are those
necessary to make room for semantic ambiguity and to avoid the
inadvertent and incoherent suggestion that senses denote. - John
Corcoran, 2005.

Friday, November 11, 2005
4:30 -6:00-P.M.
141 Park Hall

CO-SPONSOR: The C. S. Peirce Professorship in American Philosophy.

SPEAKER: Daniel Merrill, Philosophy. Oberlin College.
TITLE: De Morgan's Numerically Definite Syllogism. 

ABSTRACT: Augustus De Morgan's numerically definite syllogism (NDS) is
one of the most striking, if least-known, of the eight innovations in
his Formal Logic (1847). It comes in two forms. A simple numerical
example of the NDS is this: There are exactly 10 Ys; at least 7 Xs are
Ys and at least 5 Zs are Ys; therefore, at least 2 Xs are Zs. A
percentage example is: Most Ys are Xs and most Ys are Zs; therefore,
some Xs are Zs. This paper will (1) explain the basic forms of the NDS,
including some that are rather complex, and outline De Morgan's
justifications for them. It will then (2) show how he deduces the
traditional syllogistic laws from them and (3) how they were involved in
his controversy with Sir William Hamilton over the quantification of the
predicate. It will next (4) consider the claim, by De Morgan's
contemporary Henry Mansel, that the NDS is part of arithmetic, and not
of "formal" logic. De Morgan's response to this objection will help to
illuminate his idiosyncratic conception of the form-matter distinction
in logic. The paper will conclude by (5) considering whether, in more
modern terms, the NDS should be considered a part of formal logic.

BIOGRAPHICAL NOTE:  Daniel Merrill was born and raised in South Bend,
Indiana, where he was educated in the public schools. He attended
Princeton University, from which he graduated cum laude in 1954 with a
major in mathematics. His adviser was Alonzo Church. By that time his
interests had changed. He received his Ph.D. in philosophy from the
University of Minnesota in 1962, with a dissertation on the distinction
between logical and descriptive constants. In 1998, he retired as
Professor Emeritus of Philosophy at Oberlin College after teaching there
for 36 years. Most of his published research is on the early history of
mathematical logic, with an emphasis on the logic of relations as well
as on De Morgan and Peirce. An ACLS grant allowed him to do the research
on the De Morgan papers that resulted in his 1990 book, Augustus De
Morgan and the Logic of Relations. His article on De Morgan's
lattice-theoretical formulation of Boolean algebra appeared this summer
in HPL. He has also worked on Peirce's logic of relations, especially
the relationship between that logic and De Morgan's logic of relations.


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