__Dissertation Abstract__

Peirce's Algebra Of Logic And The Law Of Distribution

by

Nathan Houser

Degree: PH.D.

Year: 1986

Pages: 00001

Institution:

Source: DAI, 47, no. 05A, (1986): 1751

In 1880 Charles Peirce published "On the
Algebra of Logic" in which he presented a symbolic logic that provides a
complete basis for the propositional calculus. Peirce intended to base his
logic exclusively on syllogistic principles, and from that basis to derive the
remaining logical laws, including the two principles that constitute the law of
distribution: ((a x (b + c)) =((a x b) + (a x c))) ((a
+ (b x c)) = ((a + b) x (a + c)))

For these he presented no
proof, declaring that it was "easy" but "too tedious to
give." When challenged by Schroder, who insisted that part of the law of
distribution was independent, Peirce was unable to
produce his proof and decided that he had been mistaken. Peirce concluded that
Syllogistic was insufficient as the basis of the algebra of logic and that
dilemmatic principles were required. He came to regard this requirement as the
most elementary refutation of the claim that all deductive reasoning is
syllogistic. Yet Peirce never accepted Schroder's suggestion that the problematic
part of the law of distribution be adopted as an axiom of logic. In 1904 Peirce
sent to Edward V. Huntington, for publication, a proof of the law of
distribution which he claimed had been worked up for his 1880 paper.

In this dissertation I give
an account, within the above context, of Peirce's work on the law of
distribution. As part of my account I describe an unpublished Peirce manuscript
(MS 575) that contains a summary proof of the full law of distribution, and I
show that it was written before but near the publication of "On the
Algebra of Logic." I compare the MS 575 proof and the "

SUBJECT(S)

Descriptor: PHILOSOPHY

Accession
No: AAG0558692

Provider: OCLC

Database: Dissertations