Series: Logic Seminar
Date: Tuesday, November 9, 1999
Speaker: Dale Jacquette (Penn State, Philosophy)
Title: Soundness, the Liar, and the Validity Paradox
Time: 2:30 - 3:20 PM
Place: 122 Thomas Building
Abstract:
An inference is standardly said to be sound just in case it is
deductively valid and it has only true assumptions. The importance of
a coherent concept of soundness to proof theory is obvious, in that it
is only sound derivations, and not merely deductively valid arguments,
that advance knowledge by providing proofs of theorems in logic and
mathematics. The soundness paradox can be informally albeit
impredicatively formulated in this inference:
(S) 1. Argument (S) is unsound.
_______________
2. Argument (S) is unsound.
I show how to avoid impredication in the soundness paradox via
Goedelization, and compare the paradox with its apparently most
closely related cousins, the liar paradox and validity or
Pseudo-Scotus paradox. Although there are similarities among all
three paradoxes in this family of semantic diagonalizations, I shall
argue that the soundness paradox is not just a hybrid of the liar and
validity paradoxes, but belongs in a special category, that hte
soundness paradox is more fundamental than the liar, and that the
soundness paradox resists the most powerful received solutions to the
liar and validity paradoxes.