Download SEMINARI DEL LABORATORIO DI FILOSOFIA ANALITICA Giovedì

UNIVERSITÀ DEGLI STUDI DI SASSARI
DIPARTIMENTO DI STORIA, SCIENZE DELL’UOMO, E DELLA
FORMAZIONE
Laboratorio di Filosofia Analitica
SEMINARI DEL LABORATORIO DI FILOSOFIA
ANALITICA
Giovedì 26 maggio 2016
Prof. Raymond Turner (University of Essex, UK)
THE COMPLETENESS OF FIRST ORDER LOGIC AND THE
JUSTIFICATION OF DEDUCTION
Two of the central results of classical first order logic relate its proof theory with its model theory. One
result insists that whatever is provable is universally valid i.e. true in all models. This is the soundness result.
The converse states that what is universally valid is provable: in other words, a sentence that is true in all
models is derivable using the rules of the logic. This is the completeness theorem. In this lecture we provide
an account of the logic, its model theory, its soundness, and its completeness and, as a corollary, prove the
Lowenheim Skolem theorem.
One the central questions concerns the philosophical significance, if any, of these results. In
particular, is there any sense in which they justify the rules of the logic? Does the soundness theorem do
so? On the face of it the proof of soundness uses the very rules under consideration for their justification.
Thus it has an air of circularity about it: how can one justify rules by using the very reasoning codified by the
rules? And yet the theorem sare in some way enlightening: they tell us something about the proposed
semantic interpretation and the operational rules of the logic. But what? Dummett in a very influential
article argues that the theorems do not justify the logical rules but they explain them. We shall spend some
time exploring this perspective.