Seminario di Logica e Filosofia della Scienza

Seminario Logica e Informazione 2003-2004

Anno accademico: 2004-2005

Coordinatore: Andrea Cantini
Luogo: Sala conferenze

Primo semestre:

17 Novembre, ore 15,30: W. Sieg (CMU, Pittsburgh), Beyond Church Canons: Axioms for Computability

Abstract: Church's and Turing's theses assert, dogmatically, that an informal notion of computability (or effective calculability) is captured by a particular precise mathematical concept. I will present a conceptual analysis of computability that leads to precise notions, but dispenses with theses. The analysis is embedded in a rich historical and philosophical context. To investigate computability is to analyze symbolic processes that can, in principle, be carried out by calculators. This is a philosophical lesson we owe to Alan Turing. Drawing on and recasting work of Turing and Robin Gandy, I formulate finiteness and locality conditions for two types of calculators, human computing agents and mechanical computing devices; the distinctive feature of the latter is that they operate in parallel. The analysis leads to axioms for discrete dynamical systems (representing human and machine computations) and allows the reduction of models of these axioms to Turing machines. Cellular automata and a variety
of artificial neural nets can be shown to satisfy the axioms for machine computations.

3 Dicembre, ore 9,30-11: L. Crosilla (Firenze), I reali costruttivi

17 Dicembre, ore 9,30-11: W. Christiaens (Univ. Gent, Belgium), Structural realism and transcendental philosophy

Secondo semestre:

25 Febbraio, ore 11-13: P. Minari (Firenze), Metodi proof-teoretici nel lambda calcolo

4 Marzo e 11 Marzo, ore 11-13: A. Antonelli (Irvine), La logica del ragionamento plausibile

1 Aprile, ore 11-13: V. Santini (Firenze), La logica ad infiniti valori di Lukasiewicz

8, 15, 22 Aprile, ore 11-13: R. Bruni (Firenze), Introduzione alla logica lineare (dispense: parte I.pdf, parte II.pdf, parte III.pdf)