Coloquio Compostelano de Lógica y Filosofía Analítica el 22/9/11.Ivor Grattan Guiness

El jueves 22 de septiembre a las 16 hs, está programada la sesión  del Coloquio
Compostelano de Lógica y Filosofía Analítica que impartirá el distinguido profesor Ivor Grattan Guiness 


A New-old Characterisation of Logical Knowledge



To the memory of Paul Gochet (1932-2011)

Abstract

The principal aim of this tirade is to seek means of distinguishing  logical knowledge from other kinds of knowledge, especially  mathematics. The discussion is deliberately restricted to classical  bivalent logic, but not in a spirit of rejecting any other logic.  The proposition is taken as the basic notion, and the difference  between parts and moments of a totality as a fundamental  distinction, moments playing roles often given in older versions of  logic to ‘forms’. Four inter-dependent departments are proposed:  the propositional and functional calculi, which are based  respectively
upon ‘propositional’ and ‘functional moments’; rules  for (in)valid deduction or
inference, embodied in ‘deductional  moments’; and the assignment of the truth-values ‘true’ and  ‘untrue’ to propositions in ‘assertional moments’. Assertion is not  usually elaborated in logic texts; neither are the different ways  of negating a proposition: both receive detailed analysis here. A  review is then made of several mathematics-like subjects that interact profoundly with logic but  are  not subsumed under it, especially set theory and all other  theories  of collections, metamathematics and axiomatisation,  theory of  definitions, model theory, abstract and operator  algebras, and  semiotics. Then two important logico-mathematical  topics are  studied: paradoxes, especially the propositional ones;  and indirect  proof-methods, especially that by contradiction. The  final  reflections include some perplexed talk about  self-referring  self-reference.


I. Grattan-Guinness
Middlesex University Business School,
The Burroughs, Hendon, London NW4 4BT, England
Centre for Philosophy of Natural and Social Science, London School   of Economics,
Houghton Street, London WC2A 2AE, England