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)
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.
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
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