> From X,B |- # conclude X |- B -> A, for any A. But suppose it is perfectly legitimate to end up with a formalisation which, like Neil's, avoids use of ECQ I don't have very firm views on how to formalise correctly the informal 'triviality' examples which were given such as proving the empty set is a subset of any set because I think the relationship between informal and formal proof is a highly complex one and there may often by no unique right answer. Now let us suppose Neil is right about this as regards ECQ as an operational rule. Likewise Neil seems to be arguing that his philosophical logic preserves the practice of working mathematicians, at least in best practice, whilst attacking distortions and misinterpretations of that practice by formal logicians. To pick up on Martin Davis's entertaining references to Bishop Berkeley (but leaving Hegel and Marx to one side!) the good Bishop maintained that in his views on the external world he was defending common sense by attacking metaphysical mis-readings of common sense by philosophers such as Locke. But I think this in itself poses difficulties for Neil's desire to present his position as essentially non-revisionary. Uckelman said, 'ex contradictione quodlibet', ECQ) has been interesting, partly because it seems to show (unsurprisingly) that lots of the logicians commenting on the issue, though very familiar with non-classical logic in the form of intuitionism, are much less familiar with, and have difficulty getting their heads round, substructural logics in particular, logics in which structural principles such as transitivity of entailment (or derivability) are restricted. Next message: Use of Ex Falso Quodlibet (EFQ) (or ECQ).Previous message: 600: Removing Deep Pathology 1. ![]() Use of Ex Falso Quodlibet (EFQ) (or ECQ) Alan Weir Alan.Weir at glasgow.ac.uk
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