Wednesday, 6 June 2007

Disjunction in Mediaeval Logic

20th-century propositional logic allows ‘or-introduction’: the inference from P to (P v Q) for any Q. This rule is also explicitly stated in Robert Caubraith's Quadrupertitum (1510). But Peter Auriol's Scriptum (1316) denies the inference from ‹Antichrist will be› to ‹Antichrist will be or will not be›. The question is, why?

One answer might be that Auriol takes disjunction to be exclusive, so that (P v Q) is false if P and Q are both true. But although this would invalidate or-introduction as a rule of inference, it would not account for the Antichrist example, in which P and Q cannot both be true.

Another answer might be that Auriol takes ‹P or Q› to have an essential indeterminacy that renders it somehow incompatible with P – perhaps echoing Oswald Hanfling’s complaint in Philosophy and Ordinary Language (2000) that or-introduction falls foul of an ignorance condition: ‘Having been apprised of [P], I am no longer in a position to believe, or to know, that [either P or Q].’

My impression is that Auriol does somehow bind together disjunction and indeterminacy. I intend to investigate this connection.

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