Abstract

The origins of mediaeval theories of inference and entailment are shown first to lie in the work of Boethius and an account is proposed of the theory of the hypothetical syllogism that he offers in de Hypotheticis Syllogismis . Boethius is also shown to have provided some hints which led twelfth century philosophers to develop the theory of positio impossibilis for the construction of thought experiments with hypotheses acknowledged to be impossible. The ancient sources of Boethius's ideas on such hypotheses are investigated and in particular the use of them by Philoponus in arguing against Aristotle's rejection of the notion of space as three dimensional extension. Peter Abaelard is shown to be the crucial figure in the development of theories of the truth of the conditional and the validity of argument in the twelfth century and this aspect of his philosophy is explored in some detail. Abaelard's followers the Nominales were characterised especially by their acceptance of his connexive principles for the logic of the conditional and by their application of them in developing a theory of impossible hypotheses. It is argued here the Nominales' commitment to Abaelardian logic helps to explain their advocacy of the striking thesis that nothing grows and perhaps also reveals them to be discoverers of the Liar paradox in the middle ages. Finally it is argued that the distinctions made by Abaelard between two kinds of conditional, and the different logical principles governing them, are employed at least up to the time of William of Ockham and especially in the work of John Duns Scotus. Ockham's theory of the conditional is shown to make a fundamental break with the hyperintensional logical theory employed by Scotus in arguing for the central importance of the formal distinction in metaphysics