Ibn Sina on discharging assumptions in proofs
Wilfrid Hodges, Fellow of the British Academy and Emeritus Professor, Queen Mary, University of London
Ibn Sina (Avicenna, 11th century Iran) believed that the foundations of logic lie in metaphysics. He complained bitterly that this has led people to confuse logic itself with its foundations and dress up metaphysics as logic. His own description of the foundations of logic is in overtly ontological language. But from a modern perspective it becomes clear that in fact he is talking about methodological issues, like how to represent occurrences of a component within a compound, and whether the primitive notions of a theory should be stipulated from outside (as in Tarski) or incorporated into the objects (as in web ontology and object-based programming). This all has strong implications for any project to formalise Ibn Sina’s logic. My own readings of some key passages are different from the traditional metaphysical ones, and seem to me more intelligible and highly comparable with some modern metalogical and metalinguistic views; but then I have a deaf ear for metaphysics.