The Lindström Lectures series was inaugurated 2013 with lectures by Wilfrid Hodges, Emeritus Professor of Mathematics, Queen Mary, University of London and Fellow of the British Academy. He is best known for his influential and wide-ranging work in mathematical logic, as expounded in his exquisitely crafted papers and books, including a definitive 780-page graduate text on model theory. His recent research work has focused on general semantics, cognitive aspects of logic, and history of logic, especially Arabic logic.
Professor Hodges attended New College, Oxford (1959–65), where he received degrees in both Literae Humaniores and (Christianic) Theology. In 1970 he was awarded a doctorate for a thesis in Logic. He lectured in both Philosophy and Mathematics at Bedford College, University of London. He was Professor of Mathematics at Queen Mary, University of London from 1987 to 2006. He has held visiting appointments in the department of philosophy at the University of California and in the department of mathematics at University of Colorado. He was President of the British Logic Colloquium, of the European Association for Logic, Language and Information and of the Division of Logic, Methodology, and Philosophy of Science. In 2009 he was elected a Fellow of the British Academy.
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.
Ibn Sina (Avicenna, 11th century Iran) wrote thousands of pages of commentary on Aristotle’s logical works. Among them is a short section on how to understand proofs by reductio ad absurdum. For Ibn Sina the problem is how to read an RAA proof so that the conclusion self-evidently follows from the premises, making minimal changes to the written form of the proof. In remarks almost certainly based on the Arabic Euclid, he observes (like Frege) that an assumption is stated so as not to have to keep repeating it at every stage of the argument. He infers that to see what is really meant in the argument, one should restore the assumption at every step where it is used. (Again this parallels Frege, though the motivation is different.) A key question is how Ibn Sina knows that adding these assumptions preserves validity. Writing out the answer as a metaprinciple yields a powerful rule of inference, which needs not much else added to give a complete sequent calculus for first-order logic - though Ibn Sina would have strongly disapproved of treating it that way.