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Keith Hossack


Keith studied Mathematics and Physics at Edinburgh, and Philosophy at Edinburgh, Oxford and Birkbeck. He has worked in the Civil Service, as a schoolteacher, and as a lecturer at King’s College London, and was appointed to his present post as Reader in Philosophy at Birkbeck in 2007. He likes to play chess in the odd moments when he is not thinking about philosophy.

Research Activity

  • Keith’s principal philosophical interests are in epistemology, metaphysics and philosophy of mind. He would like to understand the interplay between these topics better — What is the nature of the human intellect, if it can understand and grasp the most general features of the world? And what must the most general features of the world be, if they are to be intelligible?
  • He wrestled with the problem of the interplay in his 2007 book The metaphysics of knowledge. Currently he is completing another book, The laws of mathematics, which is motivated by the same problem. The new book suggests that what mathematicians discover are the laws that connect mathematical properties and relations, just as physicists discover the laws that connect physical properties and relations. This avoids ‘Benacerraf’s Dilemma’, the notorious disconnect between epistemology and metaphysics that afflicts theories that deny mathematics its proper place as one of the natural sciences.
  • The laws of mathematics suggests that natural, real and ordinal numbers are all of them universals, of the special sort that are attributes of what Aristotle calls ‘quantities’. A quantity is an item that is divisible at least in thought: examples are pluralities, masses and sequences. The book shows that the logic of reference to a species of quantity induces a matching algebraic structure on the numbers that measure them: the logic of reference to pluralities induces the algebra of the natural numbers, the logic of mass terms induces the algebra of the real numbers, and the logic of sequential reference induces the algebra of the ordinals. Thus a great deal of mathematics is logic; but the existence of the numbers themselves was a major scientific discovery.


  • Recent publications include:
  • ‘Concept and Content’. In Reason Faith and History, ed. M.W.F. Stone (Ashgate: Aldershot) 2008.
  • ‘Précis of The metaphysics of knowledge’. Dialectica, 65: 71-73, 2011.
  • ‘Replies to Comments’. Dialectica, 65: 125–151, 2011
  • ‘A Correspondence Theory of Exemplification’. Axiomathes 23 (2):365-380, 2013
  • ‘Sets and Plural Comprehension’. Journal of Philosophical Logic, 2013.

Research Supervision

  • Keith has supervised research students who obtained their PhDs in many different areas of philosophy, including all of the following: epistemology, metaphysics, philosophical logic, Kant, philosophy of mathematics, philosophy of physics, philosophy of mind, and recently even the philosophy of social science, philosophy of music, and philosophy of photography.
  • His current PhD students are working with him on a variety of topics, including necessity, self-knowledge, philosophy of mathematics, philosophy of language, metaphysics and metametaphysics.