Skip to main content

Dr Keith Hossack

  • Overview



    I studied Mathematics and Physics at Edinburgh, and Philosophy at Edinburgh, Oxford and Birkbeck. I have worked in the Civil Service, as a schoolteacher, and as a lecturer at King’s College London. I was appointed to my present post as Reader in Philosophy at Birkbeck in 2007.


    • MA in Mental Philosophy, First Class Honours, University of Edinburgh, 1971
    • BSc in Mathematics and Physics, First Class Honours, University of Edinburgh, 1973
    • DPhil in Philosophy, University of Oxford, 1986
  • Research


    Research interests

    • Epistemology
    • Metaphysics
    • Philosophy of Mind
    • Philosophical Logic
    • Philosophy of mathematics

    Research overview

    • My principal philosophical interests are in epistemology, metaphysics, philosophy of mind and philosophy of mathematics. I 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, including its abstract features? And what must the most general features of the world be, if they are to be intelligible?

    • I wrestle with the problem of the interplay of epistemology and metaphysics in my The Metaphysics of Knowledge. The interplay is explored further in my Knowledge and the Philosophy of Number, which endorses the rationalist thesis that the human mind can apprehend the mathematical realm by reason alone.

    Knowledge, Number and Reality:Encounters with the work of Keith Hossack, a collection of papers about my work, is to be published in January 2022. The collection is edited by three of my former students, and includes a new paper by me arguing that the logic of conditionals entails that a proposition is necessary just if it is a priori.

    The Metaphysics of Knowledge (2007) presents the thesis that knowledge is an absolutely fundamental relation, with an indispensable role to play in metaphysics, philosophical logic, and philosophy of mind and language. Knowledge has been generally assumed to be a propositional attitude like belief. But I argue that knowledge is not a relation to a content; rather, it is a relation to a fact. This point of view allows us to explain many of the concepts or philosophical logic in terms of knowledge. I provide a theory of facts as structured combinations of universals and particulars, and present a theory of content as that property of a mental act that determines its value for getting knowledge. I defend a theory of representation in which the conceptual structure of a content is taken to picture the fact it represents. This permits definitions to be given of reference, truth, and necessity in terms of knowledge. Turning to the metaphysics of mind and language, I argue that a conscious state is one that is identical with knowledge of its own occurrence. This allows us to characterise subjectivity, and, by illuminating the I-concept, allows us to gain a better understanding of the concept of a person. Language is then explained in terms of knowledge as a device used by a community of persons for exchanging knowledge by testimony.

    Knowledge and the Philosophy of Number: what numbers are and how they are known (2020) argues that numbers are a part of Reality. They are numerical magnitudes, and they are just as real as physical magnitudes like inertial mass and electric charge. The physical magnitudes are known from empirical evidence, arrived at by careful experiment and observation, but I argue that our evidence that numbers exist is entirely a priori. A magnitude is a property of a special kind: its instances are not individual objects but the category of item that Aristotle calls a quantity. A natural number is the numerical magnitude of a discrete quantity, and I show that the usual axioms for the natural numbers can be obtained from Euclid’s self-evident ‘Common Notions’ and the logic of discrete quantity. Similarly, the axioms for the positive real numbers and the ordinals can be obtained from the Common Notions and the logic of continuous and serial quantity respectively.


    Geometry and the Concept of Space, DPhil Thesis (Oxford 1986).
    The Metaphysics of Knowledge (Oxford: Oxford University Press 2007).
    Knowledge and the Philosophy of Number: What Numbers Are and How They Are Known (London: Bloomsbury Academic 2020).


    A Problem about the Meaning of Intuitionist Negation, Mind 96/394 (1990): 207–219.

    Access to Mathematical Objects, Critica 23/68 (1991): 157–181.

    Constructivist Mathematics, Quantum Physics and Quantifiers, Proceedings of the Aristotelian Society, supplementary vol. 66/1 (1992): 61–97.

    Intolerant Clones, Mind, 103/409 (1994): 55–58.

    Plurals and Complexes, The British Journal for the Philosophy of Science 51/3 (2000): 411–443.

    Self-Knowledge and Consciousness, Proceedings of the Aristotelian Society 102/1 (2002): 163–181.

    Consciousness in Act and Action, Phenomenology and the Cognitive Sciences 2 (2003): 187–203.

    Reid and Brentano on consciousness, in Markus Textor (ed.), The Austrian Contribution to Analytic Philosophy(London and New York: Routledge, 2006), pp. 1–36.

    Vagueness and personal identity, in Fraser MacBride (ed.), Identity and Modality (Oxford: Oxford University Press 2006), pp. 221–241.

    Seeing an individual, in MM McCabe and Mark Textor (eds.), Perspectives on Perception (Berlin: De Gruyter 2007), pp. 47–64.

    Actuality and Modal Rationalism, Proceedings of the Aristotelian Society 107/1pt3 (2007): 433–456.

    Concept and content, in M. Stone (ed.), Reason, Faith and History: Philosophical Essays for Paul Helm (Farnham, UK: Ashgate 2008), pp. 205–218.

    Précis of The Metaphysics of Knowledge, Dialectica 65/1 (2011): 71–73.

    Replies to Comments, Dialectica 65/1 (2011): 125–151.

    A Correspondence Theory of Exemplification, Axiomathes 23 (2013): 365–380.

    Sets and Plural Comprehension, The Journal of Philosophical Logic 43/2–3 (2014):517–539.

    Necessity, Conditionals and Apriority, in N. Kürbis, B. Assadian and J. Nassim (eds.), Knowledge, Number and Reality, forthcoming.

    Book review

    Review of Stewart Shapiro’s 'Philosophy of Mathematics: Structure and Ontology', The Philosophical Quarterly, 50/198 (January, 2000): 120–123.

  • Supervision and teaching

    Supervision and teaching


    Current doctoral researchers


    Doctoral alumni



    Teaching modules

    • Research in Theoretical Philosophy (SSPL157S7)
    • Philosophy Proseminar (SSPL160S7)
  • Publications



    Book Section

    • Hossack, Keith (2022) Necessity, conditionals and apriority. In: Kürbis, Nils and Assadian, B. and Nassim, Jonathan (eds.) Knowledge, Number and Reality Encounters with the Work of Keith Hossack. London, UK: Bloomsbury. ISBN 9781350186439. (In Press)
    • Hossack, Keith (2008) Concept and content. In: Stone, M. (ed.) Reason, Faith and History: Philosophical Essays for Paul Helm. Farnham, UK: Ashgate. pp. 205-218. ISBN 9780754609261.