ÌÇÐÄlogoÈë¿Ú

Overview

Biography

I was educated at Airdrie Academy, and at the universities of Edinburgh, Oxford and London. IÌýstudied Mathematics and Physics at Edinburgh, and Philosophy at Edinburgh, Oxford and ÌÇÐÄlogoÈë¿Ú. IÌýhave worked in the Civil Service, as a schoolteacher, and as a lecturer at King’s College London. I was appointed to myÌýpresent post as Reader in Philosophy at ÌÇÐÄlogoÈë¿Ú in 2007.

Research

Research interests

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

Research overview

• MyÌýprincipal philosophical interests are in epistemology, metaphysics, philosophy of mind and philosophy of mathematics. IÌýwould 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 studyÌýthe interplay of epistemology and metaphysics in my . The interplay is explored further in myÌý, whichÌýendorses the rationalist thesis that the human mind can apprehend the mathematical realm by reason alone.

Ìý,Ìýa collection of papers about my work, wasÌýpublished 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 entailsÌýthat a proposition is necessary just if it isÌýa priori.

• The Metaphysics of KnowledgeÌýpresents 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 knownÌýargues 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.

BIBLIOGRAPHY

Books

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).

Papers

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.

Ìý

A Summary of My Current Views,Ìý in N. Kürbis, B. Assadian and J. Nassim (eds.), Knowledge, Number and Reality, forthcoming.

Ìý

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

Ìý

Knowledge of Number,ÌýElectra, forthcoming.

Ìý

Book reviews

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

Review of Lee Walters and John Hawthorne (eds.) 'Conditionals, Paradox, and Probability: Themes from the Philosophy of Dorothy Edgington',ÌýMind, 2021.
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Supervision and teaching

Supervision

Supervisions within ÌÇÐÄlogoÈë¿Ú:

4

I welcome enquiries from prospective PhD students who are interested in undertaking research in any of my areas of research interest.

Teaching

Teaching modules

• Research in Theoretical Philosophy

Publications