Alex Oliver

I read Philosophy at Cambridge, then at Yale on a Mellon Fellowship, returning to Cambridge to write my PhD on the metaphysics of sets. After a year of a Research Fellowship at Gonville and Caius College, I joined the Faculty of Philosophy where I am now a Professor and a Professorial Fellow of Gonville and Caius College. I was awarded a Leverhulme Major Research Fellowship 2002-4, a University Pilkington Teaching Prize for excellence in teaching 2005, and the Mind Association's Senior Research Fellowship in Philosophy 2012-13. In 2014 the University of Cambridge awarded me a LittD for my work in logic and metaphysics.

Research

I work mainly in metaphysics, logic and philosophy of mathematics.

I also have a strong interest in philosophy and public affairs.

In the past my research students have worked on the metaphysics of modality,  logical consequence, identity through time, reason in ethics, properties, the logic of plural descriptions, indefinite extensibility in set theory, Frege’s semantics and ontology, intellectual property, trust and digitally mediated communication, physicalism, and the semantics of fiction.

My current PhD students are

• Marco Meyer (trusting banks)
• Jens van’t Klooster (trusting banks)

Former PhD students:

• Adrian Boutel
• Emily Caddick
• Dominic Gregory
• Owen Griffiths
• Hallvard Lillehammer
• Alex Paseau
• Tom Simpson
• Lukas Skiba

Publications

Three short papers on the metaphysics of sets:

• 'The Metaphysics of Singletons', Mind 101 (1992): 129-40.
• 'Classes and Goodman's Nominalism', Proceedings of Aristotelian Society 93 (1993): 179-91.
• 'Are Subclasses Parts of Classes?', Analysis 54 (1994): 215-23.

My 'State of the Art' article:

• 'The Metaphysics of Properties', Mind 105 (1996): 1-85

poses problems for some contemporary metaphysical methods and tries to disentangle various modern versions of the so-called problem of universals. Key papers on properties are collected and introduced in

• Properties (Oxford: OUP, 1997)

which I edited jointly with Hugh Mellor. More recently I have turned to the metaphysics of predicates in

• ‘What is a predicate?’ in M.Potter and T.Ricketts (eds), The Cambridge Companion to Frege (CUP, 2010). (Frege’s metaphysics of predicates has been widely misunderstood. Different exegetes pin different, alien conceptions on him. Like him, they often argue that their chosen candidate is the right one, but in reality any will do.) A draft version is available here.

I have also written about the philosophy of mathematics:

• 'Dummett and Frege on the Philosophy of Mathematics', Inquiry 37 (1994): 349-92.
• 'Hazy totalities and indefinitely extensible concepts: an exercise in the interpretation of Dummett's philosophy of mathematics', Grazer Philosophische Studien 55 (1998): 25-50.
• 'A Realistic Rationalism?', Inquiry 43 (2000): 111-36 (critical notice of Jerrold Katz's Realistic Rationalism).
• 'Logic, Mathematics and Philosophy', The British Journal for the Philosophy of Science 51 (2000): 857-73 (critical notice of George Boolos's collected papers Logic, Logic and Logic).

Timothy Smiley and I have worked together on plural logic for some years. Our book on the topic was published in 2013. The revised and enlarged second edition was published in paperback in 2016. The book can also be viewed at Oxford Scholarship Online.

Here are some papers on plurals:

• 'Frege and Dummett are Two', Philosophical Quarterly 44 (1994): 74-82 (criticises Frege's treatment of plurals and Dummett's account of that treatment).
• 'Ghost writers' (with Alexius Schmeinong), Analysis 60 (2000): 371 (poses a dilemma for the analysis of lists which feature empty terms).
• 'Strategies for a Logic of Plurals (with Timothy Smiley), Philosophical Quarterly 51 (2001): 289-306 (explores various versions of 'changing the subject'–the treatment of a plural term as a singular term standing for a whole or a set or whatever; shows that none will work).
• 'Multigrade predicates' (with Timothy Smiley), Mind 113 (2004): 609-81 (articulates and defends the notion of a mutigrade predicate—one that takes variably many arguments; compares two rival conceptions of a list of terms—as a mere string of separate arguments or as itself a compound plural term; in a coda, assesses Adam Morton's pioneer system of multigrade logic).
• 'Plural Descriptions and Many-valued Functions' (with Timothy Smiley), Mind 114 (October 2005): 1039-68 (charts the development of Russell's theory of plural descriptions and explains why it fails; uses many-valued functions as a test case in support of a number of theses about plural reference, viz. it needs to be taken seriously, is legitimate and not reducible to singular reference; introduces a formal framework that admits plural reference).
• 'A Modest Logic of Plurals' (with Timothy Smiley), Journal of Philosophical Logic 35 (2006): 317-48 (presents a plural logic that is expressively as strong as it can be without sacrificing axiomatisability; demonstrates the soundness and completeness of the axiomatisation with respect to a genuinely plural semantics; uses the logic to chart the expressive limits set by axiomatisability).
• 'What are sets and what are they for?' (with Timothy Smiley), Philosophical Perspectives 20 (2006): 123-55 (presents a set theory based on plural logic in which the only primitive is the 'set of' functor, directly expressing Cantor's idea of collecting many objects (the arguments of the set of function) into a single one (its value). Naturally, the theory lacks an empty set and singletons. Excluding them does dramatically reduce the strength of set theory, but this has no mathematical or philosophical significance.)
• ‘Is plural denotation collective?’ (with Timothy Smiley), Analysis, 68 (2008): 22–34 (argues that plural denotation suffers a kind of indeterminacy that has no parallel in the singular realm).
• ‘Sharvy’s theory of descriptions: a paradigm subverted’ (with Timothy Smiley), Analysis 69 (2009): 412–21 (analyses Richard Sharvy’s influential ‘more general’ theory of descriptions, which corrects Russell’s analysis of singular count descriptions and extends it to cover mass descriptions, plural descriptions and generic ‘the’; argues that Sharvy is wrong in every case).
• ‘Plural logic’ (with Timothy Smiley), in E. Craig (ed.), Routledge Encyclopedia of Philosophy, on-line edition 2011.
• 'Singularist Predicative Analyses and Boolos's Second-order Pluralism' (with Timothy Smiley), in M. Carrara, A. Arapinis, and F. Moltmann (eds), Unity and Plurality: Logic, Philosophy, and Linguistics (OUP, 2016): 33-54. (argues against predicative analyses of plurality which turn an apparently plural term standing for several objects into a singular predicate standing for a concept or property; also argues against Boolos's second-order analysis of plurality; the same objection - the equivocity objection - sinks both kinds of analysis).

Alongside the study of the plural idiom of English, I have also been thinking more generally about the seductive myths surrounding the idea of logical form. One myth praises modern logic for breaking free from the grammatical confusion between names and quantifier phrases which had bewitched traditional logicians. This hoax is exposed in

• 'A Few More Remarks on Logical Form', Proceedings of the Aristotelian Society 99 (1999): 247-72; reprinted in R.Gaskin (ed.) Grammar in Early Twentieth-Century Philosophy (London: Routledge, 2001): 142-62.

One of the themes of this paper is that philosophers of language commonly underestimate the complexity of English syntax. A quite different case is addressed in

• 'The Reference Principle', Analysis 65 (2005): 177-87. (Co-referential expressions can be substituted for one another in any context without producing an ungrammatical result. This is the operative part of Crispin Wright's Reference Principle. After a discussion of his use of it to solve Frege's paradox of 'the concept horse', the Reference Principle is shown to be false, and wider morals are drawn from its failure.)

A more recent paper on logic form appears in the Festschrift for Timothy Smiley, which I edited jointly with Jonathan Lear:

• 'The matter of form: logic’s beginnings’ in The Force of Argument: Essays in Honor of Timothy Smiley (Routledge, 2010): 165–85.

We all know that it would be a bad mistake to construe the quantifier 'nothing' as a term standing for something. But Timothy Smiley and I have shown that in English 'nothing' can be used as a empty term, denoting nothing:

• 'Zilch' (with Timonth Smiley), Analysis 73 (2013): 601-13 (introduces 'zilch', defined as the 'non-self-identical thing', as a term which is empty as a matter of logical necessity. Its behaviour is contrasted with that of the quantifier 'nothing' and its uses are illustrated. The same idea is used to vindicate Locke's, Descartes' and Hume's handling of 'nothing', and Heidegger's 'das Nichts nichtet' is shown to be a straightforward logical truth.)

Philosophy and Public Affairs

With Dominic Scott, I set up and directed The Forum for Philosophy in Business, 2003–9. The Forum brought together philosophers and academics in cognate disciplines with practitioners at the highest levels of government, the professions and business. The Forum attracted research funding from IBM, Pfizer, BT, KPMG, the Newton Trust, and SHM consultants. Research conducted under its auspices included projects and conferences on pharmaceutical ethics, taxation, knowledge transfer in the Arts and Humanities, and trust in public life, the professions and the media.

I have undertaken consultancy work in the public and private sectors on topics such as customer loyalty, educational strategy, and corporate values. Recently I supervised a three-year project -'Trust on the Internet - sponsored by Microsoft. With Prof. dr. Boudewijn de Bruin (University of Groningen) I have been awarded a one million euro grant from the Dutch Research Council (NWO) for a collaborative project on trust in banking.

I have served as a member of the AHRC’s Knowledge Transfer Panel and its Strategy Group.

With Hallvard Lillehammer, and then Boudewijn de Bruin, I have taught elective courses on philosophical issues in business for the MBA programmes at the Judge Business School.  I have also conducted seminars for BT’s Industry Vision Programmes, for Imperial College’s Business School, and for the Compliance Career Academy created by Barclays and the Judge Business School. Here is a podcast recorded for the Open University on business and ethics.

I have worked on philosophical issues thrown up by notions of creativity, plagiarism and intellectual property. The law of trade marks is a rich source of puzzles:

• ‘Trade marks as property: a philosophical perspective’ (with Dominic Scott and Miguel Ley-Pineda) in L. Bently, J. Davis and J.C. Ginsburg (eds) Trade Marks and Brands: An Interdisciplinary Critique (CUP, 2008): 285–305. (By examining infringements by dilution, we show that trade marks throw up peculiar philosophical difficulties for a Lockean defence of intellectual property rights.)

Contact Details

Email:   ado10 at cam dot ac dot uk
Gonville and Caius College, Cambridge, CB2 1TA, UK