•  5
    Against Harmony
    In Bob Hale, Crispin Wright & Alexander Miller (eds.), A Companion to the Philosophy of Language, Wiley. 2017.
    This chapter concerns that harmony is a particular relationship between the introduction rule and the elimination rule for a given connective. The Harmony Thesis says that a connective is defective unless its associated introduction and elimination rules are in harmony. It also says that a connective is defective if the logical principles which regulate its use go beyond a pair of harmonious introduction and elimination rules. The chapter scrutinizes the most influential arguments which have bee…Read more
  •  46
    Reply to Øystein Linnebo and Stewart Shapiro
    Inquiry: An Interdisciplinary Journal of Philosophy 62 (7): 842-858. 2019.
    ABSTRACTIn reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis. I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so would invo…Read more
  •  25
    Logic and Existence
    Aristotelian Society Supplementary Volume 73 151-203. 1999.
    [Ian Rumfitt] Frege's logicism in the philosophy of arithmetic consisted, au fond, in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already needs to appeal in order to justify paradigmatically logical truths and paradigmatically logical forms of inference. Using ideas of Gentzen to spell out what these methods and principles might include, I sketch a strategy for vindicating this logicist claim for the special case of the ari…Read more
  •  42
    In defence of PKF
    Synthese 201 (2): 1-21. 2023.
    I advance arguments in favour of PKF as an articulation of a central sense of the predicate ‘true’, and show how it illuminates the relationship between that sense and the ‘external’ notion of truth found in such claims as ‘An utterance of the Liar Sentence does not say anything, and so is not true’.
  •  5
    Infinitesimals, Nations, and Persons
    Philosophy 94 (4): 513-528. 2019.
    I compare three sorts of case in which philosophers have argued that we cannot assert the Law of Excluded Middle for statements of identity. Adherents of Smooth Infinitesimal Analysis deny that Excluded Middle holds for statements saying that an infinitesimal is identical with zero. Derek Parfit contended that, in certain sci-fi scenarios, the Law does not hold for some statements of personal identity. He also claimed that it fails for the statement ‘England in 1065 was the same nation as Englan…Read more
  •  28
    Truth, Marks of Truth, and Conditionals
    Philosophy 97 (3): 295-320. 2022.
    This essay assesses the account of truth presented in Wiggins's 2002 paper ‘An indefinibilist cum normative view of truth and the marks of truth'. I agree with Wiggins that we should seek, not to define truth, but to elucidate it by unfolding its connections with other basic notions. However, I give reasons for preferring an elucidation based on Ramsey's account of truth to Wiggins's Tarski-inspired approach. I also cast doubt on Wiggins's thesis that convergence is a mark of truth, arguing inst…Read more
  • Neo-Fregeanism and the Burali-Forti Paradox
    In Ivette Fred Rivera & Jessica Leech (eds.), Being Necessary: Themes of Ontology and Modality from the Work of Bob Hale, Oxford University Press. pp. 188-223. 2018.
    Philip Jourdain put this question to Frege in a letter of 28 January 1909. Frege had, indeed, next to nothing to say about ordinals, and in this respect Bob Hale has followed the master. As I hope this chapter will show, though, the topic is worth addressing. The natural abstraction principle for ordinals combines with full, impredicative second-order logic to engender a contradiction, the so-called Burali-Forti Paradox. I shall contend that the best solution involves a retreat to a predicative …Read more
  •  21
    What is Logic?
    In Zsolt Novák & András Simonyi (eds.), Truth, reference, and realism, Central European University Press. pp. 125-176. 2010.
  •  46
    When I was a student in the mid-1980s, Donald Davidson loomed larger over the philosophical scene than any other living thinker. His writings figured prominentl.
  •  11
    Donald Davidson and the Mirror of Meaning
    Philosophical Quarterly 45 (178): 136-137. 1995.
  •  696
    Intuitionism and the Modal Logic of Vagueness
    Journal of Philosophical Logic 49 (2): 221-248. 2020.
    Intuitionistic logic provides an elegant solution to the Sorites Paradox. Its acceptance has been hampered by two factors. First, the lack of an accepted semantics for languages containing vague terms has led even philosophers sympathetic to intuitionism to complain that no explanation has been given of why intuitionistic logic is the correct logic for such languages. Second, switching from classical to intuitionistic logic, while it may help with the Sorites, does not appear to offer any advant…Read more
  •  47
    Reply to Crispin Wright and Richard Zach
    Philosophical Studies 175 (8): 2091-2103. 2018.
  •  30
    Précis of The Boundary Stones of Thought
    Philosophical Studies 175 (8): 2063-2066. 2018.
  •  16
    Prospects for Justificationism
    In Michael Frauchiger (ed.), Truth, Meaning, Justification, and Reality: Themes From Dummett, De Gruyter. pp. 123-152. 2017.
  •  19
    Dummett Laudatio
    In Michael Frauchiger (ed.), Truth, Meaning, Justification, and Reality: Themes From Dummett, De Gruyter. pp. 13-24. 2017.
  •  33
    Brouwer Wittgenstein on the Infinite and the Law of Excluded Middle
    Grazer Philosophische Studien 89 (1): 93-108. 2014.
  •  167
    I—Ian Rumfitt: Truth and Meaning
    Aristotelian Society Supplementary Volume 88 (1): 21-55. 2014.
    Should we explicate truth in terms of meaning, or meaning in terms of truth? Ramsey, Prior and Strawson all favoured the former approach: a statement is true if and only if things are as the speaker, in making the statement, states them to be; similarly, a belief is true if and only if things are as a thinker with that belief thereby believes them to be. I defend this explication of truth against a range of objections.Ramsey formalized this account of truth as follows: B is true =df ∃P; in §i, I…Read more
  •  41
    Donald Davidson and the Mirror of Meaning
    Philosophical Quarterly 45 (178): 136. 1995.
    Review of J.E. Malpas, *Donald Davidson and the Mirror of Meaning* (CUP)
  •  16
    Peer Reviewed.
  •  598
    This paper assesses the prospects of a pragmatist theory of content. I begin by criticising the theory presented in D.H. Mellor’s essay ‘Successful Semantics’. I then identify problems and lacunae in the pragmatist theory of meaning sketched in Chapter 13 of Dummett’s The Logical Basis of Metaphysics. The prospects are brighter, I contend, for a tempered pragmatism, in which the theory of content is permitted to draw upon irreducible notions of truth and falsity. I sketch the shape of such a…Read more
  •  184
    Ricky ponting and the judges
    Analysis 70 (2): 205-210. 2010.
    This article proposes revisions to the Laws of Cricket and to the criminal law of England. The Laws of Cricket should be revised so that an umpire may give a batsman out without having to specify precisely how he got out. The criminal law should be revised so that (e.g.) aiding and abetting a murderer is not subsumed under the crime of murder.
  •  5
    Meaning and understanding
    In Frank Jackson & Michael Smith (eds.), The Oxford Handbook of Contemporary Philosophy, Oxford University Press. 2005.
  •  2
    15 Inference, Deduction, Logic
    Philosophical Inquiry 36 (1-2): 334. 2012.
  •  267
    Sentences, names and semantic values
    Philosophical Quarterly 46 (182): 66-72. 1996.
  •  131
    On A Neglected Path to Intuitionism
    Topoi 31 (1): 101-109. 2012.
    According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, ev…Read more
  •  236
    Knowledge by deduction
    Grazer Philosophische Studien 77 (1): 61-84. 2008.
    It seems beyond doubt that a thinker can come to know a conclusion by deducing it from premisses that he knows already, but philosophers have found it puzzling how a thinker could acquire knowledge in this way. Assuming a broadly externalist conception of knowledge, I explain why judgements competently deduced from known premisses are themselves knowledgeable. Assuming an exclusionary conception of judgeable content, I further explain how such judgements can be informative. (According to the exc…Read more