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111Wittgenstein's Lectures on the Foundations of MathematicsPhilosophical Quarterly 27 (109): 370. 1977.
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1A Problem For The DialetheistBulletin of the Section of Logic 15 (1): 10-13. 1986.There has recently been revived logical interest, particularly in the context of attempts to solve the logico-semantical paradoxes, of the idea that there are true contracistions, and of semantics accomodating the glut value both true and false. By considering some generally accepted claims about assertion. I attempt to show that this dialetheist idea is untenable
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157III-A Unified Solution to Some ParadoxesProceedings of the Aristotelian Society 100 (1): 53-74. 2000.The Russell class does not exist because the conditions purporting to specify that class are contradictory, and hence fail to specify any class. Equally, the conditions purporting to specify the Liar statement are contradictory and hence, although the Liar sentence is grammatically in order, it fails to yield a statement. Thus the common source of these and related paradoxes is contradictory (or tautologous) specifying conditions-for such conditions fail to specify. This is the diagnosis. The cu…Read more
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1649The Barber, Russell's Paradox, Catch-22, God, Contradiction, and MoreIn Graham Priest, Jc Beall & Bradley P. Armour-Garb (eds.), The Law of Non-Contradiction: New Philosophical Essays, Oxford University Press. pp. 295--313. 2004.outrageous remarks about contradictions. Perhaps the most striking remark he makes is that they are not false. This claim first appears in his early notebooks (Wittgenstein 1960, p.108). In the Tractatus, Wittgenstein argued that contradictions (like tautologies) are not statements (Sätze) and hence are not false (or true). This is a consequence of his theory that genuine statements are pictures.
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Clear and Queer Thinking: Wittgenstein's Development and His Relevance to Modern ThoughtMind 110 (437): 207-211. 2001.
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Pasquale Frascolla, Wittgenstein's Philosophy of MathematicsPhilosophical Investigations 19 337-341. 1996.
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80A Buridanian discussion of desire, murder and democracyAustralasian Journal of Philosophy 70 (4). 1992.This Article does not have an abstract
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60To Let: Unsuccessful Stipulation, Bad Proof, and ParadoxAmerican Philosophical Quarterly 50 (1): 93. 2013.Letting is a common practice in mathematics. For example, we let x be the sum of the first n integers and, after a short proof, conclude that x = n(n+1)/2; we let J be the point where the bisectors of two of the angles of a triangle intersect and prove that this coincides with H, the point at which another pair of bisectors of the angles of that triangle intersect. Karl Weierstrass's colleagues, in an attempt to solve optimization problems, stipulated that the minimum area for a triangle with a …Read more
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269How original a work is the tractatus logico-philosophicus?Philosophy 77 (3): 421-446. 2002.Wittgenstein's Tractatus is widely regarded as a masterpiece, a brilliant, if flawed attempt to achieve an ‘unassailable and definitive … final solution’ to a wide range of philosophical problems. Yet, in a 1931 notebook, Wittgenstein confesses: ‘I think there is some truth in my idea that I am really only reproductive in my thinking. I think I have never invented a line of thinking but that it was always provided for me by someone else’. This disarming self-assessment is, I believe accurate. Th…Read more
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90Scientific scotism - the emperor's new trousers or has Armstrong made some real strides?Australasian Journal of Philosophy 61 (1). 1983.(1983). Scientific scotism — The emperor's new trousers or has armstrong made some real strides? Australasian Journal of Philosophy: Vol. 61, No. 1, pp. 40-57
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49Wittgenstein’s Most Important Contribution to the Philosophy of LogicIn Danièle Moyal-Sharrock, Volker Munz & Annalisa Coliva (eds.), Mind, Language and Action: Proceedings of the 36th International Wittgenstein Symposium, De Gruyter. pp. 3-20. 2015.
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77Translating Utterances, Reporting BeliefsThe Reasoner 2 (3): 3-4. 2008.Responds to Constaninescu on the Non-Substitutivity and suggests a better approach built on consideration of the way in which beliefs are (usually concisely) reported.
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20Goldstein invites the philosophical beginner to think hard about issues ranging from patriotism and racism to artificial intelligence and the mind, from love and fidelity to free will and mortality, taking an interdisciplinary approach.
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101Kripke, Pierre and ConstantinescuThe Reasoner 1 (5): 4-5. 2007.Refutes Cristian Constantinescu's proposed solution of Kripke's puzzle about belief.
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113The Form of The Third Man ArgumentApeiron 12 (2). 1978.Our interpretation of the "parmenides" 132a1 - 132b2 has the following features. (i) it stresses that the third man argument is an infinite regress and (ii) notes its epistemological thrust. (iii) a faithful translation of the last line of the argument reads "and no longer will each of the forms be for you one but each is infinite in multitude." parmenides' point is that each form, which socrates believed to be complete (one), turns out to be an unbounded, incompletable series of subforms useles…Read more
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262Fibonacci, Yablo, and the cassationist approach to paradoxMind 115 (460): 867-890. 2006.A syntactically correct number-specification may fail to specify any number due to underspecification. For similar reasons, although each sentence in the Yablo sequence is syntactically perfect, none yields a statement with any truth-value. As is true of all members of the Liar family, the sentences in the Yablo sequence are so constructed that the specification of their truth-conditions is vacuous; the Yablo sentences fail to yield statements. The ‘revenge’ problem is easily defused. The soluti…Read more
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169Stephen Clark, the laws of logic and the soritesPhilosophy 84 (1): 135-143. 2009.A standard method for refuting a set of claims is to show that it implies a contradiction. Stephen Clark questions this method on the grounds that the Law of Non-Contradiction, together with the other fundamental laws of logic do not accord with everyday reality. He accounts for vagueness by suggesting that, for any vague predicate 'F', an ordinary object is typically to some extent both F and not-F, and that objects do not change abruptly from being F to being not-F. I challenge Clark's 'decons…Read more
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University of KentRegular Faculty
University of St. Andrews
PhD, 1977