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By defining God as a maximally great being Plantinga is able to devise an ontological argument which validly infers from the possibility of there being a God that there necessarily is a God. In this article I shall argue that Plantinga’s argument is not only question-begging, as several critics have complained, but circular in the strongest sense of the term. Based on reflections on the relation between the notions of coherence and possibility, I shall defend two arguments, previously proposed by Tooley (Mind 90:422–427, 1981) and Guleserian (Nous 17:221–238, 1983), against the existence of a maximally great being. The article concludes with some critical remarks on Plantinga’s rationale for conceiving God as such a being.

The positivists defined analyticity as truth in virtue of meaning alone and advocated the view that the notion of analyticity so defined is co-extensive with both the notion of an a priori truth an...

According to Hume’s principle, a sentence of the form ⌜The number of Fs = the number of Gs⌝ is true if and only if the Fs are bijectively correlatable to the Gs. Neo-Fregeans maintain that this principle provides an implicit definition of the notion of cardinal number that vindicates a platonist construal of such numerical equations. Based on a clarification of the explanatory status of Hume’s principle, I will provide an argument in favour of a nominalist construal of numerical equations. The neo-Fregean objections to such a construal will be examined and rejected. And the implications of the nominalist construal for the use of numerals and for the understanding of ontological questions for the existence of numbers will be spelled out.

The paper provides an interpretation of Wittgenstein’s claim that a mathematical proof must be surveyable. It will be argued that this claim specifies a precondition for the applicability of the word ‘proof’. Accordingly, the latter is applicable to a proof-pattern only if we can come to agree by mere observation whether or not the pattern possesses the relevant structural features. The claim is problematic. It does not imply any questionable finitist doctrine. But it cannot be said to articulate a feature of our actual usage of the word ‘proof’. The claim can be dissociated, however, from two tenable doctrines of Wittgenstein, namely that proofs can be used as paradigms for corresponding proof concepts and that a proof is not an experiment.

The author critically examines Wittgenstein’s and Waismann’s objections to the explanation of equinumerosity in terms of one-one correlations. They are right to maintain that the actuality of a one-one correlation is not a necessary condition for equinumerosity. But, contrary to what they claim, the possibility of such a correlation is equivalent with equinumerosity. The author shows how this equivalence can be used to explain the use of ‘just as many’, thereby also responding to Husserl’s objection that this phrase is indefinable. And against all three authors it is argued that there are no semantically relevant equinumerosity criteria besides one-one correlatability.

Fine bases his influential conception of essence on a particular account of definitions. And he complements it with a specific account of analyticity. I will argue that Fine's conception of relative analyticity confuses the idea of a sentence's being true in virtue of a term's definition with the idea of a sentence's being true in virtue of a term's meaning. His idea that correct definitions specify essential properties of meanings is mistaken. The correctness of definitions can only be assessed by reference to the actual usage of the terms involved. The resulting conception of definitions leads to a deflationary interpretation of claims about essences.

The volume contains new essays on Wittgenstein and on Quine. Six essays discuss crucial aspects of Wittgenstein’s philosophy of mathematics: Wittgenstein’s ontological quietism in relation to the realism vs. anti-realism debate, his thesis that mathematical propositions are rules of grammar, his perspectives on the nature of numbers, and on equinumerosity and surveyability, his treatment of mathematical formulas, and his disagreements with Brouwer over the infinite and the law of excluded middle. Six essays are dedicated to the philosophy of Willard Van Orman Quine: they discuss Quine’s stance towards the notion of meaning in linguistics and philosophy, his thesis of the indeterminacy of radical translation, his naturalism in semantics, his brand of nominalism, and his attempt to reconstruct possible worlds within an extensionalist framework. Contributors are: Oswald Chateaubriand, Pasquale Frascolla, Dirk Greimann, Peter Hylton, Guido Imaguire, Mathieu Marion, Felix Muhlholzer, Mitsuhiro Okada, Esther Ramharter, Ian Rumfitt, Pedro Santos, Severin Schroeder, Rogerio Passos Severo