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Reply to Professor Bar-Hillel

In Imre Lakatos (ed.), Problems in the Philosophy of Mathematics. Amsterdam: North-Holland Pub. Co.. pp. 175--178 (1967)

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  1. Logic and Ontological Pluralism.Jason Turner - 2012 - Journal of Philosophical Logic 41 (2):419-448.
    Ontological pluralism is the doctrine that there are different ways or modes of being. In contemporary guise, it is the doctrine that a logically perspicuous description of reality will use multiple quantifiers which cannot be thought of as ranging over a single domain. Although thought defeated for some time, recent defenses have shown a number of arguments against the view unsound. However, another worry looms: that despite looking like an attractive alternative, ontological pluralism is really no different than its counterpart, (...)
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  • A Note on the Relation Between Formal and Informal Proof.Jörgen Sjögren - 2010 - Acta Analytica 25 (4):447-458.
    Using Carnap’s concept explication, we propose a theory of concept formation in mathematics. This theory is then applied to the problem of how to understand the relation between the concepts formal proof and informal, mathematical proof.
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  • Plurals.Agustín Rayo - 2007 - Philosophy Compass 2 (3):411–427.
    Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant.
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  • Toward a modal-structural interpretation of set theory.Geoffrey Hellman - 1990 - Synthese 84 (3):409 - 443.