David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Noûs 31 (3):307-336 (1997)
We examine the arguments on both sides of the recent debate (Hale and Wright v. Field) on the existence, and modal status, of the natural numbers. We formulate precisely, with proper attention to denotational commitments, the analytic conditionals that link talk of numbers with talk of numerosity and with counting. These provide conceptual controls on the concept of number. We argue, against Field, that there is a serious disanalogy between the existence of God and the existence of numbers. We give stronger reasons than those advanced by Wright for resisting Field's analogy. We argue that the rules governing the basic numerical notions commit us to the natural numbers as necessary existents. We also show that the latest twist in the debate involving 'surdons' leaves both sides in a stalemate
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Berit Brogaard (2007). Number Words and Ontological Commitment. Philosophical Quarterly 57 (226):1–20.
Øystein Linnebo (2004). Predicative Fragments of Frege Arithmetic. Bulletin of Symbolic Logic 10 (2):153-174.
J. P. Studd (2016). Abstraction Reconceived. British Journal for the Philosophy of Science 67 (2):579-615.
George Duke & Peter Woelert (2016). Husserl and the Problem of Abstract Objects. Pacific Philosophical Quarterly 97 (1):27-47.
Julian C. Cole (2009). Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics. Australasian Journal of Philosophy 87 (4):589-608.
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