David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Berit Brogaard (2007). Number Words and Ontological Commitment. Philosophical Quarterly 57 (226):1–20.
Jessica Carter (2008). Categories for the Working Mathematician: Making the Impossible Possible. Synthese 162 (1):1 - 13.
Julian C. Cole (2009). Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics. Australasian Journal of Philosophy 87 (4):589-608.
Similar books and articles
Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.
Chihara Charles (2006). Burgess's ‘Scientific’ Arguments for the Existence of Mathematical Objects. Philosophia Mathematica 14 (3):318-337.
Jeffrey F. Sicha (1970). Counting and the Natural Numbers. Philosophy of Science 37 (3):405-416.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159-171.
Zvonimir Šikić (1996). What Are Numbers? International Studies in the Philosophy of Science 10 (2):159 – 171.
Neil Tennant (2003). Review of B. Hale and C. Wright, The Reason's Proper Study. [REVIEW] Philosophia Mathematica 11 (2):226-241.
Eric Steinhart (2002). Why Numbers Are Sets. Synthese 133 (3):343 - 361.
Chad A. McIntosh (2010). S5, God, and Numbers. Res Cogitans 1 (1):63-78.
Peter Sullivan & Michael Potter (1997). Hale on Caesar. Philosophia Mathematica 5 (2):135--52.
Added to index2009-01-28
Total downloads45 ( #35,252 of 1,096,609 )
Recent downloads (6 months)1 ( #265,701 of 1,096,609 )
How can I increase my downloads?