David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Mind 107 (428):763-798 (1998)
Naive set theory, as found in Frege and Russell, is almost universally believed to have been shown to be false by the set-theoretic paradoxes. The standard response has been to rank sets into one or other hierarchy. However it is extremely difficult to characterise the nature of any such hierarchy without falling into antinomies as severe as the set-theoretic paradoxes themselves. Various attempts to surmount this problem are examined and criticised. It is argued that the rejection of naive set theory inevitably leads one into a severe scepticism with regard to the feasibility of giving a systematic semantics for set theory. It is further argued that this is not just a problem for philosophers of mathematics. Semantic scepticism in set theory will almost inevitably spill over into total pessimism regarding the prospects for an explanatory theory of language and meaning in general. The conclusion is that those who wish to avoid such intellectual defeatism need to look seriously at the possibility that it is the logic used in the derivation of the paradoxes, and not the naive set theory itself, which is at fault.
|Keywords||No keywords specified (fix it)|
No categories specified
(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
Stewart Shapiro (2010). So Truth is Safe From Paradox: Now What? [REVIEW] Philosophical Studies 147 (3):445 - 455.
Philip A. Ebert & Stewart Shapiro (2009). The Good, the Bad and the Ugly. Synthese 170 (3):415 - 441.
A. C. Paseau (2013). An Exact Measure of Paradox. Analysis 73 (1):17-26.
S. Shapiro (2011). The Company Kept by Cut Abstraction (and its Relatives). Philosophia Mathematica 19 (2):107-138.
Peter Verdée (2013). Non-Monotonic Set Theory as a Pragmatic Foundation of Mathematics. Foundations of Science 18 (4):655-680.
Similar books and articles
Andrea Cantini (2003). The Undecidability of Grisin's Set Theory. Studia Logica 74 (3):345 - 368.
Zach Weber (2010). Extensionality and Restriction in Naive Set Theory. Studia Logica 94 (1):87 - 104.
Michael Glanzberg (2003). Minimalism and Paradoxes. Synthese 135 (1):13 - 36.
Kazushige Terui (2004). Light Affine Set Theory: A Naive Set Theory of Polynomial Time. Studia Logica 77 (1):9 - 40.
Christopher Menzel (1986). On the Iterative Explanation of the Paradoxes. Philosophical Studies 49 (1):37 - 61.
Loïc Colson (2007). Another Paradox in Naive Set-Theory. Studia Logica 85 (1):33 - 39.
Michael D. Potter (2004). Set Theory and its Philosophy: A Critical Introduction. Oxford University Press.
Joseph S. Ullian (1969). Is Any Set Theory True? Philosophy of Science 36 (3):271-279.
Harty Field (2004). The Consistency of the Naïve Theory of Properties. Philosophical Quarterly 54 (214):78 - 104.
Added to index2009-01-28
Total downloads24 ( #80,873 of 1,413,361 )
Recent downloads (6 months)1 ( #154,160 of 1,413,361 )
How can I increase my downloads?