David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
British Journal for the Philosophy of Science 54 (1):103-163 (2003)
According to the species of neo-logicism advanced by Hale and Wright, mathematical knowledge is essentially logical knowledge. Their view is found to be best understood as a set of related though independent theses: (1) neo-fregeanism-a general conception of the relation between language and reality; (2) the method of abstraction-a particular method for introducing concepts into language; (3) the scope of logic-second-order logic is logic. The criticisms of Boolos, Dummett, Field and Quine (amongst others) of these theses are explicated and assessed. The issues discussed include reductionism, rejectionism, the Julius Caesar problem, the Bad Company objections, and the charge that second-order logic is set theory in disguise. The irresistible metaphor is that pure abstract objects [...] are no more than shadows cast by the syntax of our discourse. And the aptness of the metaphor is enhanced by the reflection that shadows are, after their own fashion, real. (Crispin Wright , p. 181-2) But I feel conscious that many a reader will scarcely recognise in the shadowy forms which I bring before him his numbers which all his life long have accompanied him as faithful and familiar friends; (Richard Dedekind , p. 33)
|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
Sean Walsh (2012). Comparing Peano Arithmetic, Basic Law V, and Hume's Principle. Annals of Pure and Applied Logic 163 (11):1679-1709.
David Liggins (2010). Epistemological Objections to Platonism. Philosophy Compass 5 (1):67-77.
Theodore Sider (2007). Neo-Fregeanism and Quantifier Variance. Aristotelian Society Supplementary Volume 81 (1):201–232.
Richard Pettigrew (2008). Platonism and Aristotelianism in Mathematics. Philosophia Mathematica 16 (3):310-332.
Katherine Hawley (2007). Neo‐Fregeanism and Quantifier Variance. Aristotelian Society Supplementary Volume 81 (1):233 - 249.
Similar books and articles
Bob Hale & Crispin Wright, Focus Restored Comment on John MacFarlane's “Double Vision: Two Questions About the Neo-Fregean Programme”.
Roy T. Cook (2003). Aristotelian Logic, Axioms, and Abstraction. Philosophia Mathematica 11 (2):195-202.
José Ferreiros (1997). Notes on Types, Sets, and Logicism, 1930-1950. Theoria 12 (1):91-124.
Roy T. Cook (2002). The State of the Economy: Neo-Logicism and Inflationt. Philosophia Mathematica 10 (1):43-66.
Alexander Bird (1997). The Logic in Logicism. Dialogue 36 (02):341--60.
Marcus Rossberg & Philip A. Ebert (2007). What is the Purpose of Neo-Logicism? Traveaux de Logique 18:33-61.
Philip A. Ebert & Marcus Rossberg (2009). Ed Zalta's Version of Neo-Logicism: A Friendly Letter of Complaint. In Hannes Leitgeb & Alexander Hieke (eds.), Reduction – Abstraction – Analysis. Ontos. 11--305.
Bird Alexander (1997). The Logic in Logicism. Dialogue 36:341�60.
Harold T. Hodes (2004). On The Sense and Reference of A Logical Constant. Philosophical Quarterly 54 (214):134-165.
Added to index2009-01-28
Total downloads90 ( #16,581 of 1,410,304 )
Recent downloads (6 months)7 ( #30,399 of 1,410,304 )
How can I increase my downloads?