Speaking with Shadows: A Study of Neo‐Logicism

British Journal for the Philosophy of Science 54 (1):103-163 (2003)
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Abstract

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.

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10.1093/bjps/54.1.103

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Fraser MacBride
University of Manchester

Citations of this work

Naturalism.Davidn D. Papineau - 2007 - Stanford Encyclopedia of Philosophy.
Abstract objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
Neo-Fregean ontology.Matti Eklund - 2006 - Philosophical Perspectives 20 (1):95-121.
Neo-fregeanism and quantifier variance.Theodore Sider - 2007 - Aristotelian Society Supplementary Volume 81 (1):201–232.
Metaontology.Matti Eklund - 2006 - Philosophy Compass 1 (3):317-334.

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References found in this work

Philosophical Investigations.Ludwig Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell. Edited by G. E. M. Anscombe.
A World of States of Affairs.D. M. Armstrong - 1996 - New York: Cambridge University Press.
Truth and objectivity.Crispin Wright - 1992 - Cambridge: Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

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