Authors
Fraser MacBride
University of Manchester
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.
Keywords neo-logicism  neo-Fregeanism  Meta-Ontology  Numbers  Abstract objects  Second order logic  Julius Caesar Problem  Bad Company Objection  Wright  Dummett
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DOI 10.1093/bjps/54.1.103
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References found in this work BETA

Philosophical Investigations.Ludwig Josef Johann Wittgenstein - 1953 - New York, NY, USA: Wiley-Blackwell.
A World of States of Affairs.D. M. Armstrong - 1997 - Cambridge University Press.
Truth and Objectivity.Crispin Wright - 1992 - Harvard University Press.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.

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Citations of this work BETA

Naturalism.Davidn D. Papineau - 2007 - Stanford Encyclopedia of Philosophy.
Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
The Functional Composition of Sense.Bryan Pickel - 2021 - Synthese 199 (3-4):6917-6942.
Neo-Fregean Ontology.Matti Eklund - 2006 - Philosophical Perspectives 20 (1):95-121.
Neo-Logicism and Its Logic.Panu Raatikainen - 2020 - History and Philosophy of Logic 41 (1):82-95.

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