Speaking with shadows: A study of neo-logicism

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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Neo-Fregean Ontology.Matti Eklund - 2006 - Philosophical Perspectives 20 (1):95–121.
Metaontology.Matti Eklund - 2006 - Philosophy Compass 1 (3):317-334.
Comparing Peano Arithmetic, Basic Law V, and Hume’s Principle.Sean Walsh - 2012 - Annals of Pure and Applied Logic 163 (11):1679-1709.
Neo-Fregeanism and Quantifier Variance.Theodore Sider - 2007 - Aristotelian Society Supplementary Volume 81 (1):201–232.
Bad Company and Neo-Fregean Philosophy.Matti Eklund - 2009 - Synthese 170 (3):393-414.

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