Speaking with shadows: A study of neo-logicism

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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Katherine Ritchie (2015). Can Semantics Guide Ontology? Australasian Journal of Philosophy 94 (1):24-41.
Theodore Sider (2007). Neo-Fregeanism and Quantifier Variance. Aristotelian Society Supplementary Volume 81 (1):201–232.
Matti Eklund (2006). Metaontology. Philosophy Compass 1 (3):317-334.
Matti Eklund (2006). Neo-Fregean Ontology. Philosophical Perspectives 20 (1):95–121.

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