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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| 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.
Science Without Numbers: A Defence of Nominalism.Hartry H. Field - 1980 - Princeton, NJ, USA: Princeton University Press.
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