Ontological Commitments, Thick and Thin

In George Boolos (ed.), Method, Reason and Language: Essays in Honor of Hilary Putnam. Cambridge University Press (1990)

Authors
Harold Hodes
Cornell University
Abstract
Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view.
Keywords Mathematics  Ontological Commitments
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Ontological Commitment.Agustín Rayo - 2007 - Philosophy Compass 2 (3):428–444.
Speaking with Shadows: A Study of Neo‐Logicism.Fraser MacBride - 2003 - British Journal for the Philosophy of Science 54 (1):103-163.
Plato's Problem: An Introduction to Mathematical Platonism.Marco Panza & Andrea Sereni - 2013 - London and Basingstoke: Palgrave-Macmillan.
On Specifying Truth-Conditions.Agustín Rayo - 2008 - Philosophical Review 117 (3):385-443.

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