Synthese 198 (Suppl 8):2001-2017 (2018)

Abstract
We may define words or concepts, and we may also, as Aristotle and others have thought, define the things for which words stand and of which concepts are concepts. Definitions of words or concepts may be explicit or implicit, and may seek to report preexisting synonymies, as Quine put it, but they may instead be wholly or partly stipulative. Definition by abstraction, of which Hume’s principle is a much discussed example, seek to define a term-forming operator, such as the number operator, by fixing the truth-conditions of identity-statements featuring terms formed by means of that operator. Such definitions are a species of implicit definition. They are typically at least partly stipulative. Definitions of things, or real definitions, are, by contrast, typically conceived as true or false statements about the nature or essence of their definienda, and so not stipulative. There thus appears to be an obvious and head-on clash between taking Hume’s principle as an implicit and at least partly stipultative definition of the number operator and taking it as a real definition, stating the nature or essence of cardinal numbers. This paper argues that this apparent tension can be resolved, and that resolving it sheds light on part of the epistemology or essence and necessity, showing how some of our knowledge of essence and necessity can be a priori.
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DOI 10.1007/s11229-018-1726-7
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References found in this work BETA

Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
The Seas of Language.Michael Dummett - 1993 - Oxford University Press.
Two Dogmas of Empiricism.W. V. Quine - 1951 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.
Aristotle on Meaning and Essence.David Charles - 2000 - Oxford University Press.

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Citations of this work BETA

Putting Modal Metaphysics First.Antonella Mallozzi - 2018 - Synthese (Suppl 8):1-20.
Superexplanations for Counterfactual Knowledge.Antonella Mallozzi - 2021 - Philosophical Studies 178 (4):1315-1337.

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