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.
Highlights
Professor Bob Hale passed away shortly after completing this paper
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
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
Summary
Certain aspects of ordinary talk and thought about number and counting, there is, it seems to me, good reason to view them as explications in something like Carnap’s sense In all of these kinds of definition, the aim is to fix the meaning of a word or other expression. Some of the theoretical identifications Kripke discusses in Naming and Necessity (Kripke 1980), not expressly presented as such, may plausibly be seen as definitions of this kind: Water is H2O Light is electromagnetic radiation between certain wavelengths Heat is the motion of molecules Lightning is an electrical discharge These are only rough and ready, but they capture the essential ideas of more accurate scientific statements of the nature of water, light, etc., as contrasted with explanations of the ordinary meanings of the corresponding words. To prepare the ground for the resolution I shall propose, it will be useful to begin with the question: How, in general, are verbal and real definition related?
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