Laws, Identities, and Reduction

Abstract

The language of a scientific theory is often assumed to consist of certain logical and mathematical symbols plus nonlogical constants.¹ In particular, the ‘logical symbols’ are often those used in set theory together with mathematical symbols definable in set theory. The nonlogical constants are considered to be predicate constants (including function symbols) which are interpreted as denoting sets, or sets of ordered n-tuples, of objects in the domain of the theory in question. Within such a language a universal law, of the simplest possible form, is represented by a sentence of the form

$$\left( x \right)\left( { \propto x \to \beta x} \right)$$

(1)

where ‘→’ is the material conditional, and α and β are predicates.

This research was partially supported by U.S. National Science Foundation grant GS-39664.