The Logic of Identity: A Broadly Hegelian Standpoint

It is vain to do with more what can be done with less. Entities must not be multiplied beyond necessity! --William of Occam

It is vain to try to do with fewer what requires more. Entities must not be reduced to the point of inadequacy. --Karl Menger

1.0 Introduction

In his review of Errol Harris's An Interpretation of the Logic of Hegel,¹ John E. Smith highlights what is mainly at issue between the Hegelian conception of logic and the formalist conception favored by modern empiricism and many forms of analytic philosophy. The Hegelian holds logic to be "internally related at every level to the real content it articulates" (p. 463). In contrast, the formalist pegs logic as neutral, both with respect to the "nature of things" and to "what there is" (ibid.).

How fares the logic of identity in this dispute? Is the logic of identity neutral, both to "the nature of things" and to "what there is"?

From a formalist standpoint, the identity-relation is indifferent to the nature of its terms: what a particular is (qua value of a variable) has no bearing on a particular's relation to itself. Unrelated to the things it relates, the identity-relation has its nature imposed from without, by classical axioms which appear in the guise of empirical observations or arbitrary stipulations, or as the inexpugnable avatars of a self-certifying logical truth.

In contrast, from the (broadly Hegelian) standpoint of 'A Theory of Complexes,' the properties of this relation have their source in the kind of entity over which individual variables range: a particular which, unlike the denatured simple of Russell, Bergmann, Allaire, et al.,² is ontologically differentiated and logically complex. The intrinsic features of this particular ground a minimal identity relation,³ which ramifies classically and non-classically.⁴ These features also ground a difference between formal identity (the identity of a and a) and material identity (the identity of a and b), which sets 'a = a' and 'a = b' apart in cognitive content.

The theory of complexes contains a sub-theory of their constituents: haecceities⁵ and individuals.⁶ To this sub-theory I now turn.

Haecceities and Individuals