Definition

Aristotle observes that the primary innovation of Plato's System is not so much its 'Forms', which Aristotle argues is implicit in Pythagoreanism, but its focus on definitions as the fundamental objects of Knowledge. For sure, Plato does argue in places that arrival at a definition is the aim of any inquiry, and, as Aristotle could not have known, the formulation of definitions has been central to most, if not all, of the subsequent intellectual tradition, e. g. scientific laws. Still, regardless of how accurate Aristotle's assessment might be, it masks a profound paradox: if the object of knowledge is a definition, then knowledge of Definition is the definition of Definition; but, if so, the effort to define Definition is impossible, since any instruction as to how to go about producing a definition of Definition is lacking at the outset. One resolution of the paradox is that the knowledge of Definition is intuitive and pre-verbal, which is what Plato's theory of Forms is traditionally taken to assert. On the other hand, so-called Nominalism asserts that Definition is arbitrarily stipulative, which is usually interpreted as an antithetical to Platonism, but, rather, is complementary to it--the basis of a theory of discursive Knowledge vs. Platonism as a theory of non-discursive Knowledge, which Spinoza distinguishes as merely two different types of Knowledge. A third alternative, Pragmatism, treats Definition as preceptive, which seems to amount to only a practical variation of Nominalism. Formaterialism regards all these notions of Definition as foundational, namely as providing a point of departure for the pursuit of Knowledge, theoretical or practical, in contrast with which it regards Definition as itself an ordering principle. That is, Definition is itself the ordering of any foundation-derivative relation, insofar as it entails both definiens and definiendum. Furthermore, Definition is self-exemplifying--the definition of Definition applies to itself--and, hence, is internally dynamic. In places, Plato seems to toy with the notions that a Form is self-predicating, and that it has causal efficacy, both of which seem to lead him into inextricable difficulties. Perhaps the notion of a Form as dynamically self-exemplifying avoids such problems.