Ways of Being Singular: The Logic of Individuality

• Author: Robert Berman
• Position: Professor of Philosophy, Xavier University, New Orleans
• Pages: 109-124

Page 109

Introduction

Ordinary thought has always operated with four distinct conceptions of individuality. The first, a minimal conception, which is ingredient in all the others, is the notion of an individual as merely the countable referent of a singular term, more precisely of a proper name. In this minimal sense of individuality, an individual is whatever is one, or single and namable, as a target for speech and thought. Thus, on the minimal conception, individuality pertains to virtually anything to which singular reference can be made. The three additional ideas of individuality presuppose, but go beyond, this minimal conception. Individuality as exclusivity is the idea of the sole or exclusive one -one of a kind. The God of monotheism is a paradigm of this conception of individuality. Individuality as virtuosity is that of a one singled out because it is the best of the bunch, the virtuoso. Finally, individuality as novelty is the idea of a one that, due to its uniqueness, escapes virtually all classification, for it is like nothing else. It is so radically different that it is literally sui generis and, for that reason, in a class by itself. An exemplary case of individuality embodying virtuosity and novelty is suggested by Hegel's understanding of Socrates' singularity as the philosopher of world-historical significance.

While many thinkers have talked about individuality in one or another of these ways, only Hegel offers an account of the logic of individuality that provides what is conceptually needed to reconstruct the pre-theoretical fourfold distinction in a systematic way. The point of this paper is to offer a set-theoretical interpretation of Hegel's systematic logical account of individuality and, in doing so, to suggest how to understand the systematic basis for the pre-theoretical conception of individuality.¹Page 110

As is well-known, Hegel's account of individuality in the Science of Logic ("Logic") is introduced early on in the subjective part of his logic; more specifically, it is the culminating phase of his account of the concept, which yields the unique tripartite logical division of the concept into universality, particularity, and individuality.² I will refer to this tripartite division from now on as the Distinction, and my strategy will be to approach the topic of individuality by way of a set-theoretical interpretation of the Distinction. While the article's limited purpose will not permit exploration beyond this narrow field, pursuing this aim leaves unexamined a set of underlying assumptions about systematic philosophy, the nature of logic, and its function as a part of that systemic whole. Because these assumptions serve as a kind of outer frame for the ensuing discussion and thus will inevitably make themselves felt throughout, they should be exposed at the outset. In particular the following interlinked claims deserve special mention:

(1) Philosophy on the systematic view is a kind of knowledge. It achieves its knowledge in part through a reconstructive enterprise. It takes the pre-theoretical givens of intuition and representation and rethinks them, conceptualizing those given contents by distilling their logical core and assigning them their rightful place in a system of knowledge.

(2) Because the reconstructive enterprise depends on independent access to that logical core, which comes through logic, the latter provides philosophy with its epistemology. Logic takes the form of a self-justifying, topic-neutral discourse, developing a regionally unrestricted theory of categories. It develops these interrelated categories from an original indeterminacy and, beholden only to strictures of immanence, culminates in the grounding logical idea, which, as the fully realized structure of self-determination, provides the privileged vehicle of philosophical knowledge.

(3) This means that philosophy is primarily knowledge of ideas, where ideas are correspondence relations between concepts and their objective realizations. While ideas are identities of concept and object, concepts are to be conceived in terms of the Distinction and, when fully determined, as individuals. It follows that philosophical knowledge isPage 111 structured and guided by knowledge of the Distinction, and thus ultimately by subject matter having the character of individuality.

(4) The treatment of the Distinction, and with it the logic of individuality in the subjective logic, emerges from the upshot of the objective logics of the categories of being and essence. The systematic logical conception of the individual is the earliest adumbration of the logical idea. The individual, in the language of the systematic logical account, is unity of universality and particularity, the unity of self-relation and determinacy, the unity of identity and difference, the determinate determinate. The individual is the particular in which the universal posits itself as itself.³ These formulations commit Hegel to a dynamic interrelation among the components of the Distinction. To begin with, the universal implies the particular, for it is the unity of identity and determinacy. As determinate, the universal requires relation to an other; hence, it particularizes itself. This implies, in turn, the difference between universal and particular. Yet, because in the end the concept is universal and therefore self-identical, there is not and cannot be a genuinely ultimate other. All conceptual relations are, at the end of the day, self-relations. Thus, the particularity of the concept as the determinacy of the universal, which in its determinacy implies relation to an other, must be at one with the universal, since universality is identity, or self-relation. Finally, the particular, as united with the universal, is the individual. The universal, in being determinate and hence particular, but nonetheless at one with itself-bei sich-is the individual. To be bei sich is to be free; thus, the logic played out in terms of the Distinction is the logic of freedom.

Before proceeding further, a terminological point should be made. Hegel himself uses several different expressions, for example, "Einzelheit" "das Einzelne" and "einzel" "Individualitat" and "In-dividuum" all of which can with justification be translated into English using either the term "individual" (as noun or adjective) or "individuality." But since the English "individuality" and "individual" literally translate into "Individualitat" and "Individuum" respectively, there is a case to be made for choosing to translate "Einzelheit" "das Einzelne," and "einzel" using a different English expression, namely, "singularity," "the singular," and "single" or "singular," respectively. Not only would this reproduce the linguistic difference in the original, but to do so would capture the presence in "Einzelheit" of the numerical term "eins"Page 112 or one (i.e., a single countable item). As will emerge in the sequel, there are other connotations of the English term "singular" that resonate in the logical discussion of individuality. Nevertheless, although one might try to argue on the basis of this linguistic evidence that Hegel actually intends his use of the distinct German terms to mark a systematic conceptual distinction, no attempt has been made here to argue this point. Instead, the terms "singular" and "singularity" will simply be used more or less interchangeably with "individual" and "individuality." The discussion that follows will proceed in two steps. Part I contains the set-theoretical interpretation of the systematic logical account of the Distinction, specifically the conception of individuality. Two major claims are at issue: (1) there are initially three possible set-theoretical interpretations of the Distinction and thus of individuality, and (2) only one of them best fits or corresponds to the systematic logical account of the Distinction. After arguing for the favored set-theoretical interpretation of the systematic logical account of the Distinction and individuality, Part II of the paper will consider three significant objections and offer replies in defense of the claims of Part I.

I The Set-Theoretical Interpretation of Individuality

A Three Models of the Distinction

Consider the following three sets of examples. Each contain five claims, all familiar enough, the first inspired by Plato, the second and third by Aristotle, and the last two taken from Hegel. Each of these sets of examples provides a different set-theoretical model for understanding the systematic logical account of the Distinction.

i The Virtuosity Model

(1) There are many kinds of cities; however, that city alone is really just whose every essential characteristic reflects the principle of justice. The single city that is ideal is the one that is most real. It is, in this sense, the true city.⁴

(2) There are diverse kinds of friendship: friendship based on pleasure, utility, and virtue. However, virtue friendship, or the friendship of the good, is the unique or singular form of friendship, for it alone fully realizes the principle of friendship. It best instantiates what friendshipPage 113 really is because it embodies the requirements specified by the concept of friendship. Friendship among the virtuous is the truth of friendship.⁵

(3) There may be a variety of ways of living well; however, there is only one way of life-the life of contemplation-that counts as the primary or outstanding form of living well or...