Consequences of Indefiniteness or Variation
I will begin by examining first the implications the inexactness under consideration might have for the diagnostic role of definitions. I argued in chapter 2 that the Socrates of Plato's Early Dialogues takes the definition of a kind F to be necessary and sufficient for determining whether some
particular is a member of that kind, whether it is an F. Although Aristotle does not seem to take this Socratic-Platonic thesis to be universally true (as Socrates and Plato do), he argues that a restricted version of it is true—at least with some matters of conduct definitions are indispensable. There must be definitions, he claims, of those things about which there are disagreements or disputes:
8.15 | But since it often happens that a man, while admitting the fact, denies the charge or the point on which it turns—for instance, admits that he took something, but did not steal it; that he was the first to strike, but committed no outrage; that he had relations, but did not commit adultery; or that he stole something but was not guilty of sacrilege, since the object in question was not consecrated; or that he trespassed, but on public land; or that he communicated with the enemy, but was not guilty of treason—for this reason it will be necessary to define [  |
There are several problems with accepting the general Socratic-Platonic or even the more restricted Aristotelian thesis that the definition of F is necessary and sufficient for knowing that some particular is F. One may, for example, deny that knowledge of the definition of F is required for determining whether some x is F.[10] One may argue that explicit knowledge of the definition of F is not required, but only an implicit or tacit one,[11] or that regardless of how exact our definition of F is, it is not sufficient for determining that any x is F.[12]
The above problems with the Socratic-Platonic thesis regarding the diagnostic use of definitions are not the problems I wish to discuss here, however. For the concern is with what follows with regard to the use of definitions from Aristotle's claims that the strict essentialism of Socrates, Plato, and at times Aristotle himself does not apply to some or all matters of conduct, or that definitions of such matters are inexact. Let us assume for the moment that the Socratic-Platonic thesis of the diagnostic use of definitions is correct: Knowledge of the definition of F is both necessary and sufficient for determining that some particular is F. The problem is with using definitions that are inexact or indefinite or defeasible for diagnostic purposes.
In the extreme case where no definitions at all are possible there would, of course, be nothing to serve the diagnostic purposes Socrates and Plato assign to definitions. In this sense, perhaps, Aristotle's claims about the inexactness of matters of conduct can be looked upon as being indirectly an argument against the general Socratic-Platonic thesis that the definition of F is necessary for determining that any x is F. For if Aristotle were to make the rather extreme claim that no definition of F is at all possible
and the claim were to be correct, it would have provided him, when taken together with the rather noncontroversial assumption that one knows that some particular x is F, with an indirect argument against the Socratic-Platonic thesis that the definition of F is necessary for knowing that x is F. It is doubtful, however, that Aristotle makes such an extreme claim, that he denies that definitions of matters of conduct are possible at all.
Even where definitions can, with the associated difficulties Aristotle himself mentions, be attained, they could not function as diagnostic tools in the way Socrates and Plato expect. For consider the Socratic view of the diagnostic use of definition that is stated by Socrates in 2.3, where he says that the definition is to be used as a model, as something by which we will "be able to say that anything you [Euthyphro] or others do that is similar to it is pious and that which is not similar I [Socrates] will be able to say that it is not." Consider also how Plato wishes to use the Forms or our accounts of their nature as models for making correct judgments about things and for realizing the proper political association (2.6, 2.7). But if Aristotle is correct, if the definition of some F is true only for the most part, if it is defeasible, it could not be a means, as Socrates says it can be, for determining all the things that are F. There will be things to which the definition does not apply or, to use Socrates' way of putting it, there will be things that do not agree with the model of F, but which are F. Perhaps, then, one can say that the definition of F will be at best useful for diagnostic purposes in most cases.
But suppose, in addition, that a definition is, as Aristotle claims, vague or indefinite. There will be further problems when one attempts to use such a definition as a diagnostic tool. A definition that does not single out a set of well-defined properties, a strict structure or essence, for a kind F will not be as effective a tool as Socrates and Plato assume it will be for determining the membership of F. Consider, for instance, Aristotle's account of gentleness in N.E. : "Gentleness is the observance of the mean in relation to anger . . . . Now we praise a man who feels anger on the right grounds and against the right persons, and also in the right manner and the right moment and for the right length of time. He may then be called gentle-tempered, if we take gentleness to be a praiseworthy quality" (1125b26ff.). A definition such as the one Aristotle gives here may have its uses, and I do not mean to claim that it gives us no information about gentleness. Of course it does, but it is obvious that this account of gentleness cannot be the model that Socrates and Plato expect it to be for determining what is an instance of gentleness and what is not.
When Aristotle finds it difficult to define things that exhibit variation or indefiniteness he argues that decisions in such things rests with perception (8.3, 8.5). Thus, he could be construed as shifting the role Socrates and Plato assign to the definition of F (or to universal features) for knowing
that some particulars are F to perception of the particulars themselves. Yet there are undoubtedly problems with the move of shifting the diagnostic role to perception. In some cases perception may make the difference by revealing features that one had overlooked and which may very well determine whether something is an instance of a particular kind—for example, perception of the particulars may be sufficient for determining that a certain act of communicating with the enemy is or is not an instance of treason (8.5). But there will also be problematic cases that the move of falling back on perception may not be able to handle. If the phenomena exhibit the degree of variation or indefiniteness, if they lack an essential pattern to the extent Aristotle at times thinks they do, how is one to decide that something belongs to a certain kind by falling back on perception? For what are we supposed to perceive or recognize by perceiving the particulars? Not the essence of the kind, for example, of gentleness or friendship, for this is precisely where, according to Aristotle, the problems lie. There may be cases, then, where perception of the particulars could be as ineffective as indefinite, vague, or defeasible definitions can be. If one cannot make determinations with regard to heaps or baldness by falling back upon perception, how likely is it that one will in the case of gentleness, irascibility, ambitiousness, and so forth?
The same sorts of problems will be encountered if we were to fall back upon perception as a means of arriving at definitions of the kinds of things that Aristotle finds difficult to define. Aristotle tends to think that in the act of perceiving the particular we also come to know the universal, that although we can distinguish these two elements of cognition they are inseparable in the act of perception.[13] Thus, the move of relying on perception of some particular belonging to a kind F as a means of arriving at the definition of F might have appeared plausible to Aristotle, but if the phenomena lack a well-defined nature or structure, it is not obvious that perception can be of any help in attaining definitions. For if there are no well-defined boundaries or the boundaries are too indefinite, one should not expect to find any or to find definite ones by falling back on perception. Perhaps, then, one may have to admit that on some occasions one might not be able to discover a clear answer to the question whether something is an instance of a kind F or to produce an exact definition of F that supposedly explicates the nature of F. Perhaps one may have to admit that in some cases an answer or definition has to be given and not discovered by perception or any other means. A decision rather than a discovery has to be made.
Thus, Aristotle himself argues in 8.7 that where things are indeterminate and no general law can be formulated to cover all cases a special ordinance becomes necessary. Similarly, one may need to decide or set the boundaries or limits that Aristotle speaks of in the case of concepts like friendship ,
gentleness, irascibility , or city . But, as the familiar arguments about vague concepts or things from ancient times to the present have shown, it is quite difficult to set such boundaries or limits. Arguments such as those of the "sorites" and "falakros" have pointed out that whereas it is clear that fifty thousand grains make a heap or that the person with a thousand hairs is not bald, fixing the upper or lower limits of such concepts is problematic. As Aristotle points out in 8.8, one can say that if the difference in merit between two persons is that which exists between Gods and humans then these two persons cannot be friends. The problem is in fixing the lower or upper limits in the difference of merit within which friendship obtains. As Aristotle says, in the case of friendship or gentleness or irascibility, this is difficult or impossible to do. There is no obvious boundary in the phenomena themselves, and if we want or need a boundary, we will have to decide on one.[14]
Yet, although Aristotle appears to recognize the difficulties with fixing any limits or boundaries in the case of vague or indefinite concepts and he himself fails to provide any such limits or boundaries for the concepts or things he cites, it is obvious that he places much weight in the existence of such limits. Perhaps he has reasons for doing so. As recent philosophers have argued, vague concepts or objects pose many problems. To some, identity statements about vague objects are problematic, for at least the transitivity of identity appears to fail.[15] But to others the problems of embracing vague objects or concepts are even greater. Russell and Frege argued that such objects or concepts violate the law of the excluded middle, which according to them is indispensable to logic.[16] Hence, they concluded that if the world consists of vague objects or is described by vague concepts, then logic cannot be about this world. In the famous words of Russell, "All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestrial life, but only to an imagined celestial existence."[17]
Aristotle, as is well known, took the law of the excluded middle and the law of noncontradiction to be the universal laws of being and thought. It is possible that it is this kind of assumption that partly motivates his insistence that boundaries or limits need to be given even for vague objects or concepts. As it has been argued recently, the semantics of his logical theory almost rules out vague predicates.[18] If one were successful in drawing a boundary or in fixing a limit for a vague concept, one would have at least made a step toward eliminating its fuzzy area that has traditionally been looked upon as posing problems for the applicability of the two laws of classical logic. Whether the limits Aristotle insists upon are sufficient for resolving the problems of truth associated with vague concepts is to be examined later.
But what are the implications of the inexactness under consideration
for the demonstrative use of definitions? As I said earlier (chap. 2), Aristotle, like Socrates and Plato before him, assigns a central role to definitions in his conception of demonstrative science or knowledge: Definitions are among the principles of demonstration (Post. Anal . 72a21) and all sciences proceed through definitions (Post. Anal . 99a23). If definitions are necessary ingredients of demonstration and if there are domains consisting of things that cannot be defined, then it would seem that no demonstrations would be possible in such domains.
Aristotle's major concern with matters of conduct is that they are difficult and not necessarily impossible to define on account of their supposed inexactness, and that their definitions are inexact by being true for the most part or by being indefinite or vague. The feature of being true for the most part that Aristotle attributes to definitions of matters of conduct would not pose problems with regard to the demonstrative use of such definitions that are any different from the ones discussed in the previous chapter. Definitions of matters of conduct will function as premises of demonstrations of the less rigorous, softer, or weaker type.
The feature of indefiniteness or vagueness that Aristotle attributes to definitions of matters of conduct may have different, as well as more problematic, consequences with regard to their demonstrative uses, however. If Russell and Frege are right, traditional logic is not applicable to vague objects (terrestrial life) or to propositions using imprecise symbols but only to an imagined celestial existence or propositions that use only precise symbols. The problem, according to these philosophers, with attempting to apply traditional logic to a vague world or to propositions using imprecise symbols is that validity has no place in reasoning about such a world or with such propositions. There is no evidence, however, that Aristotle drew the conclusion that Russell and Frege drew. Although he recognizes vague or indefinite objects, he does not deny that we can reason about them or that demonstrative inferences are possible in their case. His concern is most often to remind us of the inexactness of certain things and our accounts of them, to remind us of the deficiencies of our inferences, rather than to deny that we can make inferences.[19] Perhaps he might have thought that one can avoid the conclusion that Frege and Russell drew by assuming that boundaries or limits can be drawn somewhere.