Analogical unification. I turn now 1o what is possibly the most baffling of the ways explicitly suggested by Aristotle as being those in which what 1 am calling USM may arise. These will be cases in which the application of an epithet to a range of objects is accounted for by analogy detectable within that range; more explicitly to analogies between the specific universals which determine the application of the epithet, or (perhaps) between the exemplifications of those universals by this or that type of object. More explicitly to analogies between the specific universals U, and Up etc., which determine the application of the epithet, or (perhaps) between the exemplifications of Up, Up ete., by items of the sons 1. la ctc.. The puzzling character of Aristotle's treatment of this topic arises from a number of different factors. First there are two things which Aristotle himself might have done to aid our comprehension. He might have given us a firm list of examples of epithets, the application of which to a given range of objects is to be accounted for in this way; alternatively, he might have given us a reasonably cicar characterization of the kind of accounting which analogy is supposed to provide, leaving it to us to determine the range of application of this kind of accounting. Unfortunately he does neither of these things; he offers us only the most meagre hints about the way in which analogy might unify the various applications of an pithet; we are told, for example, that as sight is in the eye, so intellect is in the soul with the implicit suggestion that this fact accounts for the application of the word 'see' both to cases of optical vision and cases of intellectual vision, and he also suggests that analogy is responsible for the application of the word 'calm" both to undisturbed bodies of sea water and to undisturbed expanses of air. Such offerings do not get us very far, furthermore, not surprisingly, where Aristotle seems to fear to tread the commentators are most reluctant to plant their own feet. Perhaps the least unhelpful suggestion comcs from Ross who suggests as Aristotle's view that the application of the word 'good' is attributable to the fact that within one category things which are good are related to things in general belonging to that category in a way which is analogous to the way in which good things in some second category are related to the general run of things which belong to that second category. Apart from obscurity in the presentation of this idea, Ross's suggestion takes for granted something which Aristotle himself does not tell us, namely that the application of the epithet 'good' is one exemplification of unification which is the outcome of analogy: Ross's suggestion about 'good" would, morcover, be at best only a description of one special case of analogical unification, and would not give us any general account of such unification. I might add that little supplementary assistance is derivable from those who study general semantic concepts; such persons scem to adhere to the principle that silence is golden when it comes to discussion of such questions as the relation hetween analogy, metaphor, simile, allegory and parable

So far as Aristotle himself is concerned it seems fairly clear to me that lic primary notion behind the concept of analogy is that of 'proportion'.

This notion is embodied, for example, in Aristotle's treatment of justice. where one kind of justice is alleged to consist in a due proportion between return (reward or penalty) and antecedent desert (merit or demerit) but it remains a mystery how what starts life as, or as something approximating to, a quantitive relationship gets converted into a non-quantitive relation of correspondence or affinity. It looks as if we might be thrown back upon what we might hope to be inspired conjecture.

I take as my first task the provision of an example, congenial to Aristotle, of the unification by analogy of the application to a range of objects of some epithet. I shall expect this to involve the detection of analogical links between the exemplifications of the varicty of universals which the epithet may be used to signify. My chosen specimen is the verb grow. In this case a number of different kinds of shifts might be thought of as possessing an analogical unification. One of these would be examples of shifts in respect of what might be termed syntactical metaphysical category. A substance, indeed a physical substance like a lump of wax or a mass of metal, might be said to grow, and it would be tempting here to suggest that the relevantly involved universal, that of increase in size or gelting larger, provides the foundational instance of the signification of a universal by the word grow'; we have here, so to speak, the 'ground floor" meaning of the verb. But not only the physical substance itself but the various accidents of the substance may also be said to grow: not only the piece of wax but its magnitude, some event or process in its history, its powers or causal eificacy and its aesthetic quality (beauty) might each be said to grow; and it seems not unplausible to suggest that though growth on the part of these non-substantial accidents might be different, and more or, again. less boringly connected with growth on the part of the

substance, there will always be some kind of correspondence or analogical connection between growth in the case of a non-substantial item and growth in the case of a substantial item. Another and different kind of calcgorial variation may scparate some of the universals which the word

"grow" may be used to signify from others; these will be connected with differences in the sub-categories within the category of substance within which fall different sorts of entitics which may be said to grow; different universals may be signified by somcone who speaks of a plant as growing and by someone who speaks of a human being as growing, and the connection between these diverse realizations of growth may rest on analogy. In what is called the growth of a plant, internally originated increase in size may occupy a prominent place, whereas in the case of a buman being the kind of development which may be involved in growth may be much more varied and complex; the link between the Iwo distinct universals which may be signific might be provided by analogy between the roles which such changes fulfill in the development of the very different kinds of substances which are being characterized. No doubt many further kinds of analogical connection would emerge within the general practice of attributing growth.

My next endeavour will be an attempt to supply some general account of the way in which the presence of analgy may serve to unify semantic multiplicity; and if such an account should be found to offer prospects of distinguishing analogy from other concepts, particularly metaphor which belongs to the same general family, that would be a welcome aspect of the account. It is my idea that in metaphorical description a universal is signified, which though distinct from that which underlies the literal meaning of an epithct is nevertheless recognizably similar to that literal signification

I come now to the notion of analogy itscif. I shall start by considering items any one of which may be called an S; 1 shall initially suppose that being an S, consists in belonging to a substantial type or kind, St. though that supposition may be relaxed later. My first move will be to assume that being an S, consists in being subject to a system of laws which jointly express the nature of the type or kind Si; and further hat these laws, which furnish the central theory of S,, will all be formulable in terms of a finite set of S,-central properties (Ict us say P, to P,); each law will involve some ordered extract from the central sct, and their totality will govern any fully authentic S,. This totality may well not include all the laws which apply to St: but it does include all the laws which are relevant to tie identity of S,, all the laws which determine whether or not a particular item is to count as an SI-

Let us next consider not merely things each of which is an Si, but also things each of which is an Sz: it is to remain at least for the moment an open question whether or not the type S, is identical with the type S. 1 assume that, as in the case of Si. membership of Sy is determined by conformity to a system of laws relating to properties which are contral to S2. 1 shall symbolize these properties by the devices Or ... Q.. We now have various possibilitics to consider. The first is that every law which is central to the determination of S2 is a mirror image of a law which is central to S,; and that the converse of this supposition also obtains. To this end we shall assume that the properties which are central to being an S are the propertics O, through Os; and that if a law involving a certain ordered extract from the set P, through P, belongs to the contral theory of St. a law involving an exactly corresponding ordered extract from the set O, through O, will belong to the contral theory of Sa: and that the same holds in reverse. In that casc, we shall be in the position to say that there is a perfcet analogy beiween the central theories of S, and Sz; and in that case, it may also be tempting to say that the types S, and S are csentially identical. We should recognize that if we yield to this temptation we are not thereby forced to say that S, and S, are indistinguishable, they might, for example, be differently related to perception, only one of them (perhaps) being accessible to sight; we shall only be forced to allow that essentially, or theoretically, the types are not distinct; how that is to be interpreted will remain to be scen.

The possibility just considered is that of a total perfect analogy between the central theories of S, and S. There is also, however, the possibility of a partial perfect analogy between S, and S. That is to say pait of the central theory of one type (say S) may mirror the whole of the central theory of Sz, or again may mirror some part of a central theory of Sz. In such circumstances one might be led to say (in one case) that the type S, is a special case of the type S; or (in the other case that the types S, and S both fall under a common super-type, determined by the limited area of perfect analogy between the central theories of 5, and S. A third possibility will be that no perfect analogy, either total or partial, exists between the two central theories; the best that can be found are imperfect analogies which will consist in laws central to one type approximating, to a certain degree, with the status of being analogues of laws central to the other.

At this stage, I would propose a relaxation in the characterization of the signification of such symbols as 'Si', 'S¿' ctc., which till now 1 have been regarding as signifying substantial types or kinds, reference to which is made in more or less regimented discourse of a theoretical or scientific sort. I shall now think of such symbols as relating to what I hope might be legitimately regarded as informal precursors of the aforementioned

substantial types, as expressing concepts of one or other classificatory sort, concepts which will be deployed in the unregimented descriptions and explanations of pre-theoretical. Examples of such unregimented classifica-tory concepts might be the concepts of an investor, a doctor, a vehicle, a confidante, and so on. I would hopc that in many ways their general character might run parallel to that of their more regimented counterparts.

In particular, one might hope and expect that their nature would be bound up with conformity to a certain set of contral generalitics (platitudes, truisms, etc.); to be an investor or a chicle will be to do a sufficient number of the kinds of things which typically are done by investors or vehicles. One might expect, however, that the varicty of possible forms of generolization might considerably exceed the meagre armament which thcoretical enquirers nommally permit themselves to employ. One might also hope and expect that the generalities which would be expressive of the nature of a particular classificatory concept would be formulable in terms of a limited body of features which would be central to the concept in question. This material might be sufficient to provide for the presence from time to time of analogy, at least of impertect analozy, between goncralitics which are expressive of distinct classificatory concepts. When they occur, such analogies might be sufficient to provide for semantic unity in the employment of a single epithet to signify different classificatory concepts; and this semantic unity, in turn, might be sufficient to justify the idca that in such cases the expression in question is used with a single lexical meaning.