H. P. GRICE E J. L. SPERANZA: LA CONVERSAZIONE -- I VERBALI: PACIOLI

 G.: Let us begin with Pacioli rather than Aristotle, because proportion behaves better in Venetian print than analogy does in Oxford mouths. S.: You dislike analogia? G.: Not dislike. Distrust. It is one of those noble words under which commentators hide semantic laziness. S.: Whereas proportio sounds cleaner. G.: Exactly. Pacioli says proportioni and proportionalità, and at once one feels that the matter may yet be kept on the books. S.: You are thinking of analogical unification. G.: Yes. The old problem: one word applied in different cases, and the temptation to say at once that it has many senses. S.: Which you resist. G.: On principle. Senses are not to be multiplied beyond necessity. That is my improved razor: no lexical polygamy without evidence. S.: Then you prefer one sense with structured variation. G.: Precisely. A single lexical meaning, if one can get it, with different realisations unified by proportion or analogy. S.: Which is where Pacioli comes in. G.: He is useful because proportion is his native air, not an afterthought. For him a:b::c:d is not merely arithmetic furniture but a discipline of order. S.: And you want to make semantic order answer to that. G.: With due caution. I do not claim that meanings are numbers. Only that proportional structure may explain how one epithet ranges over unlike cases without forcing us into sheer equivocation. S.: Then give me the target case. G.: Let us take grow. It is a decent specimen and less pompous than good. S.: A plant grows, a child grows, a storm grows, a friendship grows, a problem grows. G.: Exactly. The vulgar semantician says at once: many senses. S.: And you say? G.: Not so fast. The word may have one central significance, with analogically related instantiations across different categories. S.: Such as increase, development, intensification, elaboration. G.: Yes, but one must avoid turning the “central significance” into a dreary abstraction so empty that anything fits. S.: Then perhaps one should begin with a type. G.: Very good. Suppose S1 is plant-growth and S2 is child-growth. S.: And each is governed by a central theory. G.: Exactly. Pacioli would have approved the bookkeeping. Let T1 be the set of central generalities governing plant-growth, and T2 the set governing child-growth. S.: With properties P1 to Pn for the first, and Q1 to Qn for the second. G.: Yes. If there is enough structural correspondence between T1 and T2, then the same word grow may apply with one lexical meaning, despite differences in the realised universals. S.: So analogy lies not in superficial likeness but in law-like correspondence between the central features. G.: Precisely. Not merely “both get bigger,” but something like this: in each case there is a development proper to the kind, internally organised, temporally extended, and constitutively connected with the flourishing or maturation of the thing. S.: That sounds more Aristotelian than commercial. G.: Pacioli need not mind. Ratio is never only arithmetic. S.: Then a:b::c:d becomes what, in semantic terms? G.: Roughly, the role of increase in the life of a plant is to the plant what the role of maturation is in the life of a child. S.: So not identity of process, but proportional correspondence of role. G.: Exactly. And that is the sort of structure that can underwrite one sense. S.: Then metaphor is different. G.: Very much. If I say “his anger grew wings,” I am not extending grow by central-theory correspondence. I am indulging myself. S.: So analogy preserves lexical unity; metaphor exploits resemblance more adventitiously. G.: That is the line I should like to keep. S.: Then what of calm, Aristotle’s own sort of example? A calm sea, calm air, a calm man. G.: A better case than many. One is tempted again to say many senses. But one may resist. In each case calm picks out the absence or subdual of characteristic disturbance in a medium or subject apt for disturbance. S.: Water without turbulence, air without agitation, soul without perturbation. G.: Exactly. Different media, one proportional role. S.: So the relation is: disturbance is to sea as disturbance is to air as perturbation is to soul. G.: More neatly, the absence of unrest in one proper field stands to that field as the absence of unrest in another proper field stands to that one. S.: Which sounds like: A:B::C:D, where A is sea-calm, B is sea-as-medium, C is psychic calm, D is soul-as-medium. G.: Yes. Or, if you prefer, calm(x) holds where x instantiates the analogue of settledness appropriate to its type. S.: That sounds almost formal enough. G.: It must not become too formal too early. Formalism is often what one reaches for when one has lost the phenomenon. S.: Yet you asked for central theories. G.: Yes, because without some theoretical articulation analogy collapses into hand-waving. S.: Then perhaps we should state the schema. G.: Let a word W apply to types S1 and S2. Let T1 and T2 be the central theories of S1 and S2. If there is a mapping F from the central predicates of T1 to those of T2 such that the relevant laws correspond under F, then W may retain one lexical meaning across S1 and S2. S.: Provided the correspondence is relevant to the role expressed by W. G.: Precisely. Otherwise everything is analogous to everything by force. S.: Which many metaphysicians have been happy to believe. G.: And many theologians, which is worse. S.: Then partial analogy matters too. G.: Very much. Total perfect analogy would almost tempt one to identify the types. More often we have partial perfect analogy or imperfect analogy. S.: Meaning that part of T1 mirrors all or part of T2. G.: Yes. Then one may say either that one type is a special case of another, or that both fall under a super-type defined by the shared analogue. S.: So semantic unification does not require total theoretical overlap. G.: Exactly. It requires enough structured overlap in the right place. S.: Which sounds almost like family resemblance, but with better discipline. G.: Much better. Family resemblance is too often what one says when one has tired of distinctions. S.: Then let us test a harder case. Good. G.: Ah yes, Ross’s favourite fog. S.: A good knife, a good man, a good argument, a good meal. G.: One may easily go astray there. If one says “good has many senses,” one gives up too fast. If one says “good means the same in all cases,” one risks vapidity. S.: Then proportion again? G.: Yes. A good x is, roughly, an x that stands in the right relation to the ends, functions, or standards internal to the kind of x. S.: So the goodness of a knife is to cutting what the goodness of a man is to rational and moral life. G.: Exactly. Not the same property, but the analogous place in distinct central theories. S.: Then a:b::c:d becomes: sharpness for knife-life :: virtue for human life. G.: More carefully, the condition that constitutes excellence in the proper role of one type stands to that type as the condition that constitutes excellence in the proper role of another type stands to that one. S.: Which lets good keep one sense as an excellence-term. G.: If one is brave enough, yes. S.: Brave or reckless. G.: Those are often proportionally related in young philosophers. S.: Then your modified razor says: prefer that unified excellence-account to multiplying lexical senses. G.: Precisely. Unless the cases resist it and force us into homonymy. S.: So the burden of proof lies with the multipliers. G.: As it should. Semantic inflation has ruined many otherwise decent pages. S.: Then where does Pacioli specifically help, beyond giving you a cleaner word than analogia? G.: In two ways. First, proportio gives one a model of intelligible relation without identity. Second, proportionalità suggests system, not merely isolated likenesses. S.: A ledger of correspondences. G.: Exactly. The same man who balances books reminds one that relations can be ordered without being collapsed. S.: So semantic unification is like double-entry bookkeeping? G.: In a mild sense. One does not let an application stand unless it can be entered on both sides: the side of the type and the side of the role. S.: That is very Paciolian. G.: And dry enough for Oxford if one removes the Venetian paper. S.: Then let us formalise a:b::c:d more explicitly. G.: Very well. Let R be a role-function assigning to a property its place within a central theory. Then analogy between P in S1 and Q in S2 holds if R(P,S1) = R(Q,S2), not numerically, of course, but by structural correspondence. S.: So W applies to both S1 and S2 if W tracks properties whose roles correspond under R. G.: Exactly. That is a decent beginning. S.: And if the correspondence is imperfect? G.: Then one gets looser analogical unification. Enough to justify one lexical meaning perhaps, but with more strain. S.: Such as grow for a city and grow for a child. G.: Yes. A city “grows” not by organic maturation strictly, but by increase and development fulfilling a comparable role within the kind’s unfolding structure. S.: Though here metaphor starts hovering. G.: It does. One must decide whether the central-theory mapping is stable enough to preserve unification or merely opportunistic enough to count as metaphorical transfer. S.: How does one decide? G.: By asking whether the mapped role is entrenched across ordinary applications and supports systematic generalisations, or whether it is a one-off flourish. S.: So ordinary-language depth matters. G.: Very much. I do not want a theory that only works for glossators. S.: Then what of spatial category-shifts? A substance grows, its magnitude grows, its beauty grows, its influence grows. G.: A fine case. Here the same word crosses metaphysical categories: substance, quantity, quality, relation, perhaps power. S.: And still you want one sense. G.: If possible. Because in each case there is an analogue of increase, development, or augmentation relative to the kind of item involved. S.: So the magnitude of the wax grows as the wax grows, but the beauty of the wax grows in a proportionally related manner. G.: Yes. Beauty does not get larger in inches. But the degree, manifestation, or realised excellence of beauty becomes more pronounced relative to the aesthetic field proper to it. S.: Again, role not material sameness. G.: Precisely. Analogical unity is almost always role-unity. S.: That sounds like the slogan. G.: A usable one. S.: Then metaphor again is role without entitlement? G.: Nicely put. In metaphor one borrows a role-structure without the full entitlement of stable central-theory correspondence. S.: “The argument limped.” G.: Exactly. We all see what is meant, but no one should build a metaphysics of lame propositions upon it. S.: Though some would try. G.: That is why one must live carefully. S.: Then your account also distinguishes analogy from mere simile. G.: Yes. Simile remains explicit comparison. Analogy, in the stronger semantic sense, helps explain why the same predicate may genuinely range across cases with one meaning. S.: So when Aristotle says intellect sees as the eye sees, he may be pointing toward analogical unification of see. G.: Quite. Optical seeing and intellectual seeing need not force two lexical senses if the role of apprehensive disclosure in one domain corresponds to the role of apprehensive disclosure in the other. S.: The eye is to visible objects as intellect is to intelligible objects. G.: Exactly. And see may retain one high-level sense of direct apprehension under suitably different realisations. S.: That will make some people nervous. G.: Good. Nervousness is often the beginning of better semantics. S.: Then perhaps we should state your razor more fully. G.: By all means. Do not multiply senses beyond necessity; where a stable proportional mapping between central theories explains the range of application, prefer monosemy with analogical unification to lexical multiplication. S.: That is admirably unromantic. G.: Pacioli would approve. Accounts must balance. S.: Then let us ask whether proportionality itself must be formally exact. G.: No. Human language rarely grants perfect mirrors. Imperfect analogy often suffices. S.: Then what keeps the account from dissolving into vagueness? G.: The requirement that the correspondence be anchored in central generalities, not merely in felt resemblance. S.: Platitudes, truisms, regular explanatory connections. G.: Exactly. To be an investor, a doctor, a vehicle, a confidante, each involves a set of central generalities. If one epithet ranges across such concepts, analogical links among those generalities may preserve one meaning. S.: For instance reliable of a car, a friend, a witness. G.: Very good. Different kinds, one proportional role: dependable contribution relative to the function or relation proper to the thing. S.: So reliability in machinery is to transport what reliability in friendship is to trust. G.: Precisely. And the one word need not be fragmented into tiny lexical republics. S.: Then there is something almost moral about your hatred of multiplying senses. G.: There is. It is a hatred of waste. S.: Venetian enough for Pacioli. G.: Oxford can be economical when it is not being ornate. S.: One further worry. What if the central theories themselves are pre-theoretical and messy? G.: Of course they are, much of the time. That is why I relaxed the model from substantial scientific types to informal classificatory concepts. S.: Investor, doctor, vehicle, confidante. G.: Yes. Even there, one can often isolate central features and generalities enough for analogical comparison. S.: So semantic unification does not require full science. G.: Thank heaven. Otherwise ordinary language would have had to wait for laboratories. S.: Then your final distinction from metaphor? G.: In metaphor, a distinct but recognisably similar universal is signified; in analogy proper, different universals are unified by stable proportional correspondence across central theories. S.: So metaphor is a brilliant visitor; analogy is a resident relation. G.: Very good. Keep that too. S.: You are in an approving mood. G.: Only because Pacioli has balanced the ledgers for us. S.: Then the closing formula would be this. Pacioli’s proportio gives you a disciplined model for keeping one lexical meaning where lesser men would multiply senses. G.: Yes. And proportionalità reminds us that semantic order may be systematic without being flat. S.: One sense, many realised roles, proportionally linked. G.: Precisely. S.: Dry enough? G.: Sufficiently Sansepolcrese, with a balanced remainder.