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

 G.: Peano’s inverted C is a tidy little emblem of a large old ambition. S.: Too tidy, I should have thought, for what you want to make it carry. G.: I do not mean to make it carry all of Rome and Turin at once, only enough of “if” to keep the Hall amused. S.: But that is precisely my objection. The inverted C, or the horseshoe if you prefer the shoe-shop version, does not do “if” in the way Strawson wants “if.” G.: No, it does not do “if” in the vernacular way, which is why it fascinates me. S.: Fascinates or irritates? G.: Both. It is the epitome of the characteristica universalis dream: one sign to replace a small cloud of human language. S.: And to replace it badly. G.: Often, yes. But one must not mock the ambition before admiring the nerve. S.: Very well. Then let us begin with the symbol. G.: The inverted C, yes, or what later students draw as a horseshoe, meant by Peano as “consequence,” “if,” “therefore,” or rather the formal relation by which one proposition follows from another. S.: Already you slide. G.: Naturally. One must. The whole point is that the sign invites sliding among “if,” “implies,” “follows from,” and “therefore,” while pretending to settle them. S.: Which is why the vernacular resists it. G.: Precisely. Strawson’s “if” is not merely a truth-functional gadget. It carries conversational expectations, hesitations, suppositions, provisionality, insinuation, and all the rest of the ordinary traffic. S.: And the horseshoe does none of that. G.: None explicitly, no. It gives one a regimented relation stripped of atmosphere. S.: More than atmosphere. It strips away what the speaker is doing in saying “if.” G.: Yes. And that is where my notion of implication begins protesting against formal tidiness. S.: Then why choose Peano’s sign as the epitome at all? G.: Because it is beautifully brazen. It says in one shape what Bishop Wilkins, Leibniz, Richeri, and a dozen others wanted to say with whole systems: that there might be one exact sign where ordinary language has a muddle. S.: And Richeri belongs in that genealogy. G.: Very much so. His Algebræ philosophicæ in usum artis inveniendi specimen primum is exactly the sort of thing one reads with alternating admiration and distrust. S.: Distrust because? G.: Because he thinks one can engineer looseness away. He sees metaphysics and discourse as things that can be purified by a lawful script. S.: A scia-grafia, as he calls it. G.: Yes. A philosophical shadow-writing for those who dislike shadows unless they can regulate them. S.: And Peano later notices him. G.: Through Padoa, yes, or at least through that whole Turin lineage of precursors and retrospective annexations. S.: With the whole and the nothing rendered by simple characters. G.: Exactly. Richeri’s U for the something, the all, the thing, and n or its partner for the nothing, the negative. A beautifully provincial universalism. S.: “Provincial universalism” is rather cruel. G.: It is also fair. Turin has always liked universal systems with local air. S.: Then the inverted C is not merely Peano’s sign but a late expression of an older dream. G.: Precisely. The dream that one may take the clutter of ordinary speech and replace it with characters whose combinatory life is cleaner than any conversation. S.: And you object because conversation is not clutter but rationally managed looseness. G.: Splendid. Keep that. S.: Gladly. But let us be exact. What does the horseshoe fail to express? G.: Many things. Strawson would say that ordinary “if” does not merely state a truth-functional relation between antecedent and consequent. It may suggest relevance, dependence, defeasibility, conditional commitment, hypothetical concession, epistemic distance, polite caution, and a little air of human uncertainty. S.: Whereas the horseshoe gives only the formal table. G.: Yes. If p horseshoe q is false only when p is true and q false. That is perfectly useful for one range of purposes and perfectly deaf to others. S.: So the vernacular contains something not expressed by the sign. G.: Better: something not encoded by the sign. Which then invites the usual philosophical mistake of calling the remainder mere vagueness or emotional upholstery. S.: You call it implicated. G.: Of course. Because what ordinary “if” often carries beyond the formal core is not noise but inferentially recoverable residue. S.: Such as? G.: “If you are going to London, there is a good train at six.” The horseshoe captures very little of why that sounds helpful rather than merely true-functionally arranged. S.: Or “If you are thirsty, there is beer in the fridge.” G.: Exactly. The antecedent does not merely stand in truth-functional relation to the consequent. It makes relevant a piece of information under a cooperative presumption. S.: So the “if” is partly guidance. G.: Yes, and partly tact. Sometimes one says “if” not because one doubts, but because one leaves the other’s state unpresumed while preparing a useful consequence. S.: Which the horseshoe cannot register. G.: No. It has no room for politeness, for one thing. S.: A defect shared by most logical symbols. G.: And by several logicians. S.: You are warming up. G.: We have a Hall to entertain in due course. S.: Then bring Richeri back in. What did he want exactly? G.: He wanted, with Leibnizian enthusiasm and Italian earnestness, an algebra of thought in which abstract characters could stand to meanings as algebraic symbols stand to magnitudes. S.: A language in which metaphysical discourse becomes calculable. G.: Or at least universally intelligible by construction. One sees the seduction. Replace the quarrels of vernacular philosophy with a lawful combinatorics. S.: A philosophically hygienic script. G.: Exactly. The sort of thing that tempts those who have suffered too much ordinary language and not enough ordinary life. S.: Yet you admit the grandeur. G.: Certainly. Plato had it in one form, Bishop Wilkins in another, Leibniz more magnificently, Richeri in his Piedmontese register, and Peano in a schoolmaster’s hand sharpened by precision. S.: Then the problem is not the dream itself. G.: No. The problem is the metaphysical excrescence that creeps in when one thinks the sign not only abridges but exhausts what the vernacular had been doing. S.: “Metaphysical excrescence” sounds as if the horseshoe had grown a fungus. G.: It usually does. The neat symbol comes to be treated as if it had purified the concept by removing everything in the vernacular that did not deserve to survive. S.: Such as relevance. G.: Such as relevance, implicature, context, speaker-intention, pragmatic force, all the little creatures the Einheitswissenschaft temperament finds untidy. S.: There is your Vienna. G.: Yes. The prejudice of Einheit von Wissenschaft, the fantasy that the unity of science is secured by a language cleaner than the life it describes. S.: You are being unfair to Vienna by way of Turin. G.: It is an old route. One should not exaggerate the opposition, of course. Peano was not a Viennese reductionist in all respects. But the family resemblance is there. S.: Then the inverted C becomes a political symbol of sorts. G.: An intellectual political symbol, yes. It announces that consequence may be rendered uniform, calculable, public, and ideally free of conversational residue. S.: Which is precisely what you deny. G.: Not deny altogether. Formal consequence is real enough. I merely deny that vernacular “if” is exhausted by what formal consequence abstracts from it. S.: Then perhaps we should distinguish “se,” “si,” “if,” and the horseshoe explicitly. G.: Good. Latin si, Italian se, English if. Three venerable vernacular or near-vernacular particles with histories in law, rhetoric, conversation, and philosophy. Then the horseshoe, a formal sign aspiring to distil one logical skeleton from that history. S.: And in doing so it leaves behind the flesh. G.: Precisely. The flesh being not mere rhetoric in the pejorative sense, but practical reason at work. S.: Suppose one says, “If he is in Oxford, he will be at All Souls.” What does the horseshoe miss? G.: It misses, among other things, that the speaker may be relying on shared knowledge of the man’s habits, not asserting a law of implication. It misses the evidential modesty, the social background, the defeasibility, and perhaps the speaker’s tone of half-dry confidence. S.: So the vernacular conditional is partly a move in a game of mutual orientation. G.: Exactly. The horseshoe is not. S.: It is a move in a calculus. G.: Which has its splendour, but also its losses. S.: Then why not say this is simply abstraction? G.: Because abstraction too easily excuses itself. I want to say that some philosophers mistake abstraction for replacement. They take the purified sign and then claim that what ordinary language had beyond it was dispensable confusion. S.: Whereas you think it was often disciplined surplus. G.: Very good. Disciplined surplus. Implicated, not encoded, but rationally there. S.: And Richeri thought to spare us the surplus entirely. G.: He wanted to spare us the negotiation, yes. The underdetermined, socially managed character of ordinary discourse offended the combinatorial imagination. S.: Yet human beings keep returning to it. G.: Because they are not algebraic polities. S.: That sounds almost Aristotelian. G.: The best dry things often do. S.: Let us be fair again. Richeri distinguishes possible, impossible, contradiction, negation, something, nothing. That is not absurd. G.: No, not absurd at all. It is rather admirable. One sees the craving for a finite repertory of primitive distinctions from which larger intelligibility might grow. S.: A finite alphabet, infinite philosophy. G.: Exactly. One cannot fail to be moved by the ambition. S.: Then what goes wrong? G.: He underestimates how much of philosophical communication depends on what is not fixed by primitive assignment alone: intended emphasis, dialectical posture, context, audience, occasion, and the whole inferential play of practical reason. S.: In short, conversation. G.: Precisely. He wants conversation to become calculation. I want calculation to be recognised as only one species of conversation’s disciplined descendants. S.: Then the horseshoe is a descendant, not an ancestor. G.: Splendid. Keep that too. S.: Happily. But you have not yet said enough about Peano’s own use. G.: Peano’s genius was to standardise with extraordinary severity. He did not merely invent signs; he put them into pedagogic and formal circulation. His notation made certain distinctions operable. S.: Including consequence. G.: Yes. The sign for implication or consequence becomes a classroom machine. It allows one to write what otherwise requires clumsy prose. S.: And that is good. G.: Very good indeed, so long as one remembers what has been omitted. S.: You really mean “what has been implicated and omitted.” G.: Of course. S.: Then perhaps the Hall should hear an example. G.: By all means. “If the bell rings, the porter will grumble.” In ordinary speech this may suggest not only a truth-function but a little world: bells, porters, habits, perhaps the speaker’s experience, perhaps an invitation to avoid ringing if one wishes to preserve peace. S.: While the horseshoe gives only p ⊃ q. G.: Exactly. A splendid skeleton and a ruined anecdote. S.: Very Oxonian. G.: We are, after all, in our proper climate. S.: And Strawson objects because the horseshoe is not the vernacular if. G.: Yes. He insists that ordinary “if” is not exhausted by material implication, and he is right, though often too airily right for a man who enjoys the vernacular as much as he does. S.: You enjoy it no less. G.: Certainly, but I prefer to explain its excesses by implicature rather than by appeal to some ineffable remainder. S.: So where Strawson says “ordinary if is not that,” you say “ordinary if says less and implicates more.” G.: Roughly, yes. The formal sign captures a core relation useful for deduction. The vernacular expression often rides that core while bringing along pragmatic riders. S.: Riders the horse-shoe does not shoe. G.: Very nice. Keep that and pretend I said it first. S.: Never intentionally. G.: Good. Then what of “se” and “si” in Roman terms? S.: Latin si already has a life broader than formal consequence: legal conditions, suppositions, threats, concessions, practical maxims. G.: Exactly. “Si vales, bene est; ego valeo.” A conditional opening that is as much social gesture as logical form. S.: Which the inverted C will never capture. G.: Not unless one lets it wear a toga and become ridiculous. S.: Then your mention of Roman “si” is not antiquarian but methodological. G.: Quite. It reminds us that the conditional has lived a long public life before it became a sign in a formal grammar. S.: And Italian “se” inherits that life. G.: Yes. Richeri and Peano may discipline it, but they do not create the territory from nothing. S.: So the universal characteristic is always a late imperial project over an older republic of uses. G.: Excellent. That is very nearly the whole lecture. S.: You may yet publish. G.: God forbid. Let us finish this first. S.: Then speak of the one sign dream. G.: Ah yes. The dream that there might be one sign for one relation, one purified notation for each fundamental operation, such that thought becomes publicly calculable. S.: Wilkins had it lexically, Leibniz combinatorially, Richeri algebraically, Peano symbolically. G.: Very good. S.: And you? G.: I am the man at the back murmuring that the audience still needs to understand the signs, and that understanding them involves more than formal assignment. S.: Because there is always an addressee. G.: Exactly. The dream of a language with no pragmatic residue is the dream of a language with no real users, or only ideal calculators. S.: We cannot blame Plato, Bishop Wilkins, or Richeri for trying. G.: No, certainly not. There is nobility in the attempt. One wants a script cleaner than faction, a sign more stable than rhetoric, an order more trustworthy than custom. S.: But one must blame those who forget the cost. G.: Precisely. The cost is that much of what makes understanding human disappears or returns disguised. S.: Disguised as what? G.: As “mere context,” “performance features,” “psychological accompaniment,” “rhetorical garnish,” all the things formalists condescend to once their main sign is safely installed. S.: And you re-promote them. G.: I give them their inferential dignity back. S.: Then the metaphysical excrescence is the belief that the cleansed sign has reached the essence. G.: Exactly. Instead it has reached a useful abstraction and then grown arrogant. S.: Like certain clerks. G.: And certain logicians. S.: Then what is the best charitable formula for Richeri? G.: He locates productivity in an algebra of signs intended to make intention and context dispensable. That is brilliant and impossible. S.: “Brilliant and impossible” is very nearly an epitaph for universal language schemes. G.: It is also a compliment. S.: And for Peano? G.: He operationalises the dream more successfully than most. His symbols genuinely clarify relations and standardise expression. But even his inverted C cannot abolish the vernacular conditionals from which philosophers and ordinary men continue to reason. S.: So the Hall should hear neither mockery nor worship. G.: Exactly. Admiration under discipline. S.: That sounds like your best tone. G.: It is the only one likely to keep both logicians and commoners awake. S.: Let us do one more example. “If you are hungry, there are biscuits on the sideboard.” G.: Good. The horseshoe gives one p ⊃ q, perhaps. But the utterance in context is an offer, an invitation, a gesture of hospitality, perhaps a slight hint not to complain. S.: So the conditional form is serving an act not named in the syntax. G.: Exactly. And that unnamed act is not mystical. It is recoverable by rational uptake. S.: Implicated. G.: Naturally. S.: Then your final quarrel with the inverted C is not that it is false, but that it is too poor to pass for the whole truth. G.: Exactly. S.: Dry enough? G.: Sufficiently Turinese, with one foreign article still unexpelled.