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Catalogue Raisonné of J. L. Speranza’s Publications – H. P. Grice e J. L. Speranza: La Conversazione – I Verbali: UN

 

Speranza, J. L. (n. d.). ‘H. P. Grice e J. L. Speranza: La Conversazione – I Verbali: Unicorno – Ossia: Grice ed Unicorno: la ragione conversazionale e l’implicatura conversazionale dell’arimmetica universale – the logically developing series. Note su De admiranda vi proportionis, eiusque necessaria cognition, ad Bergomenses oratio. Il Gruppo di Gioco di H. P. Grice Giuseppe Unicorno (Bergamo, Lombardia): Institutionally, Giuseppe Unicorno and H. P. Grice are not comparable in the modern academic sense at all, though both are learned men concerned with order, rule, and intelligibility. Grice’s formula is exact in the Oxford sense. Fellow and Tutor in philosophy at St John’s means a college office with tutorials, students, and membership in the governing life of the college. CUF University Lecturer in philosophy means a university-wide appointment in the faculty structure. So Grice combines the two classic Oxford functions: college tutor and university lecturer. Giuseppe Unicorno belongs to a completely different world: late Renaissance Bergamo and Venice, the world of practical mathematics, humanist oratory, abaco culture, mercantile calculation, and printed mathematical pedagogy. He was not a don, not a fellow, and not a university lecturer in the Oxford or Italian chair sense. He was a mathematician, arithmetician, and man of practical and speculative number. The evidence you cite, especially De admiranda vi proportionis and the later Arithmetica universale, puts him firmly in that mixed world where mathematics serves commerce, rhetoric, and cosmological order alike. So the clean institutional contrast is this. Grice belongs to the tutorial-collegiate and university-faculty world. Unicorno belongs to the mathematical, humanist, and practical-printed world of late Renaissance Italy. That institutional difference fits your philosophical comparison very well. Grice works at the micro-level of rational communication: how a hearer gets from what is said to what is meant by recognising intentions and inferring implicatures under shared norms. Unicorno, by contrast, works at the level of structural intelligibility itself. His concern is not how one speaker means more than he explicitly says in a local exchange, but how proportion, number, and rule-governed calculation make rhetoric, dialectic, and even grammar themselves possible as ordered practices. That is why the Unicorno passage you quote is genuinely striking. He does not merely say that rhetoric can be decorative, dialectic demonstrative, and grammar foundational. He argues that all of them already depend on proportion, measure, and relation. In that sense, he offers a kind of proto-formal account of discourse, though not in the Gricean register of speaker intention and hearer inference. So the sharpest formulation is this. Grice explains how conversation can mean more than it literally says. Unicorno explains how discourse itself can be orderly, intelligible, and disciplined because it is proportioned. That is the best bridge between them. For Grice, the surplus of meaning is inferential and conversational. For Unicorno, the surplus of intelligibility is formal and structural. Both are, as you say, anti-mystification projects: Grice demystifies implicature by showing how it is rationally recoverable. Unicorno demystifies discourse by showing how rhetoric, dialectic, and grammar are already governed by measure and proportion. Your final bibliographic line is also one of the stronger ones in this whole series. De admiranda vi proportionis, eiusque necessaria cognitione, ad Bergomenses oratio, Venice, Arrivabene, 1552, is exactly the sort of concrete anchor one wants here. I would only note one small correction: cognitio or cognitione should be checked against the actual title page if you intend to cite it in a finished dossier, since sixteenth-century printings can vary in form. So the short clean answer is: H. P. Grice was an Oxford don in the precise collegiate sense, both Fellow and Tutor in philosophy at St John’s and CUF University Lecturer in philosophy at Oxford. Giuseppe Unicorno, by contrast, was a late Renaissance mathematician and arithmetician from Bergamo, active in the world of practical and speculative mathematics, humanist pedagogy, and printed mathematical discourse rather than in a college or faculty office. Institutionally, Grice belongs to the tutorial-collegiate world; Unicorno to the mathematical and humanist world of proportion, calculation, and formal order. Philosophically, the contrast is equally clear: Grice analyses the inferential micro-mechanics of speaker-meaning and conversational implicature, whereas Unicorno treats rationality as a property of formally governed relations—arithmetical, rhetorical, dialectical, and grammatical—whose intelligibility lies not in conversational maxims but in measurable structure. And if I compress it into one line: Grice theorises how speakers imply; Unicorno theorises how discourse is proportioned. If you want, I can now give you a tighter one-paragraph entry in your preferred style, using the 1552 Venice oration as the main anchor and sharpening the rhetoric-dialectic-grammar triad.la ragione conversazionale e l’implicatura conversazionale dell’arimmetica universale – Grice’s theory of reason-governed conversational meaning treats “what is meant” as an inferential upshot of cooperative rational agency: given what is said plus shared assumptions about relevance, quantity, quality, etc., a hearer can (in principle) reconstruct implicated content as the speaker’s rationally accountable intention. Unicorno, as the historical Giuseppe Unicorno/Unicorni (Josephus Unicornus; Bergamo 1523–1610), belongs to a very different intellectual ecology: his Arithmetica universale (Venezia, Francesco de’ Franceschi, 1598) is a Renaissance synthesis where number is at once practical technique (abaco culture: weights, measures, exchange, mercantile problems) and a quasi-metaphysical key to order (a tradition continuous with scholastic disciplines and Neoplatonic/Pythagorean resonances), and his De mathematicarum artium utilitate (Bergamo, Comino Ventura, 1584; bibliographies also report an earlier Venetian edition dated 1561) explicitly frames mathematical arts as broadly formative of human understanding. So the clean comparison is: Grice theorizes the rational norms internal to talk-exchanges (how participants responsibly move from said to meant), whereas Unicorno theorizes rational order as instantiated in formal and semi-formal systems (arithmetical procedures, proportionality, the “series” and its lawful development) whose “implications” are not conversational in Grice’s sense but structural—what follows from definitions, operations, and numerically articulated relations. If you want to make them meet, the best bridge is that both are “anti-mystification” projects: Grice explains how seemingly implicit content can be justified as rationally derivable within cooperative discourse; Unicorno explains how seemingly opaque practical and cosmic order can be rendered intelligible by rule-governed calculation—yet for Grice the medium is intersubjective intention-and-inference in conversation, while for Unicorno the medium is the disciplined manipulability of symbols and quantities, where “reason” shows itself less as conversational maxims than as the demonstrable necessity of numerical form. -- the logically developing series -- scuola di Bergamo –filosofia lombarda -- filosofia italiana (Bergamo). Abstract. Grice: Giuseppe Uncorno, a mathematician from Bergamo, holds a distinctive place in the history of Italian philosophy due to his attempt to bridge the gap between scholastic logic, Neoplatonic metaphysics, and practical arithmetic.  His importance lies primarily in how his mathematical treatises reflected the intellectual shifts of the late Renaissance: 1. The Metaphysics of Number Uncorno's most significant work, De universis numeris et eorum proprietatibus (On All Numbers and Their Properties), is not merely a manual for calculation. It is an encyclopedic project that treats arithmetic as a philosophical discipline. In the tradition of Pythagoreanism and Neoplatonism, Uncorno argued that numbers were the fundamental building blocks of reality. His work served as a bridge for philosophers who viewed mathematics as a way to understand the "divine order" of the cosmos.  2. Scholasticism vs. Humanism In the context of Italian philosophy, Uncorno represents the transition from medieval scholasticism (which prioritized formal logic) to humanist science (which emphasized the utility of the "quadrivium"—arithmetic, geometry, music, and astronomy). By systematizing the properties of numbers, he contributed to the "mathematization of nature," a prerequisite for the philosophical shifts later championed by Galileo Galilei and the Scientific Revolution.  3. Practical Philosophy and the "Abaco" Tradition Uncorno integrated the rigorous theory of ancient Greek mathematicians (like Diophantus and Euclid) with the practical abaco tradition of Italian merchants. This fusion was philosophically significant because it elevated "low" practical arts to the status of "high" theoretical wisdom. This shift helped redefine the philosopher's role in society—from a secluded thinker to a contributor to civic and economic life.  arimmetica universale.  T: Sir, before we begin: Oxford, 1939. You want Unicorno, Venice, 1552, and you want him to sound like himself. You also want me not to steal his voice by translating him into ours. G: Precisely. Give me the Latin as an object, not as a surrender. And clean it first, because what you copied is a battlefield of long-s, printer’s habits, and OCR panic. T: Yes, sir. I will regularise the obvious letter confusions, restore spacing, and keep the Latin otherwise intact. I won’t “improve” his syntax. Here is a cleaned copy of your passage, as a continuous excerpt: Rhetores etiam istorum instar orationum suarum partes sibi proportionatis locis convenienti numero assignant; alioqui quid prius, quidque posterius dicendum esset nescientes, inconcinnam et absurdam redderent orationem. Verum cum iam ostenderimus sine Proportionis ratione non recte posse exerceri, quis Dialecticos ad syllogismorum veritatem demonstrandam, multa proportionis aut mathematicos naturam ac vim redolentia, a Mathematicis negat sumpsisse praeceptionibus? Quis tandem originem ac fundamentum omnium liberalium artium Grammaticam, dum nobis mensuram quandam in syllabis recte scribendis ac proferendis, gravibus, acutis, circumflexis accentibus suppeditat, a Proportionis legibus longe differre negaverit? Certe nemo vobis, nisi aut barbarus aut imperitus. G: Good. You’ve already done the essential service: you’ve made him legible without modernising him out of existence. T: I have kept his argumentative rhythm too: rhetoric, then dialectic, then grammar; and the cadence of the rhetorical questions. G: Now give it to me in pieces. Small enough that we can “hear” him. Begin only with the first sentence. T: Very well, sir. First segment, as Unicorno gives it: Rhetores etiam istorum instar orationum suarum partes sibi proportionatis locis convenienti numero assignant; alioqui quid prius, quidque posterius dicendum esset nescientes, inconcinnam et absurdam redderent orationem. G: The first thing to notice is the audacity of his “etiam.” “Rhetores etiam…” It is an inclusion move. He has already talked about proportion elsewhere, presumably in the familiar mathematical arts, and now he says: even the rhetoricians. T: So he is not flattering rhetoric; he is annexing it. G: Exactly. He is doing what later centuries pretend they invented: exporting a formal concept into the arts of discourse. But he does it without apology, as if it were obvious that speech is built. T: You want me to resist translating, sir, so I’ll only point at the structure. He places “partes” close to “orationum suarum.” He treats the oration as something with parts. G: And those parts are not merely parts; they are “assignant” to “proportionatis locis” and to a “convenienti numero.” That is two axes: spatial placement and numerical measure. Rhetoric becomes architecture plus arithmetic. T: A speech, then, has “places” and “numbers.” G: And if you remove proportion, you get temporal confusion: “quid prius, quidque posterius.” That’s the astonishing bit. Proportion is not just ornament; it is a condition for ordering. Without it, you do not know what comes first. T: He makes “not knowing” the cause of stylistic failure. G: He makes it the cause of conceptual failure too, if you read him strictly. If you do not know what is first and what is second, you are not merely inelegant; you are absurd. That’s a strong word to aim at a speaker. T: He is implying that discursiveness is a kind of logical error. G: Yes. In Oxford terms, he is treating bad style as a failure of rational control. Which is why your project about “arts of discourse” is justified: he is already putting rhetoric under a regime of rule-governed structure. T: Shall I give the next segment, sir? G: Proceed, but keep it short. T: Second segment: Verum cum iam ostenderimus sine Proportionis ratione non recte posse exerceri… G: Pause there. He says, in effect: we have already shown. That tells you this is a late-stage move. He has established a thesis: without “ratio proportionis” nothing is properly exercised. T: “Ratio” is doing heavy work here. G: And it’s deliberately elastic. In his mouth, “ratio” can be account, method, principle, rationale. He doesn’t choose. He wants the umbrella term so he can march from mathematics into rhetoric and then into logic and grammar without changing vocabulary. T: So he builds a bridge by keeping one word. G: And also by choosing “exerceri.” Not “intellegi,” not “dici,” but “exerceri.” Practice. Exercise. The arts are exercised. Rhetoric is not mere theory; it’s a trained activity. That, too, feels oddly modern. T: Shall I continue into the dialectic question? G: Yes. Give me the next full question. T: Third segment: …quis Dialecticos ad syllogismorum veritatem demonstrandam, multa proportionis aut mathematicos naturam ac vim redolentia, a Mathematicis negat sumpsisse praeceptionibus? G: Now we are where your marginal note said “logica” or “dialectica.” Notice the tactic: he does not argue; he asks who would deny it. T: So he treats denial as the eccentric position. G: Exactly. He does not need to prove; he needs only to shame the dissenter. “Quis… negat?” It is the classic rhetorical machinery: render the contrary view socially impossible. T: And he ties dialectic to syllogisms immediately. G: Yes, and to “veritas demonstranda.” Dialectic here is not casual disputation; it is a discipline whose target is demonstrable truth. And then he claims that in the very apparatus of syllogistic demonstration there are features that “redolent” of proportion or of the nature and power of mathematics. T: “Redolentia” is a wonderful word. It says “smelling of.” G: Dry humour is already present in him. Dialecticians, he implies, have been borrowing from mathematicians, whether they admit it or not. Their syllogisms smell like mathematics. T: And the borrowing is framed as “praeceptiones.” G: Instruction, precepts, rules. He is not claiming dialectic uses numbers. He is claiming it uses methodological forms and constraints learned from mathematical practice: the idea of rigor, of inference governed by form, of demonstration as accountable sequence. T: So you would say his “proportion” here is not merely ratio in the arithmetic sense, but structured relation. G: Precisely. He is making a philosophical move: proportion as a general schema of relational intelligibility. It has a technical home in mathematics, but its authority extends into how valid reasoning is trained and recognised. T: That seems like the “epoch-making relevance” you wanted G to press. G: Yes. The epoch-making part is that he refuses to let the “arts of discourse” claim autonomy from mathematical discipline. He doesn’t say rhetoric is mathematics; he says rhetoric requires proportion, dialectic borrows mathematical precepts, and grammar itself is proportion-law in miniature. T: Grammar next, sir? G: Give me the grammar question whole. T: Fourth segment: Quis tandem originem ac fundamentum omnium liberalium artium Grammaticam, dum nobis mensuram quandam in syllabis recte scribendis ac proferendis, gravibus, acutis, circumflexis accentibus suppeditat, a Proportionis legibus longe differre negaverit? G: Now he does something bold. He calls grammar the origin and foundation of all the liberal arts. T: He is placing grammar beneath everything. G: And he does it in a way that suits your thesis: if proportion can reach grammar, it has reached the base layer of discourse. Rhetoric is the art of persuasion; dialectic is the art of valid inference; grammar is the condition for having articulate units at all. T: He ties grammar to “mensura.” G: Yes, and that is the whole point. He is saying: grammar supplies measure in syllables, in writing and utterance, and in the accents. He is thinking of quantity, stress, pitch, duration: the metrical and phonological governance of speech. T: So “proportion” here is literally audible. G: Exactly. It’s not metaphor. It is the measure that makes a syllable count as this syllable rather than a mush. He is treating the material of language as already ruled by quantitative relation. T: And then: “a Proportionis legibus longe differre.” G: This is his punch: who would say grammar differs far from the laws of proportion? In other words: if you accept that grammar teaches measured articulation, you have accepted proportion in the very teeth of speech. T: So rhetoric, dialectic, grammar: all under proportion. G: That is the trifecta. If someone wanted to make a Renaissance case for what we would call “formal constraints across disciplines,” this is it. And he does it without seeming to know he’s being interdisciplinary. For him it’s obvious: the mind is trained by measure. T: There is still his final sting, sir. G: Yes. Give the last sentence. T: Fifth segment: Certe nemo vobis, nisi aut barbarus aut imperitus. G: And there it is: the refusal becomes barbarism or ignorance. T: That is rather sharp. G: It is sharp, and it is useful for your later staged dialogue. It gives G a way to tease T in 1939: “are you denying Unicorno, Thomson? Take care: he has a category ready for you.” T: Sir, that is unkind. G: It is historically accurate. Now, for our vignette: you want T to feed Latin, and G to “teach” in English. We have the Latin. We have the analytic spine. The rest is expansion: how to make “proportion” plausible as the hidden discipline of discourse. T: Shall we keep the setting in a college room, sir? Books open, rain outside, faint threat of war, and you insisting it is only a footnote? G: No melodrama. Dry. It is Oxford: the war is in the corridor, but the talk pretends it is in Venice, 1552. T: Then may I propose the running joke, sir: that Unicorno has discovered the maxims before you have named them? G: Careful. Not “before.” But: he has discovered that talk has architecture, that reasoning has borrowed rigor, and that grammar has measure. He is a predecessor in temperament, not in doctrine. T: So I should not have him be “proto-Grice.” G: Precisely. No anachronistic coronation. Let him be Unicorno: a man who thinks “proportion” is the spine of intelligibility, whether in numbers or in speech. T: And you, sir, will keep reminding me that “vi” is force, not six. G: Yes. That will be our recurring correction. Because it is funny, and because it is philologically sane. T: Then I will insert, as needed, that the title is “De admiranda vi proportionis,” and that the marginal “Rhetorica” is not the numeral VI pretending to be theology. G: Good. And when we come to your later “G and T” dialogue, the rhythm can be: T produces Unicorno; G refuses to translate; G explains what the Latin is doing as an act; T tries to force an English paraphrase; G refuses; and we end with the punchline that even grammar, the humblest, is already “mathematical” in the sense that it is measured. T: And the punchline, sir? G: Something like: “So, Thomson, if you cannot keep quantity in your vowels, do not boast of clarity in your arguments.” T: I see. The war outside; the accent marks within. G: Exactly.Grice: Professore Unicorno, mi permetta una battuta aritmetica: quando lei parla di “arimmetica universale” – con quella grafia così evocativa – intende forse dire che 5 = 7 = 12? O è solo un tentativo per far impazzire i contabili e i filosofi, usando quell’esempio famigerato che mette tutti in crisi? Unicorno: Ah, caro Grice, se la mia “arimmetica universale” fosse davvero così elastica, i negozianti di Bergamo farebbero festa ogni giorno! Ma la verità è che, per me, i numeri sono come maschere in commedia: si scambiano, si confondono, ma dietro c’è sempre una logica – anche se a volte è quella della buona cucina bergamasca, dove ogni ricetta ha il suo misterioso equilibrio. Grice: Dunque, professore, lei sostiene che, per capire la “arimmetica universale”, bisogna essere un po’ filosofi, un po’ matematici e, mi sa, anche un pizzico di poeti? Allora propongo: se 5 è la somma delle nostre battute, 7 il numero delle risate, e 12 la quantità di dolci al prossimo convivio filosofico, la matematica diventa davvero universale! Unicorno: Grice, lei ha colto il segreto: l’arimmetica universale serve a scoprire che, nella vita e nel pensiero, il risultato migliore si ottiene quando si mescolano numeri, idee e un po’ di ironia. E se qualche volta 5 = 7 = 12, beh, basta che la conversazione non perda il suo equilibrio – e che nessuno, magari, si ritrovi con meno dolci di quanto sperava! Unicorno, Giuseppe (1552). De admiranda vi proportionis, eiusque necessaria cognition, ad Bergomenses oratio. Venezia: Arrivabene.