(iv) Mill disregards Hobbes’s theory of signification and reads Computation or Logic as if it belonged to a wholly Ockhamistic line of thought.
(v) Mill no doubt decided to oppose “denotation” (instead of nomination) to “connotation” under the influence of Hobbes’s own use of denotare.
The above are of course merely hypotheses. The whole story of the give and take between Ockham and Hobbes and Hobbes and Mill has still to be written.
9.12. Conclusions
In the history of these philosophical terms, issues are clearly at stake which continue to be of considerable relevance from the semiotic and philosophical points of view. Mahoney (1983: 145) remarked on a curious contradiction, or at least a hiatus, between Bacon’s epistemology and his semantics. From a gnoseological point of view, we can know a thing through its species, and we cannot name a thing if we do not know it. When we utter a vox significativa, then, it is because we have something in mind. From a semiotic standpoint, however, the opposite is what happens, or at least something substantially different: we apply the word directly to the thing, without any mediation of the mental image or the concept or the species.
Such is the paradox of any extensional semantics concerned with the relationship between a sentence and its truth conditions. Every extensional semantics, from Bacon to Tarsky, rather than considering the relation between words and meaning, concentrated on the relation between words and something that is the case. An extensional semantics so conceived does not address the problem of how we can know that p is the case. If instead we were to focus on this problem, we would need to be able to identify the mental processes or the semantic structures that make it possible to know or to believe that p is the case. We would need to identify the difference between knowing or believing that p is the case, and the fact that p is the case. But a strict extensional semantics is not concerned with these kinds of epistemological questions, seeing that its exclusive object of study is the formal relation between propositions and what is assumed to be the case. “Snow is white” is true only if snow is white. For an extensional semantics, the marginal and accidental fact that it is hard for us to know on what basis we may assume that snow really is white is not a problem
An intensional semantics on the other hand is invariably concerned with the description of our cognitive structures. It may not be capable of determining whether snow is or is not really white, but it seeks to imagine and reflect upon the mental organization and encyclopedic structures that permit us to assume that snow is white.
Thus, in the last analysis, the history of the alternate fortunes of denotation (and the fact that its status remains moot) turns out to be a symptom of the unending dialectic between a cognitive and a truth-conditional approach.
The original version of this essay was published in English with the title “Denotation” in Eco and Marmo (1989), and subsequently in Italian as an appendix to Eco (1997a). [Translator’s note: This appendix was not included in the English translation of Eco (1997).] I would like to thank Mariateresa Beonio Brocchieri Fumagalli, Andrea Tabarroni, Roberto Lambertini, and Costantino Marmo for discussing the content with me and for their valuable suggestions.
1. Here and elsewhere references to the standard edition of the Collected Papers (Peirce 1931–1958) appear under the abbreviation CP.
2. Recently, Lo Piparo (2003) has proposed a different interpretation of the passage in question, according to which the passions of the soul are not mental images of things, but ways of being of thought, cognitive modalities (like reflecting, being afraid, feeling joy). In the same way, the pragmata cannot be things that already exist or facts in general, otherwise how are we to explain why, in other parts of his opus, Aristotle claims that we can think of nonexistent or false things like the chimera, or events that might exist but whose existence it is impossible to demonstrate. See the earlier references to Lo Piparo’s theory in Chapter 4 of this volume, section 4.2.5. Nevertheless, even if we were to accept his reading, I do not think it would alter the nature of the problem under discussion.
3. On Boethius’s use of the term “nota” see our Chapter 4.2.4. For an English translation of this work by Boethius, see Boethius 1988.
4. In the Dialectica (V, II, De definitionibus; De Rijk 1956: 594), it is clear that a nomen is determinativum of all the possible differences of something, and it is by hearing a name pronounced that we are able to understand (intelligere) them all. The sententia includes within itself all these differences, while the definitio posits only certain of them, those, that is, needed to determine the meaning of a name in the context of a proposition, eliminating all ambiguities: “Sic enim plures aliae sint ipsius differentiae constitutivae quae omnes in nomine corporis intelligi dicantur, non totam corporis sententiam haec definitio tenet, sicut enim nec hominis definitio animal rationale et mortale vel animal gressibile bipes. Sicut enim hominis nomen omnium differentiarum suarum determinativum sit, omnes in ipso opportet intelligi; non tamen omnes in definitione ipsius poni convenit propter vitium superfluae locutionis.… Cum autem et bipes et gressibilis et perceptibilis disciplinae ac multae quoque formae fortasse aliae hominis sint differentiae, quae omnes in nomine hominis determinari dicantur … apparet hominis sententiam in definitionem ipsius totam non claudi sed secundum quamdam partem constitutionis suae ipsius definiri. Sufficiunt itaque ad definiendum quae non sufficiunt ad constituendum.”
5. “Unde haec vox, homo est asinus, est vere vox et vere signum; sed quia est signum falsi, ideo dicitur falsa” (I, iii, 31). “Nomina significant aliquid, scilicet quosdam conceptus simplices, licet rerum compositarum …” (I, iii, 34).
6. The preposition per “denotes the instrumental cause” (IV Sent. 1, 1, 4). Elsewhere he affirms that “praedicatio per causam potest … exponi per propositionem denotantem habitudinem causae” (I Sent. 30, 1, 1). Or “dicitur Christus sine additione, ad denotandum quod oleo invisibili unctus est …” (Super Ev. Matthaei 1, 4). In all these and in similar cases the term denotatio is always used in the weaker sense.
7. De Rijk (1962–1967: 206), for example, affirms that in Abelard “a point of view appears to prevail that is not based on logic” and that the term impositio “stands in most cases for prima inventio” and that “rarely is it encountered with the sense of denoting some actual imposition in this or that proposition emitted by some actual speaker. When even the voces are separated from the res, their connection with the intellect leads the author into the realm of psychology, or confines him to that of ontology, since the intellectus in its turn is referred to reality. The theory of predication too appears to be extremely influenced by the prevalence of perspectives that do not belong to logic.” Hence, the medieval logicians “would have obtained better results if they had completely abandoned the very notion of signification” (De Rijk 1982: 173). But we cannot expect the medievals to think in terms of modern truth-functional semantics.
8. In the Vienna commentary on Priscian (see De Rijk [1962–1967]: 245), a name “significat proprie vel appellative vel denotando de qua manerie rerum sit aliquid.” Thus, denotare still appears to be connected with the significance of universal nature.
9. “Suppositio vero est acceptio termini substantivi pro aliquo. Differunt autem suppositio et significatio, quia significatio est per impositionem vocis ad rem significandam, suppositio vero est acceptio ipsius termini iam significantis rem pro aliquo.… Quare significatio prior est suppositione” (Tractatus VI, 3).
10. See Chapter 4 in the present volume.
11. We have in mind the first and more reliable part of the text, dedicated to the true Scotus and not to Thomas of Erfurt.
12. Concerning this issue, see Pini (1999).
13. For significare, see Boehner (1958) and for denotari, Marmo (1984).
14. “Item repraesentatum debet esse prius cognitum; aliter repraesentans nunquam duceret in cognitionem repraesentati tamquam in simile. Exemplum: statua Herculis nunquam duceret me in cognitionem Herculis nisi prius vidissem Herculem; nec
aliter possem scire utrum statua sit sibi similis aut non. Sed secundum ponentes speciem, species est aliquid praevium omni actui intelligendi objectum, igitur non potest poni propter repraesentationem objecti” (Quaest. In II Sent. Reportatio, 12–13). See also Tabarroni (1984).
15. “Sicut per istam ‘Homo est animal’ denotatur quod Sortes vere est animal. Per istam autem ‘Homo est nomen’ denotatur quod haec vox ‘homo’ est nomen … Similiter per istam “Album est animal,” denotatur quod illa res, quae est alba, sit animal, ita quod haec sit vera: ‘Hoc est animal,’ demonstrandum illam rem, quae est alba et propter hoc pro illa re subjectum supponit.… Nam per istam: ‘Sortes est albus’ denotatur, quod Sortes est illa res, quae habet albedinem, et ideo praedicatum supponit pro ista re, quae habet albedinem.… Et ideo si in ista ‘Hic est angelus,’ subjectum et praedicatum supponunt pro eodem, propositio est vera. Et ideo non denotatur, quod hic habeat angelitatem … sed denotatur, quod hic sit vere angelus.… Similiter etiam per tales propositiones: ‘Sortes est homo,’ ‘Sortes est animal’… denotatur quod Sortes vere est homo et vere est animal.… Denotatur quod est aliqua res, pro qua stat vel supponit hoc praedicatum ‘homo’ et hoc praedicatum ‘animal’ ” (Summa, II, 2). There is at least one example, taken from the Elementarium logicae and cited by Maierù, of denotare in the active voice, in which Ockham distinguishes between the two meanings of appellare. The first meaning is Anselm’s, while, apropos of the second, Ockham writes: “aliter accipitur appellare pro termine exigere vel denotare seipsum debere suam propriam formam.” It would seem that here denotare stands for “govern” (or “require”) or postulate a coreference within the framework of the linguistic context.
16. For a similar use of denotari, see Ockham’s Quaestiones in libros Physicorum III, partial edition by Corvino (1955).
17. Maierù (1972) cites Peter of Mantua: “Verba significantia actum mentis ut ‘scio,’ ‘cognosco,’ ‘intelligo,’ etc. denotant cognitionem rerum significatarum a terminis sequentibus ipsa verba per conceptum.” Right after this sentence, Peter gives an example: “Unde ista propositio ‘tu cognoscis Socratem’ significat quod tu cognoscis Socratem per hunc conceptum ‘Socratem’ in recto vel oblique” (Logica, 19vb–20ra). It is evident that denotare and significare mean more or less the same thing, and that both terms are used to speak of propositional aptitudes—an intensional theme if ever there was one.
10
On Llull, Pico, and Llullism
We have only to leaf through a few studies on Christian Kabbalism (for instance, Secret 1964; French 1972; Evans 1973) to meet up with the cliché of Ramon Llull the Kabbalist, served up with minimal variations. Llull as magus and alchemist appears in the context of magic in the Prague of Rudolf II, as well as in the library of John Dee, who “was deeply immersed in Llullism and apparently accepted the traditional attitude toward the Llullist-cabalist synthesis” (French 1972: 113). Llull is present in the works of professed Kabbalists (such as Burgonovus, Paulus Scalichius, and the superficial and credulous Belot)1 as well as in those of the enemies of Kabbalism, like Martino Del Rio,2 to the point that, when Gabriel Naudé came to write his Apologie pour tous les grands hommes qui ont été accusés de magie (Paris, 1625) he felt obliged to defend the poor Catalan mystic energetically against any suspicion of necromancy. To add to the confusion, “in a later Renaissance transformation, the letters B through K used in the Llullian Ars became associated with the Hebrew letters that the cabalists contemplated and that supposedly signified angel names and the attributes of God. These Hebrew letters, which were thought to have a summoning power over the angels, were the same ones used by practical cabalists like John Dee” (French 1972: 49).
Numerology, magic geometry, astrology, and Llullism are inextricably confused, in part because of the series of pseudo-Llullian alchemistic works that invaded the sixteenth-century scene. Furthermore, the names of the Kabbalah could also be carved on seals, and a whole magical and alchemical tradition made seals with a circular structure popular (Llull practiced his art on a circular wheel). And, for his part Athanasius Kircher, in his 1665 Arithmologia, also illustrated a number of magic seals in the form of numerical tables.3
However, what influence the Kabbalistic tradition had on Llull is not something we need to discuss in the present context. Llull was born in Majorca—a crossroads on the margins of Europe where encounters took place among Christian, Arabic, and Hebrew cultures, and it is certainly not impossible that someone living where three great monotheistic religions met could have been subject to the influence, visual at least, of Kabbalistic speculation. Llull’s Ars combines letters on three concentric wheels and, from the very beginnings of the Kabbalistic tradition, in the Sefer Yetzirah (“Book of Creation,” written at an uncertain date between the second and sixth centuries), the combining of the letters is associated with their inscription on a wheel. What is certain, however, is that nothing is further from Kabbalistic practices than Llull’s Ars, at least as formulated by its founder.
10.1. What Exactly is Llull’s Ars?
If we are to understand the internal mechanics of the Ars, we must first review a few principles of Llull’s system of mathematical combinations.
We have permutation when, given n different elements, every possible change in their order has been realized. The typical case is the anagram.4 We have disposition when n elements are arranged t by t, but in such a way that the order also has differential value (AB and BA, for instance, represent two different dispositions).5 We have combination when, if we have to arrange n elements t by t, inversions of order are not relevant (AB and BA, for instance, represent the same combination).6
The calculus of the permutations, dispositions, and combinations may be used to solve a number of technical problems, but it could also be used for the purposes of discovery—to delineate, in other words, possible future “scenarios.” In semiotic terms, what we have is a system of expression (made up of symbols and syntactic rules) such that, by associating the symbols with a content, various “states of things” (or of ideas) can be imagined. In order for the combinatory system to be most effective, however, it must be assumed that there are no restrictions on thinking all possible universes. Once we begin to designate certain universes as not possible, either because they are improbable in the light of the evidence of our past experience or because they do not correspond to what we consider to be the laws of reason, then external criteria come into play that induce us, not merely to discriminate among the results of the system of combinations, but also to introduce restrictive rules into the system itself. In the case of Llull, what we have is a proposal for a universal and limitless system of combinations, which as such will fascinate later thinkers, but which at its very inception is severely limited, for reasons both theological and logical.
Llull’s Ars involves an alphabet of nine letters, from B to K (no distinction is made between I and J), and four combinatory figures. In a Tabula Generalis, Llull establishes a list of six sets of nine entities each (the six are: Absolute Principles or Divine Dignities, Relative Principles, Questions, Subjects, Virtues, Vices). Each entity may be assigned to one of the nine letters (our Figure 10.1).
Taking Aristotle’s list of categories as a model, the nine Divine Dignities or attributes of God’s being (Bonitas, Magnitudo, Aeternitas or Duratio, Potestas, Sapientia, Voluntas, Virtus, Veritas, and Gloria) are subjects of predication while the other five columns contain predicates.
Figure 10.1
The Ars includes four figures or illustrations, which in the various manuscripts are highlighted in different colors.7
PRIMA FIGURA. Llull’s first figure represents a case of disposition. The nine Absolute Principles are assigned to the letters. Llull explores all the possible combinations among these principles so as to produce propositions such as Bonitas est magna (“Goodness is great”), Duratio est gloriosa (“Duration is glorious”), and so on. The principles appear in nominal form when they are the subject and in adjectival form when they are
the predicate, so that the sides of the polygon inscribed in the circle are to be read in two directions (we may read Bonitas est magna, as well as Magnitudo est bona). The possible dispositions of nine elements two by two, when inversions of order are also allowed, permit Llull to formulate seventy-two propositions (see Figure 10.2).
Figure 10.2
The figure permits regular syllogisms “ut ad faciendam conclusionem possit medium invenire” (“if the middle term be suitable for reaching a conclusion”) (Ars brevis II).8 To demonstrate that Goodness can be great, it is argued that “omne id quod magnificetur a magnitudine est magnum—sed Bonitas est id quod magnificetur a magnitudine—ergo Bonitas est Magna” (“everything made great by greatness is great—but Goodness is what is made great by greatness—therefore Goodness is great”).
SECUNDA FIGURA. Llull’s circle (unlike the one in his first figure) does not involve any system of combinations. It is simply a visual-mnemonic device that allows us to remember the connections (already foreordained) among various types of relationships and various types of entities (see Figure 10.3).
Figure 10.3
For example, both difference and concordance, as well as contrariety, can be considered with reference to (i) two sensitive entities, such as stone and plant; (ii) one sensitive and one intellectual, such as body and soul; and (iii) two intellectual entities, such as soul and angel.
TERTIA FIGURA. This figure evidently represents a case of combination, considering that in it all possible pairings of the letters are considered, excluding inversions of order (the table includes BC, for example, but not CB), and the doublets generated are thirty-six, inserted into what Llull dubs thirty-six chambers. But the chambers are virtually seventy-two, because each letter may indifferently become subject or predicate, that is, a BC can also be read as a CB (Bonitas est magna also gives Magnitudo est bona, see Ars magna VI, 2, and Figure 10.4).9