Abstract
In the categorial grammar adopted here as interpretative framework, the semantic component is introduced following the standard procedure for modal predicate logic: we define a model structure, an assignment of values to variables and, based on these, the interpretation of well-formed expressions. According to the principle of compositionality, the expressions which are object of a syntactic rule take on a meaning such as to play the role of functor or argument with respect to the meaning of the other expression constructed according to the same rule.1
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Reference
Cf. Montague (1973)[(1974)] 258–259, where, however, the intermediate’ language, to which the semantic interpretation applies, is that of an intensions logic: see Appendix A.l.
Quine (1953), p. 42.
De Inst. Arith. 8; In Cat. 202.
De Inst. Arith. 57.
In Isag. 25, 1; 79, 2–3.
De Inst. Arith. passim.
In Isag. 213 – 216.
In Cat. 180 A.
Log. Ingred. 72, 1–5: “definitionis compositio naturalem rei ordinem imitatur [...] unde res speciei cum in materia naturaliter incipiat, non est completa nisi qualitate superposita” (cf. also Log. Nostr. 567, 26–30). On the abstractness of the concept of nature, see Jolivet (1966)[(1987)].
As to these expressions, we refer to some places devoted to the specific difference: Intr. 32, 26–39; 33, 22–24. Dial. 560, 9 – 561, 2. Log. Ingred. 72, 1–8; 74, 2–4; 83, 16–24.
Log. Ingred. 290, 9–10.
On (a) see infra 4.2, 4.3, 4.5; on (b): 4.4; on (c) 2.5, 3.4, 5.1, 5.2.
Jolivet (1975a) [(1987)] 128–132.
Log. Ingred. 13, 19; 149, 36. Log. Ingred. 28, 4; Dial. 157, 15; 565, 38. Log. Ingred. 64, 20; 113, 29.
Log. Ingred. 70, 28; 83, 18–19; cf. also Log. Ingred. 216, 36–37: “relationes sunt res”.
Log. Ingred. 125, 16. Cf. also: Log. Ingred. 76, 5; 84, 23; 99 passim.
Log. Ingred. 167, 17–18.
Log. Ingred. 20, 31–32.
Log. Ingred. 13, 5–17; Log. Nostr. 515, 14–31. Abelard criticizes this thesis. On the problem of identification, see Gracia (1984).
In Isag. 161, 16–18: “omne quod commune est uno tempore pluribus, id unum esse non poterit”.
Log. Ingred. ITA, 27: “tale quid quod non est aliqua aliarum rerum”. The characterization of ‘singularity’ should also be bome in mind: “dicunt res singulas non solum formis ab invicem esse diversas, verum personaliter in suis essentiis esse discretas, nec ullo modo id quod in una est esse in alia [...] earum discretio personalis secundum quam [...] haec non est illa [..] est per ipsam essentiae diversitatem” (Log. Ingred. 13, 19–25).
Cf. Log. Ingred. 72, 4–8; 78, 16–17; 80, 2–4; 84, 23; 99, 7–15; 99, 31–34; etc. The expressions ‘res specieV and ‘res generis’ are rather ambiguous. Anyway, it is advisable to believe that the term ‘res’ occurs in the singular form, as for example in “res dicitur genus quae est essentia diversarum specierum” (Log. Ingred. 125, 16). See Jovilet (1975) [(1987)] 128–132. In the realist interpretation ‘translated’ into Abelard’s language, these res are called ‘naturae communi’ or ‘status’; these notions recur together with the variants esse and maneria rerum, in the whole logical work and, in their twofold logical-philosophical guise, have an important history in the twelfth century; cf. the information in John of Salisbury about Walter of Mortagne (Metalogicon II, 17); the text edited by Hauréau (1891), 298–320; Ars Meliduna [de Rijk (1967)] 306–390, in particular pp. 306–318. The concepts of esse and naturae rei are widely used in Chartres (see the works edited by Haring (1971)).
Log. Ingred. 23, 26–27. 24 Log. Ingred. 171, 39–41.
Log. Ingred. 170, 24.
One of the meanings of ‘genus’ according to Porphyry is that of ‘family’; in the Boethian translation: “genus enim dicitur et aliquorum quodammodo se habentium ad unum aliquid (= founder of a family) et ad se invicem collectio” (In Isag 171, 33–34); although this meaning is not exactly the one which interests commentators, Abelard notes, following Porphyry and Boethius, that the philosophical meaning ‘illud cui supponitur species’ is in some way derived through a form of translatio (cf. infra), from the non-philosophical meanings of principium and, precisely, collectio. (Log. Ingred. 34, 28–30; ibid. 38–39; 35, 4–9). Boethius recalls the analogy between philosophical and non-philosophical meanings in In Isag. 37, 2–14 and 178, 14 – 179, 17; species and genera, meant in a philosophical sense, are called collectiones, collectiva, colligentia (e.g. In Isag. 78) and defined respectively as “cogitatio collecta ex individuorum dissimilium numero substantiali similitudine” and “cogitatio collecta ex specierum similitudine” (op.cit. 166, 16–18).
De Gen. et Spec. [Cousin (1836)] 524–530. The author of De Gen. et Spec, uses the notion of collectio to solve the problem of universals, whereas Abelard is critical towards a ‘set-theoretic’ solution. It should be noted that according to Abelard, species and genera when considered as real universals (i.e. as essences inherent, as a whole, in a plurality of single things) are not collectiones; the possibility remains for species and genera to be collectiones when differently intended.
On discretio as a differentiating character, cf. Log. Ingred. 19, 24–26 (only what has the property of being so and so is a discrete thing); 29, 6 (discrete things are denoted by common nouns); Log. Ingred. 142, 21–36; 149, 36–37 (the discretio is the differentiating character of primary substances). On non-differentiating discretio, cf. the definition of unum and the texts quoted on numerical discretio. ’ See Frege (1892).
By considering a type rising or a distinction between objects, in the sense explained in Appendix A.2.
Cat 2, lb 3–4.
I do not regard Marenbon’s argument against the identification of status and significata as conclusive (cf. Marenbon (1997a) 190–195). As a matter of fact, we have texts in which expressions have a meaning relation (demonstratio: Log. Ingred., 17, 20–21; denotatio: Log. Ingred., 150, 22–23) with status, and with the close notion of natura (designatio: Log. Ingred., 24, 17–18; 157, 40; demonstratio: Log. Ingred., 22, 18; 50, 17–18; 111, 26–27; notatio: Log. Ingred. 78, 39–40; determinatio: Log. Ingred., 157, 41–42; significado: Log. Ingred., 170, 41–42). Besides, status is embodied in signification according to Log. Ingred. 158, 16–18. Since status is the communis causa impositions, I think that texts which refer to meanings regarded as causes must also be considered (e.g.: “sumpta propter adiacentem formam significanda sunt reperta”, “nomina propter naturam demonstrandam sunt reperta”...). In this connection the terminological similarities between the different semantic relations (cf. next paragraph) must be borne in mind.
What we said about ‘Socrates’ is closer to the treatment of proper nouns in Montague (1970), where such terms constitute the proper argument of intransitive verbs. Later on, in Montague (1973), the same author assigns categorial index t/IV to term like ‘Socrates’ (which means that, according to the formation rules, they take an intransitive verb and form a sentence): in this case, the relation function-argument is reversed. The categorial index e (=entity), which characterizes terms which occur only as arguments of intransitive verbs, is not assigned to any natural language expression. As for proper nouns, things may be more complicated for Abelard too. Pronouns, demonstratives and expressions used in a function similar to the one of modern variables play a specific role when indicating a certain thing in a ‘definite’ way. Furthermore, Abelard sometimes assigns proper nouns a property meaning similar to that of common nouns and verbs.
Therefore we cannot agree with Tweedale’s thesis (1976), according to which Abelard’s aim is to eliminate all kinds of abstract entities (cf. in particular pp. 133–211).
Cf., among other texts, Log. Ingred. 157, 12–13: “non aliae res nominantur ab universalibus quam a particularibus”.
Log. Ingred. 16, 39–40; cf. also Log. Ingred. 58 – 59.
Log. Ingred. 45, 28–30; Log. Ingred. 148, 10–12.
Cf. Frege (1892) and Jacobi (1983a). A different approach can be found in Appendix, where ‘be predicable’ means ‘be composable with the copula’ and where the function assigned to common nouns is not a truth function.
On the identity of meaning see Log. Ingred. 308, 27–28; 353, 33–37. On the copulative function: Dial. 123, 15–28; 129, 22–23. On the problem of predication: Jacobi (1986) and infra 5.2.
Jacobi (1986) 153–154.
In order to understand this aspect, we can refer to Montague’s work in which common nouns and intransitive verbs are assigned a different syntactic role and, at the same time, a meaning of the same kind. On this matter, cf. Montague (1970), (1973). The most detailed analysis of the relation between nouns and verbs is contained in Abelard’s commentaries on De Interpretatione. Abelard holds that it is possible to maintain the same signification of things (significato rerum) of nouns and verbs, and, at the same time, distinguish their syntactic behaviour in terms of conceptual meaning (cf. the final paragraph for an analysis of this issue).
On the doctrine of dictum compare in particular the following passages: Log. Ingred. 365–370, 390–393; Dial. 154–160; 489 and ff. On the same problem, cf. Kretzmann (1970), Nuchelmans (1973), de Rijk (1975), de Libera (1981), King (1982), Iwakuma (1997b). On the dictum in the Logica Modernorum, see the Ars Meliduna, the Ars Burana [de Rijk (1963)] 357–390, 208–213; Pinborg (1972) 57. On later medieval developments, see Perler (1994); the distinction of entities into four classes attributed to Gregorius of Rimini (p. 155) is somehow similar to Abelard’s position on denoted ‘things’.
Among the authors which have followed this path in recent times there are Marenbon (1997a), Brower (1997). The real problem is: what is category theory? I have tried to explain my point in 4.1.
Wade (1963) 171.
De Libera (1981).
For some explanations see Appendix A.1.
On the grammar of infinitive constructions, cf. Kneepkens (1980).
Montague (1969), (1970), (1973). See A.l.
Log. Ingred. 58, 12–13; 140, 28–29; 157, 23–28. After Abelard, the term ‘appellatio’ will be used in a different way: cf. Pinborg (1972) 61; Maierù (1972) 47–137; de Rijk (1982) 161–173.
Log. Ingred. 49, 22–23; 157, 31–32; ibid. 40–42; 158, 18–20; 246, 7–9; Dial. 111, 30–31.
Log. Ingred. 22, 4–6.
Meaning at least partially coincident with that of the universals predicable of the same singular term: Log. Ingred. 49, 22–23; 157, 31–32.
Cf. (in order): Log. Ingred. 157, 40–42: “‘homo’ [...] animalis quoque naturam determinat”; 171, 3–4: ‘“homo’ eandem naturam iam denotabat”; 50, 20: “nullam vel naturam vel formam indivíduum notat”; 157, 39–40: “(secundae substantiae) certam essentiae naturam designant”; 112, 34–36: “qui vocabulum invenit [...] rei naturam consideravit, ad quam demonstrandam nomen imposuit”.
As an illustration, the terms ‘ventas’ and ‘falsitas’ occur as objects or subjects of verbs: ‘obtinere’, ‘ coniungere’, ‘haerere’, ‘carere’, ‘pronuntiare’ , ‘habere’, ‘tenere’, ‘custodire’, ‘distribuere’, ‘conspirare’, ‘(non) discrepare’, ‘constare’, ‘consonare’, ‘discordare’, ‘dissentire’, ‘possidere concordiam’... (whose subject or object, respectively, is constituted by terms denoting sentences). In relevant cases as the present ones, the blending of Boethius’ logical terminology into a kind of literary prose causes some problems to whoever wishes to identify terminological and doctrinal constants.
Cf. (in order): Log. Ingred. 136, 24–25 : “substantia tam in designatione verae quam fictae substantiae” vs Log. Ingred. 115, 19–20: “substantialia vocabula [...] rem subiectam [...] nominant”; Log. Ingred. 209, 33–35 : “‘albius’ rem denotat secundum statum” vs Log. Ingred. 158, 18–20: “‘album’, licet substantiam [...] nominet, non tarnen naturam [...] determinat”; Log. Ingred. 60, 8 : “‘homo’ notat rem in eo quod homo est” vs Log. Ingred. 115, 20: “‘homo’ rem subiectam in essentia nominat”; Log. Ingred. 32, 16–19 : “genus rem demonstrat in statu naturaliter priori” vs Log. Ingred. 78, 37–39 : “‘animal’ ipsam rem quae homo est in essentia sua nominat secundum statum naturaliter priorem”.
Cf. the positions of the grammarians in 1.5.
Log. Ingred. 23, 26–27.
So this view turns out to be quite similar to that of collectio theorists: see Kneepkens (1993), p. 75. See also supra the position of William of Conches (1.5).
Log. Ingred. 52, 22–25.
Dial. 582 and following.
On this issue, among others, cf. the following works: Spade (1973), (1982), (1975) (which contains a list of the published and unpublished sources); Bottin (1976), Pozzi (1987). In the theology, Abelard quotes the apostle Paul: “Cretes semper mendaces, malae bestiae, ventres pigri” (Theol. Christ. 132). This might show a certain curiosity for the implicit paradoxical contents. Abelard might have said something about paradoxes in the Libri Fantasiarum (cf. Dial. 448, 3–4). Unfortunately, however, this work has gone lost.
Log. Ingred. 68, 18–40; the final remark on the status of the objects of philosophical-scientific knowledge is worth noting (“vel forte dicamus philosophos cum ad doctrinam loquuntur saepe res aliter accipere quam sese habent”).
As a matter of fact, it is precisely the difficulty of imagining a composition of meanings independent of the oratio which drives Abelard to elaborate the theory of compound dictio: on this, see 2.5.
E.g. Log. Ingred. 122, 34–123, 1. On adjacency as real relation, see Log. Ingred. 260.
Dial. 149, 5–11.
Cf. also Dial. 122, passim.
There are ambiguous cases; cf. Dial. 122, 23–24: “‘album’ circa substantiam albedinem tamquam presentialiter inhaerentem determinat”; for the same ambiguity in ‘adiectivum copulat formam’, see Log. Ingred. 384, 8–9.
Log. Ingred.73, passim.
Log. Ingred.19, 1–5; Dial.539, 30–35.
Cf. 2.5.
Dial. 118, 17–20.
Dial. 119, 7–8.
Dial. 120, 19–20.
Log. Ingred. 248, 30–32.
Dial. 448, 31–34.
Other indications, similar to these, can be drawn from the discussion about other ‘indefinite’ parts (quantifiers, modalities, negation): cf. supra 2.5. Obviously the greater the attention for the categorematicity of both conjuncts, the more relevant the semantic counterpart of the syntactic apposition.
Boethius, In Cat. 166 D
A. Jolivet (1982) lists possible terminological and doctrinal precedents: Cicero, Top. IV, 31–32; De orat. in, 36, 155; Quintilian, Inst. Orat. VIII, 6; Boethius, In Cic. Top. 1107 B
B; Donatus, Ars Grammatica 399. To these passages we should add the Boethian ones and those of De Generibus et Speciebus 529. As to the problem, we can find some indications in Jolivet (1982) and Luscombe (1988). Something more about it is said in de Rijk (1962) 49–61, (1967–1) 492 ff. On the whole, however, not much attention has been devoted to the translatio terminorum.
Log. Ingred. 121, 11–15.
Log. Ingred. 336, 20–21.
Log. Ingred. 478 – 479 passim.
Log. Ingred. 121.
Log. Ingred. 336, 12–20; 378, 9–17; 399, 26–30.
Log. Ingred. 30, 21–26. The issue of the duplicity of the point of view (i.e. nominal and real) in Aristotle and Boethius is a central theme in Abelard’s interpretation: cf. Pinzani (1986–87) 165–170.
Log. Ingred. 30, 18–20. The expressions ‘res specieV and ‘res generis’ suggest that Abelard wants to signal a shift from a nominal point of view to a real one. A more detailed passage on this theme, which seems to develop and clarify the issue, is that of De Generibus et Speciebus 529.
Log. Ingred. 23, 26–27.
On this theme the dispute between Burley and Ockham is significant. See Henry (1963), (1981).
Log. Ingred. 350, 10–11.
Cf. A.I. Montague (1970), (1973) defines the intensional meaning of a sentence as a function from indices to truth values. The meanings of other linguistic expressions are built up in such a way as to result sensitive to index variations (where indices express contextual or temporal factors).
Concise, but interesting on this theme, is the contribution of Evans (1978). See also Bonanni (1996).
Theol. Christ. 245.
Dial. 82, 7–11.
De Gen. et Spec. 529.
Theol. Christ. 245.
Log. Ingred. 187, 15 and following
Dial. 137, 32–35: “sicut enim dictum est in impositione hominis, dicatur ista res homo, sic etiam dictum est in huiusmodi re non existente: dicatur ista res opinabilis, ut sic etiam non-existentium nomina inventa sint ad agendum de ipsis secundum quod in impositionem veniunt”.
Dial. 282, 30–33: “patet [...] differentia cathegoricae et hypoteticae enuntiationis, cum haec [...] actum inhaerentiae rerum, ilia necessitatem consecutionis ostenderet, quae quidem ut diximus, ipsi quoque rebus destructis incommutabilis consistir”. See the whole passage: pp. 271–286. For instance, in the case of the subject losing its denotation, the hypothetical: ‘si est homo, est animaV is true, whereas ’homo est animaV is false. On the same issue: cf. infra 5.6.
We assume that intransitive verbs and common nouns denote (the characteristic function of) a set of individuals, rather than sets of individual concepts as in Montague (1973).
Remusat (1845) (actually according to this author, Abelard would be also conceptualist); Hauréau (1872) 362–380; Sikes (1932). Nowadays the conceptual thesis is no longer asserted in such a distinct way; however, we can still find traces of it in authoritative interpretations: e.g. de Rijk (1975) follows Vignaux (1931) in some positions about the concept as res in anima obiectiva.
Pinborg (1972), 50–55; Jacobi (1983a).
Boethius, In Cat. 163 A; In Isag. 393 – 419.
Urbani Ulivi (1976) and Marenbon (1997a) share this opinion.
Log. Ingred. 308, 19–22.
On this point, cf. the analogies with the notion of modus significandi (cf. 2.1). However, there is actually a subtle difference between the différent modi significandi of nouns and verbs, and the respective concepts, which differ when considered with respect to the constitution of a sentence.
Cf. on this issue, in the grammatical tradition, Fredborg (1999), 200–201.
A position similar to ours is proposed by Broadie (1987), 10. In Montague (1973), the translation into the language of intensional logic aims at making explicit the logical-grammatical form of a certain expression. More generally, the same approach can serve to clarify the exact sphere of the symbolic expressions attributed to medievals by the current logical historiography, even if, in this particular case, it is not easy to find a connection between the problem of a logical form and that of an conceptual meaning.
Given two relations, R between A and B, and S between B and C, the product relation Sl°R is the relation between C and A defined as follows: “zSl°Rx when there exists at least a y in B such that zSy and yRx”.
Boethius, In Per. II, 43, 26 and ff.
“est autem una oratio enuntiativa vel quae unum significat vel coniunctione una, plures vero quae plura et non unum vel inconiunctae”.
In Per. 107, 23–25; 448, B-C. The term anteiligere’ does not seem to have any particular technical relevance in this context.
Log. Ingred. 378, 3 – 388, 33.
The relative frequency of the terms ‘sensus’, ‘significatio-significatum’ ‘intellectus’, in loc. cit. are respectively: 20, 11 and 7. We are lead to believe that the intellectus must coincide with the sensus (significatum), in order to maintain the relevant role promised at the beginning of the treatise and justify the interchangeability with concurrent notions in similar contexts. It should also be noted that the higher frequency of terms alternative to ‘intellectus’ suggests progressive liberation of the semantic terminology from psychologists connotations.
Log. Ingred. 326, 30–34.
Abelard does not discuss the case, but we may wonder in what sense the concept of a proper noun could be effective. In order to give an answer it seems necessary to admit a certain influence of (contextual or temporal) circumstances on the meaning of such expressions; this once again appears to be more complex than an object of perception.
See, also, Log.Ingred. 309, 4–8.
By construction of our model: the multiplicity of contexts and denotations is not represented in terms of ambiguity, and only in the presence of a plurality of impositive meanings we would assign more than one translation to an expression.
Cf. supra 2.1 for a similar use of ‘modus significandi’.
Log. Ingred. 325, 27–29.
In Montague (1970), (1973), for instance, the meaning of an adjective is a function from meanings of common nouns to meanings of common nouns; this explains how ‘animal rationale’ and ‘homo’ can signify the same kind of thing.
Log. Ingred. 327, 1–13.
Ibid. 25–26.
Log. Ingred. 330, 11–18.
Cf. respectively Dial. 123, 16; 148, 37–38; 149, 3; 225, 13; 226, 30. In the context of the discussion about unae and multíplices propositions, the term ‘sensus’ still has a primary function. The relative frequencies of ‘sensus’, ‘intellectus’ and ‘significatum’ are respectively: 33, 12 and 6; see note 106.
Dial. 111–114.
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Pinzani, R. (2003). Meaning. In: The Logical Grammar of Abelard. The New Synthese Historical Library, vol 51. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0239-3_5
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