The verb "to be" and the common nouns in Medieval "scientific" Latin

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1. The languages of scholasticism

In historiography the expression "scientific Latin" denotes, rather ambiguously, the language used by the scholastics. As a matter of fact, in medieval logic treatises, various languages can be identified, such as (a) the languages of the quadrivium sciences, (b) a simplified fragment of the natural language object of the logical-grammatical theories, (c) formal languages, (d) the meta-languages used to describe (a), (b), and (c) above. Modern research has enlightened how many medieval logic formulae can be interpreted from the point of view of the modern symbolic logic. This could mean that in certain cases people of the Middle Ages used expressions of the natural language in a standardised and quasi-symbolic way. It should not be forgotten that schematic and variable letters were at that time used in a way simililar to the Aristotelian one. Since only a part of medieval logic language can be translated in terms of modern symbolic logic, we are faced with the problem of how to deal with the remaining linguistic elements previously referred to, in particular with the expressions belonging to the natural language, the grammar of which is outlined in the treatises on proprietates terminorum.
Among the linguistic theories which we can analise in our search for an adequate interpretative model, (a variant of) the Montague grammar¹ allows us to represent the different analysis levels of the terminism. This grammar describes a fragment of the natural language, like the "De Interpretatione", a compulsory stepping stone for scholasticism, is directed towards the study of the affirmative discourse and its parts. We have a semantic component which finds its expression in both the lexical categories and the interpretation (for Montague the "intensional model"); correspondingly medieval magistri adress the problem of meaning by discussing the "proprietates termini" out of its propositional context². Furthermore, the categories language is sometimes considered as a way to express the meaning of terms or a useful lexical form for differentiating the terms also under a semantic light³. We finally have an "intermediate" logical language which corresponds to the medieval use of quasi-symbolic formulae in order show the depth form of the natural expressions⁴.

2. The verb "to be"

Recently doubts have been put forward regarding the attribution of different meanings to the verb "to be" by ancient and medieval philosophy and logic⁵. The Russellian-Fregean ambiguity, as defined by J. Hintikka⁶, emerges from the following formulae:

1-1 Socrates is wise
1-2 Socrates is Plato's teacher
1-3 Socrates is

In 1-1 the copula has a predicative function, in 1-2 it stands for an identity, in 1-3 it means "exists". In the course of the history of ancient logic B. Mates has put into evidence how the ambiguous occurrences of "is" can be substituted by "fundamental" occurences⁷. Mates also proposes amongst others the following defining equations:

1-4 "A is (a) B" (ordinary prediction) is true if and only if "A is B" is true.
1-5 "A is the same as B" (A=B) is true if and only if "A is B" and "B is A" are true.
1-6 "A is" is true if and only if, by some term D, "A is D" is true.

With reference to 1-4 one may think that the definiens is the same as the definiendum; probably this does not occur since the author deems that the language expressing the definiens is somewhat different (maybe as "unambiguous language") from the one expressing the definiendum. In any case the similarity is not accidental and makes us understand how in reality the use of "is" which is considered as "fundamental" is close to the predicative one, if not actually coinciding with it. Mates states that he has worked on some ideas of Leibnitz and Lesniewski. The same Polish philosopher is utilised by D.P. Henry in the context of medieval historiography⁸. The definitions of some functors by the Lesniewskian ontological primitive sign (not available in this electronic format; we shall utilize the sign x for it) are close to those proposed by Mates. In particular the equations 1-4, 1-5 and 1-6 correspond to the following formulae in Henry:

1-7 a x b
1-8 [ab] : a = b .if and only if . a x b . b x a (singular identity. Reads: "a is the same object as b")
1-9 [a] : ex(a) .iff. [Eb] . b x a (the first functor of existence. Reads: "at least an a exists".)

The formula 1-7 represents the right-hand side of the equation 1-4. In it the functor "x" translates a particular occurrence of the verb "to be" into symbolic language. Even if the natural language for Lesniewski was Polish, the formula 1-7 can be utilized for a language where the (translation of) the verb "to be" links two terms without articles⁹. The definiendum of 1-8 and 1-9 contains morphologically different signs in relation to the different occurrences of the copula (its equivalent in English or Polish or..); in the definiens we only find the (substitute of) ontological primitive symbol ("x") which express a "basic" use of the conjunctive verb.
Let us suppose that R is a relation between formulae that have an "ambiguous" occurrence of the copula and formulae containing a singular "basic" occurrence; R can be seen as a relation between an unambiguous (possibly symbolic) language and an ambiguous one, or as a definite congruity on the natural language. The second case, which I find more interesting, demands some explanation on the intuitive acceptance by the speakers (in our case the scholastics) of the syntactic representation of R so interpreted. The following equations contribute in establishing such a relation:

1-10 "Socrates est homo" iff "Socrates est homo"
1-11 "Socrates currit" iff "Socrates est currens"
1-12 "Socrates est Plato" iff "Socrates est idem quod Plato"
1-13 "Socrates est" iff "Socrates est ens"
1-14 "homo est animal" iff "homo est species animalis"

1-11 is an Aristotelian dogma accepted by all medieval logicians; 1-13 is a consequence of 1-11¹⁰; whilst the definiens of 1-12 is an obvious variation of the definiendum, 1-14 is apparently so, from the medieval point of view, when the terms of the definiendum are meant in suppositio simplex. We can say that according to the linguistic intuition of the scholastics (which finds its expression in our definitions) "est" is implicit in each verb; the formulae in which the predicate is explicit seem to contain a fundamental occurrence (that is no longer susceptible of an analysis in terms of 1-11) of the conjunction. The "is" found on the left-hand side of the equation should not be considered as less fundamental or ambiguous, but simply elliptical of a predicative clause (except 1-10 of course). As a first result we obtain (especially from 1-13) the exclusion of the possible ambiguity between "est" secundum adiacens and "est" tertium adiacens (in practice between a predicative use of "est" and an existential use). In order to show the unicity of the grammatical role of the copula we turn our attention to its inner role in the predicative complex.
In medieval literature a syncategorematic value is assigned to the conjunctive "est"; nevertheless its verbal meaning and power are also traced¹¹. The verbal nature attached to the copula reminds us that the way by which it contributes to the meaning of the predicate is that of transferring a nominal pound into an intransitive verb¹²: we can say that in 1-10, -11, -13 it behaves so. Whereas in 1-12, -14 it cleary constitutes a transitive verb. A way to reconcile these functions it is to assume that both the common nouns and the clauses "idem quod" play, at some level, the role of verbs and that "est" transform identically its quasi-verbal arguments.

3. The common nouns

The problem of common nouns is somehow linked to that of the copula. One can say that the people of the Middle Ages agree on that a common noun plays various syntactical roles (the problems are more or less relevant to the meaning) both in suppositio personalis and suppositio simplex. But this difference is enough to create a further difficulty regarding the copula. If "homo" in "homo est species animalis" is syntactically different from "homo" in "Socrates est homo", it is expected that the copula react differently in the two cases. Such an expectation in historiography is found in Hintikka (for ancient logic) and in Henry (for medieval logic)¹³. The drawback that such an interpretation creates is to have to admit a multiplicity of signs for the copulative "is" for each level to which each argument belongs. On the other hand the challenge posed by a linguistic theory which tries to mantain the univocity of the verb "to be" is that of avoiding that predicates (common nouns) of different levels become arguments of "is" through some rule of formation. As it is more satisfying for a linguistic theory to explain the behaviour of a copula without assuming its own fundamental ambiguity, the same can be said of the common nouns (with regard to the possible ambiguity introduced by the different suppositio); if we succeeds to maintain the univocal use of the above mentioned expressions, there is no need to worry about further ambiguities of the functors of which they are arguments.
Another recurrent subject of late-medieval logic is the difference between significatio and suppositio¹⁴. Meaning is something which is, to say, carries along by each term in the contexts in which it occurs. If the medieval theory of suppositio is seen from the modern linguistic point of view, that is the first fact to keep in mind. On the other hand it is necessary to assume some grammatical difference (either syntactic or semantic) to describe the behaviour of a term under various suppositiones.
Let us consider the following propositions:

1-15 Quidam homo est animal
1-16 Genus hominis est animal

We can interpret the different syntactic role played by the term "homo" (in suppositio personalis in 1-15 and in suppositio simplex in 1-16) as if it somehow "gravitated", in a syntactic meaning of the term, within the syncategorematic clause "quidam" or "genus". On the other hand, from a semantic point of view, whilst the meaning of "homo" in both cases remains the same, a different meaning of the complete clauses "quidam homo" and "genus hominis" should be expected. It may represent an advantage, on philosophic ground, to not attribute a different meaning or logical level to "homo" in suppositio simplex that the same term has in suppositio personalis. Furthermore there is not the risk, pointed out when we dealt with the different levels of the copula, that an actual universal, such as species hominis, occurs as a subject of a transitive verb. Socrates cannot eat an essence as he eats an apple in that "species..." or "genus..." do not belong to a category such that they can occur as subjects of transitive verbs; nor do the same clauses allow any verbal subjects (either transitive or intransitive).





Footnotes

1. The point of departure for our re-elaboration is "The Proper Treatment of "The Proper Treatment of Quantification in Ordinary English", now in R.Montague, Formal Philosophy, New Haven, 1974. See our re-elaboration in "Suppositio Terminorum and Modern Logic" forthcoming.

2. According to Lamberto d'Auxerre "significatio est sicut perfectio termini et proprietates termini supra significationem fundantur" (Summa Lamberti, ed. F. Alessio, Firenze 1971, p. 205)

3. This lectio, introduced by Abelardo in the 12th century, is still present in the late scholastic; as an example we will quote the words which in Ockham's Summa Logica immediately follow the comment on the Categorie: "Dicto de significatione terminorum restat dicere de suppositione.." (Summa, ed. Boehner - Gàl - Brown, St. Bonaventure, N.Y.,1974, 193,2). De Rijk clames that the semantic interpretation should be considered as a constant in the history of the Categorie and is fully justified by the aristotelian text: cfr. "'Categorization' as a Key Notion in Ancient and Medieval Semantics", Vivarium, XXVI (1981); "Logic and Ontology in Ockham, Some Notes on his View of the Categories of Being and the Nature of its Basic Principles" in Ockham and Ockhamists, Nijmegen, 1987.

4. A characteristic of the Montague grammar is that of expressing, by means of functions, the relationship between the expressions which make up a phrase: from a syntactic point of view, a certain term will therefore be the argument of another term which latter acts as a functor or vice versa. This approach is able to supply the instruments to interpret qualifying aspects of the suppositio theory; in fact, by making use of an adequate level of analysis to describe the relationship between the terms in a proposition, we can represent proprietates terminorum in the suppositio context. In this introduction the argument is briefly outlined under the section dealing with common nouns.

5. See amongst others the articles found in The Logic of Being, ed. S. Knuuttila e J. Hintikka, Dordrecht, 1986.

6. "The Varieties of Being in Aristotle", in The Logic of Being, cit., pp. 81-114; "Game-Theoretical Semantics: Insight and Prospects", Notre Dame Journal of Formal Logic, 23 (1982), pp. 219-241.

7. B. Mates, "Identity and Predication in Plato", in The Logic of Being, cit., pp. 29-47.

8. Particular reference is being made to Medieval Logic and Metaphysics, London, 1972.

9. For example "a" and "b" in 1-7 stand for both common and proper nouns in Latin. In a language like Italian only a proposition of the 1-1 type appears as grammatically correct (where the subject is a singular term). It should be also kept in mind that in Lesniewski, like for contemporary logicians, the symbolic forms do not translate expressions of the natural language literally, being instead understood as a representation of a subordinate structure which is subject to the logic-philosophic analysis.

10. It is explicitely assumed for eg. in Burleigh: "Sed hoc verbum 'est' ut praedicatur secundum adiacens, sic includit praedicatum, quia suum participium eiusdem temporis et eiusdem significationis est praedicatum, quando hoc verbum 'est' praedicatur secundum adiacens.": Walter Burleigh, De Puritate Artis Logicae, ed. P. Boehner, St. Bonaventure, N.Y., 1955, 54, 29-32.

11. A reference to the syncategorematic characteristic of "est" is made, amongst others, by Burleigh (op. cit., 54 e ss.), Ockham (Elementarium Logicae, ed. E.M. Buytaert, in Franciscan Studies, XXV, 1965, pp. 170-276; XXVI, 1966, pp. 66-173; I, p.219), Buridano (Tractatus de Suppositionibus, ed. M.E. Reina, in Rivista critica di storia della filosofia, XII, 1957, pp. 175-208, 323-352;pp. 207-208) (the latter texts are quoted in A.Maierù, Terminologia logica della tarda scolastica, Roma 1972, pp.214-215). The verbal meaning is stressed by William of Shyreswood as follows: "Et dicunt quidam quod hec particula 'est' est tertia pars que scilicet est copula, sed non est ita. Cum enim sit verbum, significat id quod de alio predicatur et sic erit predicatum, sed consignificat compositionem quia est copula.." (Introductiones in Logicam, ed. M. Grabmann, Sitzungsberichte der Bayerischen Akademie der Wissenschaften, Phil.-hist. Abteilung 1937, 10; p.33).

12. A verb which, according to N.Kretzmann, constitutes the paradigm of a categorical verb (cfr. . "Syncategoremata, exponibilia, sophismata", in The Cambridge History of Later Medieval Philosophy, Cambridge 1982 (rist. 1989), pp. 211-245).

13. This ambiguity is discussed by Hintikka (in op.cit., pp 96-99) as a categorical one: a term (implicit) in the quantificational clauses should be able to select a kind of quantifying domain. Hight order functors (in part morphologically coinciding with x) are considered, by Henry (Medieval Logic, p43), with respect to different logical levels of the component terms of a proposition like "...est___".

14. Lamberto d'Auxerre (op.cit., 206) employs the following terms: "Differt autem significatio a suppositione in hoc quod prior est significatio quam suppositio; significatio enim est intellectus rei qui per vocem representatur... suppositio vero est quedam proprietas termini sic constituti. Alia est differentia quia significatio solum extenditur ad rem ad quam significandam imponitur terminus, sed suppositio non solum extenditur ad rem que per terminum significatur".