WAS SAINT ANSELM REALLY A REALIST? By D. P. HENRY THE stock story about early medieval logic tells of a battle between realists and nominalists in the matter of universals. I am concerned with that part of the story according to which Saint Anselm, in his opposition to a certain Roscelin, showed himself a realist. John of Salisbury appears to be the main fount of the general story, but it is probably to Cousin, followed by Prand, Haureau, and practically everyone else since, that we owe the prevalence of the thesis that Anselm is a realist. The appeal is usually to the following passage from his Epistola de Incarnatione Verbi, I: Our contemporary dialecticians, heretics indeed in respect of logic, who think that universal substances are but the breath of a word, and who are incapable ofunderstanding colour to be anything other than body, or the wisdom of a man to be anything other than the soul, are to be altogether kept out of discussion of spiritual problems. Indeed, in their souls reason, which should be the prince and judge of everything appertaining to man, is so wrapped up in corporeal imaginations, that it cannot disentangle itself from them, nor can it distinguish those imaginations from those things which should be contemplated alone and in isolation. For how shall he who does not yet understand how many men can be specifically one man, understand how in that most hidden and high nature many persons, each of whom is wholly god, are one god? And how can he whose mind is unable to distinguish between his horse and its colour distinguish between one god and his many relationships? Does this passage show Anselm to be a realist? The answer to this question depends on that broader question: By what criteria can I detect that someone is a realist? W. V. O. Quine concludes1 that quantification over predicate variables is a mark of realism; this conclusion is in turn based on the doctrine that to be is to be the value of a variable, such values being the things in place ofwhose names the variables stand. 2 Use of predicate variables is hence alleged to involve riference to universal entities and such reference is generally taken to constitute the basic nature of realism in the present sense of the term. Thus, the binding of predicate variables commits one to assertions such as 'There is a class such that ' or, more generally, to 'There are universal entities such that '3 Since Anselm does 1 From a Logical Point of View, p. 15. 2 Ibid., p. 108. 181 3 Ibid., p. 105. D. P. HENRY not use variables, bound or unbound, these latter versions of Quine's criterion are particularly useful here. For in the passage quoted above Anselm seems to oppose 'universal substances' to the 'flatus vocis' of Roscelin in such a way as to make it reasonable to suppose that he would assent to the Latin equivalent of the proposition 'There are universal substances', which is close enough to Quine's 'universal entities' for us to assume that by the criterion described, Anselm must indeed be a realist. However, a closer inspection of the passage quoted shows that its general theme is the crudity of the ideas of the logicians who are false to logic, and it soon becomes evident that not just some more obvious facet of a discussion of universals, but something rather more subtle, is also in question. In fact, in the first phase of the quotation we have at least two prima facie distinguishable topics mentioned, while the second phase exemplifies these topics in more detail. The first topic is that of the 'universal substance', the corresponding example later given being that of the many men who are specifically one man: the second topic is first indeterminately constituted by the parallel distinctions between colour and body, wisdom and soul, and its later determinate example is that of the distinction between the colour of a horse and the horse. The precise nature of the connection of this second topic with the problem of universals is not here made clear, but it is certainly intended as a second pointer to the dimness of Anselm's opponents. Now there does exist an early dialogue of his-an obscure dialogue of which no one has hitherto been able to make much sense, namely, his De Grammatico-which contains a long and illuminating discussion concerning exactly this case of the horse and its colour. No one seems to have noticed this expansion of the second topic of the present passage; had they done so, and had they been able to make sense of De Grammatico, then the realist verdict on Anselm might not have been so readily pronounced. It is now my intention to question that verdict, thanks to the lead provided by the contact thus established between Epistola de Incarnatione Verbi and De Grammatico. This questioning will in its turn indicate the inadequacy of the contemporary logic in terms of which a conclusion agreeing with Cousin's was reached, so that my exercise has an interest which goes beyond the merely historical. De Grammatico, XIV, uses the example of the horse and its colour to bring out what might be termed the distinction between meaning and reference. For Anselm 'white', precisely speaking, signifies only '... having whiteness'. He considers two cases, one in which use of the word 'white' in respect of a white horse fails to convey to the hearer that the horse is the intended referent, and one in which it WAS SAINT ANSELM REALLY A REALIST? succeeds in so doing. In the first case we are asked to suppose that the white horse is invisible to the hearer, because it is enclosed within some building; in this context the information that [a] white is within the building does not tell the hearer that the horse is within. Secondly, we have the following situation: the hearer is faced with the white horse and a black bull; someone commands him: 'Give it a thwack!' and he receives the reply: '[The] white' in response to his question as to which of the two beasts he should strike. In both cases 'white' conveys'... having whiteness', but in the second situation the hearer is able, by the use of his sight, to fill in the intended reference of 'white'; this supplement is not, however, the meaning of 'white' in the strict (per se) sense of 'meaning', although it may be said to be so in an oblique (per aliud) sense. Similarly, the extended object which an experientially generated disposition might tempt the hearer to anticipate in the first of these two situations is not part of the meaning of 'white'. 4 Given this doctrine, it becomes plain that Anselm, in his fulmination against the logical heretics, is accusing them of missing the distinction between meaning and reference, and of incorporating actual or anticipated reference (called 'imagi:~lation' in the passage from Epistola de lncarnatione Verbi) into meaning which, as the latter says, should be considered in isolation for logical purposes (quae sola et pura contemplari debet). At the same time Anselm's example repels any suggestion that he believes the use of 'white' involves riference to a universal entity; Anselm does not here betray any sign of being a realist in this primitive sense which lies behind Quine's criterion. However, the fact still remains that Anselm is prepared to use talk involving such terms as 'universal substances'. Is there any evidence that this need not make him a realist? The answer to this question is more involved and will in fact lead to a questioning of Quine's criterion and the presuppositions which lie behind it. But I think it can be shown that further material from De Grammatico at any rate supplies the basis for a way of understanding talk about 'universal substances' which does not commit one to the existence of such substances at the 'familiar' level of which Quine speaks, 5 and to which his quantifiers are geared. Such a mode of understanding would be of interest in that it would cohere well with the spirit exemplified in the discussion of the case of the white horse. Thus, parallel to the statements on the meaning of words which we find in De Grammatico (statements which Anselm tickets as de voce) we also find therein statements as to how things are (called by Anselm de re statements);6 4 See the Appendix, hereafter provided, for the text here paraphrased. 5 From a Logical Point of View, p. 105. 6 De Grammatico, XVIII. D. P. HENRY the two are obviously inferentially equivalent for him. For example, having decided that 'grammaticus' signifies habens grammaticam or grammatica (de voce decisions), he is prepared to assert the correlated de re sentences 'grammaticus est habens grammaticam' and 'grammaticus est grammatica', the latter being a rank grammatical scandal, clean contrary to usus loquendi. 7 So likewise, as a correlate of the meaning (de voce) statements of that chapter XIV which has been paraphrased above, he gives 'albus est idem quod habens albedinem' (de re) which, while it does not overtly offend against usus loquendi, must certainly not, according to Anselm, be interpreted in this context in the prima facie obvious way, as a sentence in which the functor 'est' has two nominal arguments; it must not be interpreted as 'omnis qui est albus est aliquid habens (or qui habet) albedinem';8 this permits us to infer that these arguments must here be interpreted in the verbal, predicative sense, which Anselm's employment of the participial '... habens albedinem', coupled with Priscian's view of the participle as a cross between verb and noun, would seem to indicate. In fact Anselm's deliberate use of grammatical nonsense, and his explicit denial of the nominal nature of the arguments of the de re sentences mentioned, suggest that he is doing all he can, in the absence of an artificial language, to bring out the inadequacy of natural language to express his realizationthat there can be many types of 'est' (and correspondingly many types of 'entity'). And he is, of course, quite right: de re statements such as 'grammaticus est grammatica', 'albus est idem quod habens albedinem', 'grammaticus est qualitas' (and hence correspondingly 'homo est substantia' and 'homo est species'), all of which are present in his discussion, do in this context involve an 'est' which takes as arguments not names, but verbs (predicates). It is this higher type of 'est', suggested by Anselm's own dialogue, which provides a means of showing that the use of 'universal substance' does not necessarily commit the user to realism; in other words, there need be no discordance between such terminology and the impression conveyed by the example of the white horse. It is quite easy to bring out the possibilities of the higher type of 'est' since it is definable in Ldniewski's Ontology9 in the following terms. Primitively we have a groundlevel 'est' (in English 'is' or 'is a') symbolized by 'e', having names or name-like expressions as arguments, e.g. (i) a e b which is true when either 'a' and 'b' name the same individual and 7 Ibid., XI-XII. 8 Ibid., XX-XXI. 9 Cf. 'On Ldniewski's Ontology', Ratio, vol. I, no. 2, by C. Lejewski, to whom I am indebted for guidance in the remarks here made. WAS SAINT ANSELM REALLY A REALIST? only that individual, or 'a' names only one of several individuals named by 'b'. 'Socrates est homo' or 'Elizabeth is queen' would exemplify this ground-level 'e'. This is the 'is' used by Lesniewski as a primitive term in his I 92 I axiom of Ontology: (ii) [ab]:: a e b. ==:. [3c]. c ea:. [c]: c e a. :::>. C e b:. [cd] : c e a.d e a. :::>. c e d Given the definition of weak identity ('0') as (iii) [ab]:. a 0 b. ==: [c]: c e a. -. c e b one has (using' q>' and \V' as predicate variables); (iv) [q>YJ]:: q> e YJ. ==:. [3a]:. YJ (a):. [b]: q> (b). -. a 0 b i.e. a completely unproblematical but higher type of 'is',1° Theses involving the 'e' of (iv) instead of the 'e' of (ii), and completely isomorphic with (ii) and its consequences, are derivable from (ii), hence the subtlety of the confusions which centre round 'is' and the functors definable in terms of 'is'. (Incidentally, thanks to the unrestricted quantification used by Ontology,ll quantification does not here commit onc, as it would Quine, to the existence of entities. '[3 ....]' is to be read as 'For some ...' and not as 'There exists a ... such that ... ' In particular, quantification over q> and YJ does not commit one to the existence of 'abstract entities'.) Now even as, in terms of the lower order 'e' one can define 'There exists exactly one', thus: (v) [a]: ob (a). ==. [3 b]. a e b so also, in terms of the higher order 'e', one can define an analogous 'There exists exactly one', thus: (vi) [q>]: ob < q> >. ==. [3 YJ] • q> e YJ Further, in view of, for example, (xii) below, the following is a thesis: (vii) [3 <p]. q> e q> (With (vii) may be contrasted (viii) [3a]. a e a 10 That the 'is' represented by (iv) is ofa semantical category diverse from that figuring in (i) is assumed, for the purposes of this paper, to be clear from the diversity of the argument-signs. Ldniewski's system would, strictly speaking, require the difference to be shown by diversity in forms ofbrackets. 11 Cf. C. Lejewski, 'Logic and Existence', British Journal for the Philosophy of Science, vo!. 5,1954. 186 D. P. HENRY which is not a thesis for Ontology). In view of (vii), by (vi), we can assert: (ix) [3 <p]. ob < <p > (Once again, we have here a contrast with (x) [3a]. ob(a) which is not a thesis of Ontology; It IS, however, presupposed in systems employing restricted quantification). Now it is possible to define a functor which is a particular value of <p, thus: (xi) [ab]. Cl{a}(b). ==. a 0 b Here 'Cl{ }', the verb-forming functor thus defined, may be variously interpreted in natural language : 'being ...', and 'forming the class of ...', are some examples of its correlates. Further, since (xii) [a]. Cl{a} e Cl{a} is a provable thesis, use of definition (vi) can now lead us to the thesis: (xiii) [a]. ob < Cl{a} > which will serve below as a convenient suggestion for the elucidation ofAnselm's meaning. The scraps of artificial language reproduced above exhibit to a fuller extent the possibilities of the 'est' which Anselm's dialogue itself suggests. They show how neither the copular 'is' nor the 'is' of 'There is' are univocal, as they appear to be for Quine, for whom, in his terms, there is but one 'sort of language to which "there is" belongs',I2 and which he claims is the familiar quantificational form of discourse; his 'there is' is shackled to restricted quantifiers having a ground-level sense, in a way in which that of Ontology is not. The latter, as the last paragraph has shown, offers the possibility of parsing a sentence such as 'homo est species' in the way envisaged by Anselm, i.e. in such a fashion, with the 'est' as the 'e' of (iv) , as to eliminate any question of 'homo' naming some entity in the lower level sense. Anselm's intentions having been thus far illuminated, it is now possible to dispose of the mention of 'universal substances' in the way suggested by Anselm's own practice in De Grammatico-a way which fails to commit him to realism. The words 'universal substances', as his subsequent example towards the end of the quoted passage shows, are intended to remind us of those 'secondary substances' with which we are concerned when terms having the status of 'homo' in 'homo 12 Op. cit., p. 105. WAS SAINT ANSELM REALLY A REALIST? est species' are used. The occurrence of the expression 'specifically (in specie) one man' can then be simply interpreted as calling attention to that higher-order exactly-one-hood exemplified in (xiii). For if the constant noun 'homo' (abbreviated as Ch') is introduced, (xiii) shows a sense in which 'There exists exactly one man' is true at that level of discourse involving the word 'species' which Anselm here uses; his expression can be understood as (xiv) ob <Cl{h} > The evidence accumulated from De Grammatico, and developed as shown above, points to the fact that (xiv), rather than any crude ground-level realism, is the more feasible interpretation of Anselm's intentions at this point. Suppose, however, that indications of the sort provided by De Grammatico are not available. What alternative pointer towards a decision as to the realism or otherwise of a writer working in a natural language might be suggested? Here a passage from John of Salisbury's Metalogicon 13-a passage in which he is writing against realism-is most apposite, since its sentiments could issue from a consideration of the possibilities opened up by the language suggested by Ansdm, and enlarged on by Ontology, whereas some of those sentiments would, by Quine's criteria, make John of Salisbury, in this anti-realist passage, into a realist; this would clearly be a most unsatisfactory state of affairs. John is prepared to concede that one might say that there are universals, or even that universals are things; the important point, he continues, is that this admission no more commits one to an increase in the number of things than refusal to make the admission commits one to a decrease in the number of things. Universals can be counted; individual objects can be counted; the two, however, do not add. In a similar sort of way colleges are not connumerated (non connumerantur) with heads of colleges, or animal heads with animal bodies; a number embraces only those things which are of the same type (que eiusdem rationis sunt). Now thanks to the clarifications suggested above, we can with John say that in a sense there are universals, that they are in a sense individual things (ob < >, cf. (vi) and (xiii)) but that as the semantical category of the cardinal 'are' is here higher than that of the 'E' of (ii), with a corresponding category-difference of argument, individuals of such diverse types cannot be summated. John's principle of non-connumerability is at least one alternative test of non-realism provided that one of the non-connumerables is an object in the sense provided for by 'ob( )' (cf. (v)). 13 Ed. Webb, p. 101. 188 D. P. HENRY The lesson which emerges, therefore, is that a language, artificial or otherwise, in terms of which the medieval universals controversy is measured, must be at least as rich in definitionally distinct parts of speech at appropriate points as the medieval Latin in which that controversy was conducted. That both Cousin's French and Quine's artificial language, together with the natural language which he allows to be influenced by it, fail in this respect, has now been shown to be extremely probable. Medieval philosophical and logical Latin is, as Anselm was already aware, a semi-artificial language designed to express truths which involve semantical categories not distinguished by ordinary grammar; its very barbarity in the eyes of unphilosophical renaissance philologists should warn its reader to expect assertions beyond the capacity of current natural language, requiring that for their satisfactory elucidation advantage should be taken of the cognate resources of a fully artificial language such as that of Ontology. APPENDIX The case of the white horse (De Grammatico, XIV) TUTOR. Suppose that, unknown to you, a white horse were enclosed in some building or other, and someone told you, ' [A] white is in this building'-would that inform you that the horse was within? STUDENT. No; for whether they speak of [a] white, or of whiteness, or of that within which the whiteness is enclosed, no definite circumstance is brought to my mind apart from the essence of this colour. T. Even though you did happen to understand something over and above the colour, it is at least definite that the name in question conveys to you nothing as to exactly what that something is in which the colour is to be found. S. That is quite definite. True, that name brings to mind a body or surface, but this is simply because my experience has shown me that whiteness is usually found in such things (expertus sum in his solere esse albedinem) ; of itself the name white signifies none of them, as was shown in the case of literate. And now I'm waiting for you to show me what in fact it does signify. T. Suppose you were to see a white horse and a black bull standing together, and someone gave the order, 'Give it a thwack!', thereby meaning the horse, but without giving any indication as to which he intended: would you then know that he was referring to the horse? WAS SAINT ANSELM REALLY A REALIST? I8g s. No. T. But suppose, while still in ignorance, you were to ask, 'Which?' ;lIld he were to reply, '[The] white!', would you then gather his rderence? S. I would gather from the name white that he meant the horse. T. Thus for you the name white would signify the horse. S. It certainly would. T. And do you notice that this would be in a fashion other than t 11; I t proper to the name horse? s. I quite see that. I notice that before I know the horse to be \\' 11 ite, the name horse signifies to me the substance horse precisively (jIiT se), not obliquely (per aliud). On the other hand, the name white signifies the substance horse not precisively, but only obliquely, that is, t hanks to my being aware that the horse is white. Now the name If*lii/{' is equisignificant with the phrase having whiteness: similarly, the pr\'cisc efI'ect of this phrase is to bring to my mind the understanding or whitcness, but not of the thing which has the whiteness, so that the \\onl lflltile has the same effect. However, because I know, otherwise t ILllt by means of the name white-by sight, for example-that the \\llit('l\('ss is in the horse, when whiteness has been thus conveyed by IIW;IIIS orthat word, I also gather the reference to the horse because I kilo\\' that the whiteness is in the horse. Nevertheless, this is otherwise 11 L III by mcans of the name white, even though that word refers to the hors\' . IINIVI':RSITY OF MANCHESTER