Peter of Ailly: Concepts and Insolubles: An Annotated Translation

Description

Peter of Ailly put forward a theory of meaning in an attempt to solve the semantic paradoxes. In mediaeval terms this means that he thought that the paradoxes—the so-called "insolubles''—arise only in written and spoken language and not in mental language. For if one looks at the role played by the notion of mental language in mediaeval philosophy and in Ailly in particular, one sees that it constitutes a manner of explanation very similar to that played in this century by the notion of an ideal language (in, say, G. Frege and B. Russell) or a theory of meaning (in, say, M. Dummett or D. Davidson). The meaning and references of spoken and written sentences are to be explained by their linking by conventions of usage to corresponding mental sentences. But mental sentences also (by their very name) were supposed to have psychological reality: by their presence, understanding was also to be explained. If truth-conditions are to be reified, then a proposition (Russell) or a mental sentence (the mediaevals) fits the bill. And if meaning is correlative to understanding, then understanding a sentence means knowing its truth-conditions—the proposition or mental sentence expressed by it.
In the case in point—the semantic paradoxes—Ailly's idea is that self-reference can arise only in written or spoken language, not in the mental ideal language. (Recall, e.g., Frege's demand that vague predicates be removed from an ideal language or notation.) This is a fine start. But here disappointment follows. A close examination of Ailly's argument reveals that he distinguishes mental language "properly so called'' from that "improperly so called''. In the latter self-reference can arise; in the former it cannot. But sentences of mental language properly so called are simply by definition those "that are not likenesses of utterances or inscriptions signifying by convention'' (Section 94, p. 36). What we need then is a demonstration that the meaning and understanding of all written and spoken language can be explained within the framework of this conception of mental language properly so called. (Just as we need a demonstration—if there is one—that vague predicates can always be replaced by precise ones, for Frege's project, or that all the required T-schemata are theorems of a recursive truth-theory, for Davidson's.) Ailly gives no such demonstration.
However, let us set aside any doubts we may have concerning Gödel numbering and representability. Suppose then that we do have a mental language capturing the meaning of every spoken and written sentence, and yet lacking any form of self-reference. Consider an insoluble (written or spoken) sentence k. The meaning of k is given by some corresponding sentence of mental language, l, and an understanding of k is given by a grasp of l. Ailly's idea for explaining the insolubles, building on theories of Bradwardine and Gregory of Rimini, is that k is in fact equivocal and corresponds to two different mental sentences, l and l′. l says that k is false; l′ says that l is false. That k is equivocal in this way, and so is both true (taken one way) and false (taken the other), depending on what sense is attached to it, contrasts with Rimini's view, that k asserts the conjunction of l and l′, and so, having the form "l, and l is false'', is necessarily false. For Ailly, k is both true and false, but not by corresponding to a proper mental sentence which is both true and false (for no proper mental sentence can be that, he says), but by equivocating between two mental sentences—two senses.
We are given here an admirable translation of Ailly's text, accompanied by an introduction, an exhaustive set of notes, and a fine index. The apparatus is very well organised, and of great help to the reader. (It might have been better, however, to separate the purely textual from the critical notes.) The translator rightly rejects a number of Ailly's arguments as confused or feeble, but shows how others are striking and sound. The translator's judgment is generally reliable, but occasionally he misses his mark; one instance in particular must be noted. Ailly at a number of points relies for his argument on distinguishing p' from "p' is true', in the case wherep' signifies by convention. He correctly observes that they are not logically equivalent. For example, "A man is an ass' is true' does not entail A man is an ass', for the first is possible while the second is impossible—the first can be true while the second cannot (see pp. 52–53). The translator rejects Ailly's claim (see note 722). He notes that what is at stake is whatA man is an ass' signifies: if it signified that God exists, then not only would "A man is an ass' is true' be true, but so too would A man is an ass', since it would signify that God exists, and not that a man is an ass. This is to miss the point. A situation whereA man is an ass' signified that God exists would indeed be one in which A man is an ass' was true (or at least so Ailly believed), but it would not be one in which a man was an ass. So the consequence (or inference), "A man is an ass' is true, so man is an ass', would be invalid. (There are problems about the converse,A man is an ass, so A man is an ass' is true', given what seems to have been Ailly's, and others', account of the validity of consequences (see notes 655–656), for sinceA man is an ass' is impossible, the truth of the consequence results from an implicational paradox. But other instances of p' can be used to show thatp' does not in general entail "p' is true'—e.g., by taking p' to be a necessary truth such asGod exists'.)
Ailly's observation is of important contemporary relevance, for it shows that a Tarski-style truth theory is not trivial. The T-schemata, "p' is true if and only if p', are not logically true. They depend on the conventional signification of p'—they state facts about the meaning, the use, of sentences. "Snow is white' is true if and only if snow is white' does not state a necessary truth, nor can we claim to know its truth a priori. Given the homophony of sentences with different meanings—in different languages, e.g.,Jam dies', in different dialects, e.g., I stay in St. Andrews', or even in a single idiolect containing ambiguous sentences, there are false instances of "p' is true if and only if p', where phonetically or typographically the same sentence is substituted forp'. p' and "p' is true' are not equivalent, and indeed the one can be necessary or impossible while the other is not. Lastly, there is a confusing misprint on p. 10: in line 14, forA man is an animal' read `Every man is an animal'.

Reviewed by Stephen Read

2 Peter of Aillyl wrote his Concepts and Insolubles, according to the best 3 estimate, in 1372. He was at that time only about twenty-two years old. He was born around 1350" in Compiegne in the De de France, although his 5 family name associates him with the village of Ailly in Picardy. In 1364 he entered the University of Paris as a 'bursar' (i. e. , the recipient of a scholarship) at the College de Navarre. He received the degree of Bachelor of Arts in 1367 and taught there until 1368, when he entered the Faculty of Theology. He became a Doctor of Theology in 1381. In the years that followed, Peter was very active in the 'conciliar' movement and in negotiations to bring about the end of the Great Schism of the West. He was elevated to the rank of Cardinal in 1411 by Pope John XXIII, the successor of Alexander V in the 'Pisa' line of Popes. He took an active part in the Council of Constance (1414-1418), which ended the Great Schism and elected Pope Martin V. Peter died on August 9, 1420. Most of the secondary literature on Peter of Ailly concerns his role in church politics, his writings on the Schism and on ecclesiastical reform, and various aspects of his theology. But Peter was active in a number of other areas as well. He wrote several works, for instance, on geography and astron­ 6 omy, including an Imago mundi read by Christopher Columbus.

**

Language Notes

Text: English, Latin (translation)