Wittgenstein's Solution of the Paradoxes and the Conception of the Scholastic Logician Petrus de Allyaco

Wittgenstein's Solution of the Paradoxes and the Conception of the Scholastic Logician Petrus de Allyaco ANTON DUMITRIU I. INTRODUCTION We have very few facts about Wittgenstein's life, and these are practically only those given by Malcolm and by yon Wright. They inform us that Wittgenstein was not a scholar, that he was a spontaneous genius (I should say, an explosive one), and that his work is less an original organization of others' ideas or of his own than a collection of intellectual intuitions. This assertion is confirmed by the fact that neither the Tractatus Logico-Philosophicus nor the Philosophical Investigations are systematically expounded as theories, but are only lapidary and aphoristical notations of intellectual fulgnrations. The origins of his inspiration are thus hard to identify and, outside Frege's and Russell 's works (which, according to his own acknowledgement, influenced him greatly), there can be only speculation. As for the logic of the Middle Ages, we cannot say whether and to what extent Wittgenstein knew it. We do know, however, that he mentions Occam's motto in the Tractatus twice. At 3.328 he says, "Wird ein Zeichen n i c h t g e b r a u c h t, so ist es bedeutungslos. Das ist der Sinn der Devise Occams" (or, in our translation, the first English translation having deviated from the original meaning: "If a sign is not used then it is meaningless. That is the meaning of Occam's motto"). And at 5.47321 we find that "Occams Devise ist natfirlich keine willkiirliche, oder durch ihren praktischen Effolg gerechffertigte, Regel: Sie besagt, dass u n n/5 t i g e Zeicheneinheiten nichts bedeuten" ("Occam's motto is, of course, not an arbitrary rule, nor one justified by its practical success: it says that unnecessary sign elements mean nothing"). Note that in the first English translation from the Tractatus the expression "Occam's razor" appears, but in German it is only "Occams Devise." Can we infer from these two propositions that Occam's philosophy was familiar to Wittgenstein, or, even more, that he was acquainted with the whole logic of the Middle Ages? We cannot make such an affirmation, all the more so since Occam's motto has become in philosophy a sort of aphorism that Wittgenstein could have known without reading Oecam's books. This economical law, which had been expressed by others too, was stated by Oceam in his treatise on the Sentences: "Nunquam ponendo est pluralitas sine necessitate" (One never must use more without necessity). Or, in another form, in the famous treatise Summa totiua logicae, "Frustra fit per plura, quod potest fieri per paneiora" (It is useless to make with more what can be made with less). Now it is obvious that we can conclude nothing with respect to the knowledge Wittgenstein could have had about Occam's logic. But there is a great scholastic logician, Petrus [227] 228 HISTORY OF PHILOSOPHY de Allyaco, whose conception of the problem of paradoxes is almost identical to Wittgenstein 's. Is this only a mere coincidence? Wittgenstein himself refuses to give the sources of his thought. He writes in the preface of the Tractatus, "How far my efforts agree with those of other philosophers I will not decide. Indeed what I have here written makes no claim to novelty on points of detail, and therefore I give no sources, because it is indifferent to me whether what I have thought has already been thought before me by another." This statement and its obvious sincerity makes it difficult to discover any connection of inspiration with that of the scholastic logician. This paper has a threefold aim: (1) To show that Wittgenstein gives a logical solution to the logico-mathematical paradoxes, which we think has not been taken into consideration only because of its brevity. (2) To prove that this solution does not reject the theory of types but interprets it in the simplest way. (3) To show that Wittgenstein's solution is the solution given to the paradoxes called Insolubilia by the famous scholastic logician, Petrus de Allyaco (Pierre d'Ailly). We must still add that those who have dealt with the exegesis...