Foreword: Part One

Foreword

This book will perhaps only be understood by one who has himself already at some time thought the thoughts that are expressed herein – or at least similar thoughts. –It is therefore not a textbook.—Its end would be reached if it gave pleasure to one person who read it with understanding.

Compare Russell on Frege: Of Frege’s Begriffsschrift Russell writes “I possessed the book for years before I could make out what it meant. Indeed, I did not understand it until I had myself independently discovered most of what it contained.” (Autobiography p. 65, cf. Principles of Mathematics p. xxiii, says Michael Beaney in the Cambridge Companion to Russell p. 131)

More speculatively, also compare Kant[i]: “Analytic judgments really teach us nothing more about the object than what the concept which we have of it already contains; they do not extend our knowledge beyond the concept of the object, but only clarify the concept. They cannot therefore rightly be called dogmas (a word which might perhaps be translated doctrines).” (A 736/B 764) The German word translated as doctrines is Lehrsprüche. A book consisting of the clarification of concepts, according to Kant, could not rightly be said to give Lehrsprüche. Similarly, Wittgenstein’s book is no Lehrbuch – textbook, or book of doctrines. Cf. 4.112 which characterizes philosophy very much in these Kantian terms of conceptual clarification and states: Die Philosophie ist keine Lehre – philosophy is not a subject, or theory, or body of doctrine.

But, you might object, Kant is talking about analytic judgments, whereas Wittgenstein is talking about thoughts that the reader has already had. These are not the same thing. True enough, but Wittgenstein looks as if he thinks there is something parallel going on, some similarity between the analysis of concepts and the process of going through certain thoughts that one has already had. Analytic judgments do not extend our knowledge because they only bring out what was already implicit in what we knew. Similarly, perhaps, Wittgenstein aims to show us what was all along implicit in our own (or in his ideal readers’) thoughts. If we continue to follow Kant, then we will not expect this process to consist in definitions since, Kant says, “mathematics is the only science that has definitions.” (A 729/B 757) And philosophy, he has said, is not mathematics, however much Frege and Russell might have wanted to connect the two disciplines. Instead, concepts can be made explicit (see A 727/B 755 on the impossibility of defining empirical concepts) and, if a definition is to be offered, then, “the definition in all its precision and clarity ought, in philosophy, to come rather at the end than at the beginning of our enquiries.” (A 731/B 759) It would not be proper, then, for a philosophical work to proceed as if it were a mathematical work, beginning, for instance, with definitions. If the Tractatus appears to do this, then we should beware that it is going against the great Kant in doing so. This is not to say, of course, that whatever Kant says must be true. It is simply a reminder that what might seem simple or uncontroversial is not always so in philosophy.

Speaking of Kant, bear in mind that in 1944 Wittgenstein wrote an addition to a short biography of himself that John Wisdom had prepared, which read: “Wittgenstein’s chief contribution has been in the philosophy of mathematics.” This is quoted on p. 466 of Monk. At that time, the TLP was the only philosophical book he had published, so perhaps he had that in mind. (Of course, he might have been thinking of the ‘publication’ of his ideas by way of teaching, circulating notes, etc.) According to Schopenhauer’s Fourfold Root p. 160 “The whole of pure mathematics” consists of truths such as “Nothing happens without a cause” and “3 x 7 = 21.” In other words, what Kant regards as synthetic a priori truths. Schopenhauer claims that the principle of sufficient reason is this kind of truth. So if Wittgenstein was primarily concerned with the so-called synthetic a priori, then he would be concerned with the philosophy of mathematics and simultaneously be going into the heart of Kant’s and Schopenhauer’s philosophies. This would also be relevant to Russell and Frege. In this connection see also the final paragraph of the Philosophical Investigations, which begins: “An investigation is possible in connexion with mathematics which is entirely analogous to our investigation of psychology.” The nature of this category of statement is clearly very important to him, throughout his career. Maybe it is even his sole concern. Especially since he once wrote that he was trying to say the same thing over and over again in different ways. In other words, Kant is so important to philosophy, and the synthetic a priori is so important to Kant, that it is worth considering the possibility that Wittgenstein identified philosophy with a concern with synthetic a priori judgments. After all, Schopenhauer appears to have identified the synthetic a priori with the whole of pure mathematics, and Wittgenstein, who was significantly influenced by Schopenhauer, identified his own contribution to philosophy as having been chiefly in the philosophy of mathematics. But, obviously, I’m speculating somewhat idly here.

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[i] For more on the relevance of Kant for Wittgenstein see P. M. S. Hacker Insight and Illusion: Themes in the Philosophy of Wittgenstein Thoemmes Press, Bristol, England, 1997, Erik Stenius Wittgenstein’s Tractatus: A Critical Exposition of its Main Lines of Thought Cornell University Press, Ithaca, NY, 1960, and Alfred Nordmann Wittgenstein’s Tractatus: An Introduction Cambridge University Press, Cambridge, 2005.