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Wittgenstein's Debt to Mach's Popular Scientific Lectures

In the Logisch-philosophische Abhandlung Wittgenstein says so little about physics that commentators have had the greatest trouble to comment on it. (See, for example, Black (I964).) It even happened that a misprint in the first edition of this elliptic treatise went unnoticed for sixty years. The explanation seems to be that it did not occur to anyone that Wittgenstein in his philosophy of physics did little more than summarize parts of a few articles Mach wrote in his Popular-wissenschaftliche Vorlesungen. (Ryle (195 I) even said of Wittgenstein: 'He was influenced by Frege and Russell, not by Mach.') In order to show that Wittgenstein was directly influenced by Mach, I will confine myself to the following subjects on which Wittgenstein commented: (i) chronometry, geometry and problems of space and time (6.36I I, 6.36I I I), and (2) physical principles 6.32-6.34). Mach wrote on the first of these subjects in the last essay that appeared in the fourth edition of the aforementioned book, 'Eine Betrachtung fiber Zeit und Raum'. The second he treated in his articles 'Ueber das Princip der Erhaltung der Energie' and 'Werden Vorstellungen, Gedanken vererbt?' (Mach (I91o).) I am not concerned here with the influence of Part VI of Russell's Principles of mathematics on Wittgenstein's Abhandlung, nor with the influence of Hertz's Prinzipien der Mechanik on both works, I only want to point out that the similarity of Wittgenstein's remarks with some of Mach's popular-scientific agruments is so striking that one cannot but conclude that Wittgenstein had read at least some of the articles of Mach's Popular-wissenschaftliche Vorlesungen. First, there are Wittgenstein's comments on Kant's problem of the right and left hand which cannot be made to cover one another: (i) this problem occurs already in the plane, and even in one-dimensional space; (2) the right and left hand are in fact completely congruent; (3) a right-hand giove could be put on a left hand if it could be turned in four-dimensional space (cf. 6.36III). Mach made similar remarks, but he at least did not omit his source: according to Mach, M6bius remarked about I827 'that a linear figure abc, that can be seen as the symmetrical counterpart of a'b'c'mirrored in SS on the same straight line, can never be made to cover the latter on this line; for this purpose one has to take the figure out of the straight line and turn it; in order to do that at least two dimensions are needed, so a plane' (ibid., pp. 502-503). In addition Mach mentioned M6bius' generalisation, not only for triangles in a plane, but also for congruent three-dimensional bodies, that cannot be made to cover each other in any way in space: 'But one could