Abstract
Ludwig Wittgenstein had enough first-rate ideas to influence a variety of thinkers; he expressed some ideas vaguely enough to keep hosts of interpreters busy; he changed them often enough to provide work for some score of biographers and historians; and he shrouded them (and himself), in enough mystery to originate a cult.
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Notes
Here and in the sequel,‘Tr.’ stands for Tractatus. The numbers of the propositions in Tr. follow the system of numbering borrowed from Peano, which Whitehead and Russell used in the Principia Mathematics. But in contrast to books on mathematics, in which the main purpose of such numbers is to serve as short references to theorems in proofs of subsequent theorems, there are hardly any cross references or, for that matter, proofs in Tr. A 4-digit number in Tr. rather indicates that the proposition is a comment on a comment on a comment on one of the seven propositions with a 1-digit number, e.g. Tr. 3.142 is a comment on Tr. 3.14, which is a comment on Tr. 3.1, which is a comment on Tr. 3. Similarly, Tr. 4.003 is a comment of ‘minor logical weight’ (less than that of, say, Tr. 4.01) on Tr. 4.
Mauthner has indeed remained little known and badly underrated. In J. Passmore’s in many ways excellent book A Hundred Years of Philosophy (2nd edition), he is not even mentioned, Weiler’s book (see III,2) will probably make him better known in the English-speaking world.
Here, ‘or’ is the so-called inclusive ‘or’, often called ‘and/or’ in legal language; that is to say, ‘p or q’; means that at least one of the propositions p and q is true. The Romans expressed this usage by the particle ‘Vel’ and wrote ‘aut p aut q’ to indicate that exactly one of the propositions p and q is true. The latter is parallel to the use of ‘or’, ‘ou’, and ‘oder’ in English, French, and German, where however, no sharp distinction between the two kinds of disjunction exists.
American Journal of Mathematics 43, 1921.
Lukasiewicz, Jan and Tarski, Alfred, ‘Untersuchungen über den Aussagenkalküil’, Comptes Rendus des Séances de la Société des Lettres de Varsovie, Classe III, v. 23 (1930) pp. 30–50.
Moreover, Post’s thesis contained the discovery of n-valued logics in which the propositions are divided into n classes of logical significance, not only into the two classes of true and false propositions — a discovery made simultaneously with and independently of Post by Lukasiewicz.
Russell develops a cumbersome and unnecessarily complicated symbolism. He refers to the property of blackness or the predicate ‘is black’ by writing ‘x is black.’ More generally, for ‘is f ‘or ‘the predicate f belongs to’ he writes ‘f x’ though the letter x has no meaning whatsoever and might as well be replaced by y or any other letter or be omitted. Occasions arise, however, where Russell must distinguish the predicate f from the propositional scheme f x and in such cases he uses for f the symbol f x, which still includes the superfluous letter x. He uses ‘f’ indiscriminately for predicates as well as relations instead of indicating them by symbols such as, f and F or f1 and f2, respectively. Yet, on occasion, Russell wants to indicate that ‘f ‘at that place stands for a predicate. To this end, he introduced for the predicate (which he might simply denote by the letters f or f1) the grotesque symbol f!x. This carrying along the ubiquitous letter x in logical formulas, even where it means nothing and might be replaced by any other letter or simply omitted, is of course a heritage from the mathematicians, who since Descartes have indulged in a symbolism that I have once described as x-omantic.
A priori means before, or at least independent of, experience. Kant had embarked on his critique of pure reason mainly in order to explain how synthetic (i.e., essentially, nontautological) propositions a priori were possible. Propositions that Kant regarded as synthetic and a priori included in particular all statements of Euclid’s geometry. In the Circle, no one except the phenomenologist Kaufmann believed in the existence of synthetic a priori propositions.
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Menger, K. (1994). Wittgenstein’s Tractatus and the Early Circle. In: Golland, L., McGuinness, B., Sklar, A. (eds) Reminiscences of the Vienna Circle and the Mathematical Colloquium. Vienna Circle Collection, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1102-7_8
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