Wittgenstein and Philosophy of Logic

This page discusses Wittgenstein's influence on contemporary Philosophy of Logic.

Goldstein, Laurence, 'Smooth and Rough Logic', Philosophical Investigations 15 (1992), pp.93-110.

Brief Discussion
A logic that reflects correct practices of reasoning may be called (following Wittgenstein, PI sect. 107) a ‘rough’ logic, and contrasts with, for example, the pure or ‘a priori’ conception that is common among formal logicians. I show that, in a rough logic, contradictions cannot be asserted, thus vindicating Aristotle and refuting modern dialetheist logicians. This leads to a discussion of the meaning of the word ‘not’ and to some remarks contrasting a dialetheist solution to the logico-semantical paradoxes with a solution that I favour.

Goldstein, Laurence, 'Wittgenstein and Paraconsistency, a chapter contributed to G. Priest', F.R. Routley and J. Norman (eds.), Paraconsistent Logic. Essays on the Inconsistent (Munich, Philosophia Verlag, 1989), pp.540-562.

Brief Discussion
Although Wittgenstein never elaborated a formal logical system, remarks in both the Tractatus and in the transitional works clearly indicate that, had he done so, the system would have been non-classical. Later writing on the foundations of mathematics indicate that Wittgenstein would have been receptive to a paraconsistent system, and that he flirted with dialetheism. Still later, he abandoned that stance.

Goldstein, Laurence, 'The Development of Wittgenstein's Views on Contradiction', History and Philosophy of Logic, 7 (1986), pp.43-56.

Brief Discussion
In the Tractatus, Wittgenstein argued that tautologies and contradictions are not pictures of reality and hence are not propositions — they are sinnlos and have no truth-value. In the ‘transitional’ works, there is some discussion of the ‘harmlessness’ of contradictions in mathematics (a view that, as is evident from the transcription of discussions that took place in Wittgenstein’s 1939 Lectures on the Foundations of Mathematics, Alan Turing found particularly repugnant. Right into his latest writings on the subject, Wittgenstein held that contradictions are not false, but his rationale is different form that offered in his early work. In the later work, he is concerned with the use of language, and he reckons that (with exceptions, such as when a speaker is being ironical or allusive or funny etc.) someone uttering an explicit contradiction should not be credited with mastery of the language, and we should not wish to say that the speaker had succeeded in saying anything false or true.

Goldstein, Laurence, 'Tautology and Contradiction - An Introduction to the Sinnlos', in
J. Shank et al. (edd.), Language, Logic and Philosophy (Vienna, Hölder-Pichler-Tempsky, 1980), pp.350-353.

Brief Discussion
According to the Tractatus, propositions picture possible situations; there are no possible situations that tautologies and contradictions depict, hence tautologies and contradictions are senseless (sinnlos), are not propositions and fail to have truth-value. But they are not nonsensical (unsinnig) for, although they do not depict reality, they show the inferential relations that exist between genuine propositions.

Fann, K.T, ed., Ludwig Wittgenstein The Man and His Philosophy, New York: Delta (Dell Publishing Co. Inc.) 1963.

Book Information:
Paperback: 412 pages

Brief Discussion:
An interesting early collection of essays notable for its high proportion of personal recollections, and for its inclusion of a number of essays relating to mathematics and logic. All the pieces except for the contribution by Wolf Mayes previously published elsewhere, Contains the following essays:
G.H.Von Wright: A Biographical Sketch; 4 Memoirs of Wittgenstein individually by Bertrand Russell, Rudolph Carnap, G.E. Moore and John Wisdom; D.A. Gasking & A.C. Jackson: Wittgenstein as a Teacher; Karl Britton: Portrait of a Philosopher; A Symposium: Assessments of the Man and the Philosopher individually by Erich Heller, M.C.O.Drury, Norman Malcolm & Rush Rhees; Jose Ferrater Mora: Wittgenstein, A Symbol of Troubled Times; Gilbert Ryle: Ludwig Wittgenstein; George A. Paul: Ludwig Wittgenstein; Morris Lazerowitz: Wittgenstein on The Nature of Philosophy; O.K. Bouswma: The Blue Book; Leonard Linsky: Wittgenstein on Language & Some Problems of Philosophy; Norman Malcolm: Wittgensteinʼs Philosophical Investigations ; Paul Feyerabend: Wittgensteinʼs Philosophical Investigations ; Rush Rhees: Wittgensteinʼs Builders; Alice Ambrose: Wittgenstein on Some Questions in Foundations of Mathematics; Joseph L.Cowan: Wittgensteinʼs Philosophy of Logic; Arnold Levison: Wittgenstein and Logical Laws; George Pitcher: Wittgenstein, Nonsense and Lewis Carrol; Alice Ambrose: Wittgenstein on Universals; John Wisdom: A feature of Wittgensteinʼs Technique; Albert W. Levi: Wittgenstein as Dialectitian; Dennis Oʼ Brien: The Unity of Wittgensteinʼs Thought

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