Friday, May 14, 2010
Wittgenstein, Logicism, and Ideology
Absent from Wittgenstein's discussion of the indefinability of 'game' is any consideration of examples of activities which are plainly not called 'games', which should not have been difficult to find in the Europe of the early 1940s. Similarly, how the pleas of a beggar qualify as a 'language-game' is unclear. More generally unclear is the extent of Wittgenstein's repudiation of Logicism, i. e. whether or not he regards Logicism as implicitly prejudicial. On the one hand, Russell believes that, as universally valid, Logic and Mathematics transcend all social divisions. On the other, Dewey argues that such purported transcendence is itself a product of, and, hence, an implicit defense of, socio-economic class polarity. Now, while embedding Language in non-linguistic activity, Wittgenstein's representations of the latter remain as cloistered as Russell's. So, it is unclear whether Wittgenstein's 'fly' has indeed escaped, only to return into the bottle, in order to lead other flies out, or, has not escaped, knows that there is an escape route, but is reluctant to leave familiar surroundings behind.
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Wittgenstein's repudiation of Logicism is a fundamental observation which implies that logic, or more accurately, a mathematical reliance on equality (expressed by = sign) may be untrue if some factors are omitted in a given equation. In other words, what Wittgenstein states can be illustrated by a statement: logic proves nothing if it excludes unknown factors. Case and point, subatomic particles defy common sense and behave in wacky ways but nobody can deny they exist based just on a fact they are "non-logical".
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