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Wittgenstein's Concept of Identity


Wittgenstein represented in the early 30s in Cambridge a new perspective on mathematical logic,
which should lead to better reliability and applicability of mathematics. Not only the concept of
'grammar' arises for the identity-sign, which triggers the horror of the Trinity Mathematical Society
in 1930 and of E. G. Moore 1932. But additionally Wittgenstein does not use formal language to
treat problems of mathematical logic. Otherwise, his formal conceivement of the concepts becomes
obvious, if the early criticism in the Notebooks of 1914 and the Tractatus Logico-Philosophicus is
taken into account. His idea how to modify logical leads to an operational use of identity constants
as an assignment operator. This becomes obvious in the thirties. But at that time, he intermingled
methodologically formal concepts and rather hermeneutical concepts. Hence, that he speaks about
incompleteness in Gödel's sense, and not merely of 'unvollständig' in a very general sense, has to be
noticed by awareness for his methodology, to ensemble concepts from different contextual realms
together, to create tensions that initialize a comparative understanding and an improved concept
formation. Within the 30s, this improvement focused on the use of identity and quantification,
which Wittgenstein changed into a sign for coding like an assignment operator in informatics.
Special examples he gives for the reduction of logical constants, and the operational and visual
criteria he developes for the correct application of a rule show how he provided the foundations for
the genuine Turing-machine within mathematics.

English version

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Wittgenstein's Concept of Identity

Wittgenstein's Concept of Identity

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