This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus Logico-Philosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)

Tuesday, April 1, 2008

A proposition must have just as many degrees of freedom as the situation it represents.

They must possess the same logical multiplicity. (See Hertz's Mechanics on dynamical models.) This mathematical multiplicity, of course, cannot itself be depicted and one cannot get out of it while depicting.

If, for example, we wanted to express ((x) . fx) by a prefix such as (Gen. fx), we would not know what was being generalized. If we wanted to signalize it with an index 'α' by writing (f(xα)), we would not know the scope.

If we were to try to do it by introducing a mark into the argument position by writing
((G,G) . F(G,G))
we could not establish the identity of the variables. And so on.

All these notations are inadequate because they lack the necessary mathematical multiplicity. For the same reason, the idealist's explanation of seeing of spatial relations with 'spatial spectacles' is inadequate because it cannot explain the multiplicity of these relations.

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