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Wittgenstein, Ludwig, 1889-1951

"Tractatus Logico-Philosophicus"

.. , in
the following way /0'x, /0+1'x, /0+1+1'x, /0+1+1+1'x, ... . Therefore,
instead of '[x, E, /'E]', I write '[/0'x, /v'x, /v+1'x]'. And I give the
following definitions 0 + 1 = 1 Def., 0 + 1 + 1 = 2 Def., 0 + 1 + 1 +1 = 3
Def., (and so on).

6.021 A number is the exponent of an operation.

6.022 The concept of number is simply what is common to all numbers, the
general form of a number. The concept of number is the variable number. And
the concept of numerical equality is the general form of all particular
cases of numerical equality.

6.03 The general form of an integer is [0, E, E +1].

6.031 The theory of classes is completely superfluous in mathematics. This
is connected with the fact that the generality required in mathematics is
not accidental generality.

6.1 The propositions of logic are tautologies.

6.11 Therefore the propositions of logic say nothing. (They are the
analytic propositions.)

6.111 All theories that make a proposition of logic appear to have content
are false. One might think, for example, that the words 'true' and 'false'
signified two properties among other properties, and then it would seem to
be a remarkable fact that every proposition possessed one of these
properties. On this theory it seems to be anything but obvious, just as,
for instance, the proposition, 'All roses are either yellow or red', would
not sound obvious even if it were true.


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