(Even
if this proposition is never correct, it still has sense .)
5.5303 Roughly speaking, to say of two things that they are identical is
nonsense, and to say of one thing that it is identical with itself is to
say nothing at all.
5.531 Thus I do not write 'f(a, b) . a = b', but 'f(a, a)' (or 'f(b, b));
and not 'f(a,b) . Pa = b', but 'f(a, b)'.
5.532 And analogously I do not write '(dx, y) . f(x, y) . x = y', but '(dx)
. f(x, x)'; and not '(dx, y) . f(x, y) . Px = y', but '(dx, y) . f(x, y)'.
5.5321 Thus, for example, instead of '(x) : fx z x = a' we write '(dx) . fx
. z : (dx, y) . fx. fy'. And the proposition, 'Only one x satisfies f( )',
will read '(dx) . fx : P(dx, y) . fx . fy'.
5.533 The identity-sign, therefore, is not an essential constituent of
conceptual notation.
5.534 And now we see that in a correct conceptual notation pseudo-
propositions like 'a = a', 'a = b . b = c . z a = c', '(x) . x = x', '(dx)
. x = a', etc. cannot even be written down.
5.535 This also disposes of all the problems that were connected with such
pseudo-propositions. All the problems that Russell's 'axiom of infinity'
brings with it can be solved at this point. What the axiom of infinity is
intended to say would express itself in language through the existence of
infinitely many names with different meanings.
5.5351 There are certain cases in which one is tempted to use expressions
of the form 'a = a' or 'p z p' and the like.
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