But it is
remarkable that a thinker as rigorous as Frege appealed to the degree of
self-evidence as the criterion of a logical proposition.)
6.13 Logic is not a body of doctrine, but a mirror-image of the world.
Logic is transcendental.
6.2 Mathematics is a logical method. The propositions of mathematics are
equations, and therefore pseudo-propositions.
6.21 A proposition of mathematics does not express a thought.
6.211 Indeed in real life a mathematical proposition is never what we want.
Rather, we make use of mathematical propositions only in inferences from
propositions that do not belong to mathematics to others that likewise do
not belong to mathematics. (In philosophy the question, 'What do we
actually use this word or this proposition for?' repeatedly leads to
valuable insights.)
6.22 The logic of the world, which is shown in tautologies by the
propositions of logic, is shown in equations by mathematics.
6.23 If two expressions are combined by means of the sign of equality, that
means that they can be substituted for one another. But it must be manifest
in the two expressions themselves whether this is the case or not. When two
expressions can be substituted for one another, that characterizes their
logical form.
6.231 It is a property of affirmation that it can be construed as double
negation. It is a property of '1 + 1 + 1 + 1' that it can be construed as
'(1 + 1) + (1 + 1)'.
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