For it is because of this method that every proposition
of mathematics must go without saying.
6.24 The method by which mathematics arrives at its equations is the method
of substitution. For equations express the substitutability of two
expressions and, starting from a number of equations, we advance to new
equations by substituting different expressions in accordance with the
equations.
6.241 Thus the proof of the proposition 2 t 2 = 4 runs as follows: (/v)n'x
= /v x u'x Def., /2 x 2'x = (/2)2'x = (/2)1 + 1'x = /2' /2'x = /1 + 1'/1 +
1'x = (/'/)'(/'/)'x =/'/'/'/'x = /1 + 1 + 1 + 1'x = /4'x. 6.3 The
exploration of logic means the exploration of everything that is subject to
law . And outside logic everything is accidental.
6.31 The so-called law of induction cannot possibly be a law of logic,
since it is obviously a proposition with sense.---Nor, therefore, can it be
an a priori law.
6.32 The law of causality is not a law but the form of a law.
6.321 'Law of causality'--that is a general name. And just as in mechanics,
for example, there are 'minimum-principles', such as the law of least
action, so too in physics there are causal laws, laws of the causal form.
6.3211 Indeed people even surmised that there must be a 'law of least
action' before they knew exactly how it went. (Here, as always, what is
certain a priori proves to be something purely logical.
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