of equations to new equations, replacing expressions by others in accordance with the equations.
6.241 Thus the proof of the proposition 2x2 = 4 runs:
- (Ων)μ'x=Ων×μ'x Def.
Ω2×2'x=(Ω2)2'x=(Ω2)1+1'x=Ω2''Ω2'x=Ω1+1'Ω1+1'x
=(Ω'Ω)'(Ω'Ω)'x=Ω'Ω'Ω'Ω'x=Ω1+1+1+1
6.3 Logical research means the investigation of all regularity. And outside logic all is accident.
6.31 The so-called law of induction cannot in any case be a logical law, for it is obviously a significant proposition.—And therefore it cannot be a law a priori either.
6.32 The law of causality is not a law but the form of a law.[1]
6.321 "Law of Causality" is a class name. And as in mechanics there are, for instance, minimum-laws, such as that of least action, so in physics there are causal laws, laws of the causality form.
6.3211 Men had indeed an idea that there must be a "law of least action", before they knew exactly how it ran. (Here, as always, the a priori certain proves to be something purely logical.)
6.33 We do not believe a priori in a law of conservation, but we know a priori the possibility of a logical form.
6.34 All propositions, such as the law of causation, the law of continuity in nature, the law of least expenditure in nature, etc. etc., all these are a priori intuitions of possible forms of the propositions of science.
6.341 Newtonian mechanics, for example, brings the description of the universe to a unified form.- ↑ I.e. not the form of one particular law, but of any law of a certain sort (B. R.).
