Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/177

Rh of equations to new equations, replacing expressions by others in accordance with the equations.

Thus the proof of the proposition 2x2 = 4 runs:


 * (Ων)μx=Ων×μx Def.

Ω2×2x=(Ω2)2x=(Ω2)1+1x=Ω2Ω2x=Ω1+1'Ω1+1'x''

=(Ω'Ω)'(Ω'Ω)x=Ω'Ω'Ω'Ωx=Ω1+1+1+1

Logical research means the investigation of all regularity. And outside logic all is accident.

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.

The law of causality is not a law but the form of a law.

"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.

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.)

We do not believe a priori in a law of conservation, but we know a priori the possibility of a logical form.

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.

Newtonian mechanics, for example, brings the description of the universe to a unified form.

Rh