Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/171

Rh We prove a logical proposition by creating it out of other logical propositions by applying in succession certain operations, which again generate tautologies out of the first. (And from a tautology only tautologies follow.)

Naturally this way of showing that its propositions are tautologies is quite unessential to logic. Because the propositions, from which the proof starts, must show without proof that they are tautologies.

In logic process and result are equivalent. (Therefore no surprises.)

Proof in logic is only a mechanical expedient to facilitate the recognition of tautology, where it is complicated.

It would be too remarkable, if one could prove a significant proposition logically from another, and a logical proposition also. It is clear from the beginning that the logical proof of a significant proposition and the proof in logic must be two quite different things.

The significant proposition asserts something, and its proof shows that it is so; in logic every proposition is the form of a proof.

Every proposition of logic is a modus ponens presented in signs. (And the modus ponens can not be expressed by a proposition.)

Logic can always be conceived to be such that every proposition is its own proof.

All propositions of logic are of equal rank ; there are not some which are essentially primitive and others deduced from these.

Every tautology itself shows that it is a tautology.

It is clear that the number of "primitive propositions of logic" is arbitrary, for we could deduce Rh