Quotes About Logic

The world is the totality of facts, not of things.

In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax. (The logical symbolism of Frege and Russell is such a language, which, however, does still not exclude all errors.)

If a sign is not necessary then it is meaningless. That is the meaning of Occam's razor. (If everything in the symbolism works as though a sign had meaning, then it has meaning.)

The form is the possibility of the structure.

The thought is the significant proposition

Philosophieren ist: falsche Argumente zurückweisen.

The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations.

Tautology and contradiction are, however, not senseless; they are part of the symbolism, in the same way that "0" is part of the symbolism of Arithmetic.

to be considered an important event in the philosophical world.

The logical forms are anumerical. Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.

The specification of all true elementary propositions describes the world completely. The world is completely described by the specification of all elementary propositions plus the specification, which of them are true and which false.

Thence we pass successively to Theory of Knowledge, Principles of Physics, Ethics, and finally the Mystical (das Mystische).

the conditions for sense rather than nonsense in combinations of symbols;

Don't treat your common sense like an umbrella. When you come into a room to philosophize, don't leave it outside but bring it in with you.

We say of a proof that it convinces us of a logical law.—But of course a proof starts somewhere. And the point is: What convinces us of the primitive propositions on which the proof is based? Here there is no proof.

The sense of a truth-function of p is a function of the sense of p.   Denial, logical addition, logical multiplication, etc. etc., are operations.   (Denial reverses the sense of a proposition.)

Contradiction is the external limit of the propositions, tautology their substanceless centre.

That ?, ?, etc., are not relations in the sense of right and left, etc., is obvious.

The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.

The basic evil of Russell's logic, as also of mine in the Tractatus, is that what a proposition is is illustrated by a few commonplace examples, and then presupposed as understood in full generality.

A good objection helps one forward, a shallow objection, even if it is valid, is wearisome. ... The objection does not seize the matter by its root, where the life is, but so far outside that nothing can be rectified even if it is wrong. A good objection helps directly towards a solution, a shallow one must first be overcome and can, from then on, be left to one side. Just as a tree bends at a knot in the trunk in order to grow on.

Mathematics is a method of logic.

Perché trovarsi davanti a un pazzo sapete che significa? Trovarsi davanti a uno che vi scrolla dalle fondamenta tutto quanto avete costruito in voi, attorno a voi, la logica, la logica di tutte le vostre costruzioni! - Eh! Che volete? Costruiscono senza logica, beati loro, i pazzi! O con una loro logica che vola come una piuma!

trovarsi davanti a un pazzo sapete che significa? trovarsi davanti a uno che vi scrolla dalle fondamenta tutto quanto avete costruito in voi, attorno a voi, la logica, la logica di tutte le vostre costruzioni!