Propositions show what they say: tautologies and contradictions show that they say nothing.

It is obvious that an imagined #‎ world , however different it may be from the real one, must have something - a form - in common with it.

Mathematics is a logical method. . . . Mathematical propositions express no thoughts. In life it is never a mathematical proposition which we need, but we use mathematical propositions only in order to infer from propositions which do not belong to mathematics to others which equally do not belong to mathematics.

The truth of the thoughts that are here set forth seems to me unassailable and definitive. I therefore believe myself to have found, on all essential points, the final solution of the problems. And if I am not mistaken in this belief, then the second thing in which the value of this work consists is that it shows how little is achieved when these problems are solved.

If you tried to doubt everything you would not get as far as doubting anything. The game of doubting itself presupposes certainty.

People often say that aesthetics is a branch of psychology. The idea is that once we are more advanced-all the mysteries of art-will be understood by psychological experiments. Exceedingly stupid at this idea is, this is roughly it.

My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, when he has used them--as steps--to climb up beyond them. (He must, so to speak, throw away the ladder after he has climbed up it.) He must transcend these propositions, and then he will see the whole world aright.