In logic there is no side by side, there can be no classification.
In logic there cannot be a more general and a more special.
The solution of logical problems must be neat for they set the standard of neatness.
Men have always thought that there must be a sphere of questions whose answers—a priori—are symmetrical and united into a closed regular structure.
A sphere in which the proposition, simplex sigillum veri, is valid.
When we have rightly introduced the logical signs, the sense of all their combinations has been already introduced with them: therefore not only “p∨q” but also “~(p∨~q)”, etc. etc. We should then already have introduced the effect of all possible combinations of brackets; and it would then have become clear that the proper general primitive signs are not “p∨q”, “(∃x).fx”, etc., but the most general form of their combinations.
The apparently unimportant fact that the apparent relations like ∨ and ⊃ need brackets—unlike real relations—is of great importance.
The use of brackets with these apparent primitive signs shows that these are not the real primitive signs; and nobody of course would believe that the brackets have meaning by themselves.
Logical operation signs are punctuations.
It is clear that everything which can be said beforehand about the form of all propositions at all can be said on one occasion.
For all logical operations are already contained in the elementary proposition. For “fa” says the same as “(∃x).fx.x=a”.
Where there is composition, there is argument and function, and where these are, all logical constants already are.
One could say: the one logical constant is that which all propositions, according to their nature, have in common with one another.
That however is the general form of proposition.
The general form of proposition is the essence of proposition.
To give the essence of proposition means to give the essence of all description, therefore the essence of the world.
The description of the most general propositional form is the description of the one and only general primitive sign in logic.
Logic must take care of itself.
A possible sign must also be able to signify. Everything which is possible in logic is also permitted. (“Socrates is identical” means nothing because there is no property which is called “identical.” The proposition is senseless because we have not made some arbitrary determination, not because the symbol is in itself unpermissible.)
In a certain sense we cannot make mistakes in logic.
Self-evidence, of which Russell has said so much, can only be discard in logic by language itself preventing every logical mistake. That logic is a priori consists in the fact that we cannot think illogically.
We cannot give a sign the wrong sense.
Occam’s razor is, of course, not an arbitrary rule nor one justified by its practical success. It simply says that unnecessary elements in a symbolism mean nothing.
Signs which serve one purpose are logically equivalent, signs which serve no purpose are logically meaningless.
Frege says: Every legitimately constructed proposition must have a sense; and I say: Every possible proposition is legitimately constructed, and if it has no sense this can only be because we have given no meaning to some of its constituent parts.