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All inference takes place a priori.
There is no causal nexus which justifies such an inference.
The events of the future cannot be inferred from those of the present. Superstition is the belief in the causal nexus.
The freedom of the will consists in the fact that future actions cannot be known now. We could only know them if causality were an inner necessity, like that of logical deduction.—The connexion of knowledge and what is known is that of logical necessity.
Contradiction is something shared by propositions, which no proposition has in common with another. Tautology is that which is shared by all propositions, which have nothing in common with one another.
Contradiction is the external limit of the propositions, tautology their substanceless centre.
Here it becomes clear that there are no such things as “logical objects” or “logical constants” (in the sense of Frege and Russell).
Truth-functions are not material functions.
The general form of proposition is the essence of proposition.
A possible sign must also be able to signify. Everything which is possible in logic is also permitted.
This shows that there is no such thing as the soul—the subject, etc.—as it is conceived in contemporary superficial psychology.
Logic precedes every experience—that something is so.
Logic fills the world: the limits of the world are also its limits.
The thinking, presenting subject; there is no such thing. If I wrote a book “The world as I found it”, I should also have therein to report on my body and say which members obey my will and which do not, etc. This then would be a method of isolating the subject or rather of showing that in an important sense there is no subject: that is to say, of it alone in this book mention could not be made.
It also becomes clear why logic has been called the theory of forms and of inference.
Logic is not a theory but a reflexion of the world. Logic is transcendental.
Mathematics is a logical method. The propositions of mathematics are equations, and therefore pseudo-propositions.
Mathematical propositions express no thoughts.
The logic of the world which the propositions of logic show in tautologies, mathematics shows in equations.
Mathematics is a method of logic.
Logical research means the investigation of all regularity. And outside logic all is accident.
necessity for one thing to happen because another has happened does not exist. There is only logical necessity.
Hence also there can be no ethical propositions. Propositions cannot express anything higher.
It is clear that ethics cannot be expressed. Ethics are transcendental. (Ethics and æsthetics are one.)
The first thought in setting up an ethical law of the form “thou shalt . . . ” is: And what if I do not do it. But it is clear that ethics has nothing to do with punishment and reward in the ordinary sense. This question as to the consequences of an action must therefore be irrelevant.
Death is not an event of life. Death is not lived through.
Our life is endless in the way that our visual field is without limit.
Scepticism is not irrefutable, but palpably senseless, if it would doubt where a question cannot be asked. For doubt can only exist where there is a question; a question only where there is an answer, and this only where something can be said.
There is indeed the inexpressible. This shows itself; it is the mystical.
The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other—he would not have the feeling that we were teaching him philosophy—but it would be the only strictly correct method.
Whereof one cannot speak, thereof one must be silent.