Over an agonizing seven-year period that included his military service in World War I, Wittgenstein wrote his brief Logische-Philosophische Abhandlung, named Tractatus Logico-Philosophicus by G. E. Moore. In it Wittgenstein claimed to have solved all the problems of philosophy (at least all that could be shown in logic).

Wittgenstein also claimed that such problems could not be said or thought (only shown), and so everything written in the Tractatus was strictly speaking nonsense (unsinnung). Everything that had not been said in the Tractatus, Wittgenstein claimed was his truly important work on ethics and the meaning of life.

Despite the negative result for logic, Russell used some of Wittgenstein's work to rewrite Principia Mathematica. It was published as revised by Russell and Whitehead, but shortly thereafter Whitehead disavowed the changes, all actually made by Russell alone. To add to Russell's difficulties, Wittgenstein accused him of misunderstanding the Tractatus and misusing it.

Nevertheless, there grew up around Wittgenstein and Russell (now not talking to one another) a school of philosophy that attracted a diverse group of European science-minded philosophers like Moritz Schlick and his Vienna Circle.

Although Wittgenstein saw his logical philosophy as a failure and turned his interest to the proper use of language, this school of logical positivism (based on Wittgenstein's logical atoms) and logical empiricism (based on verification of atomic facts) has grown to dominate Anglo-American Analytic philosophy.

5 A proposition is a truth-function of elementary propositions.

5.1 Truth fuctions can be arranged in series.
      That is the foundation of the theory of probability.

5.12 In particular, the truth of a proposition 'p' follows from the truth of another proposition 'q' if all the truth-grounds of the latter are truth-grounds of the former.

5.123 If a god creates a world in which certain propositions are true, then by that very act he also creates a world in which all the propositions that follow from them come true. And similarly he could not create a world in which the proposition 'p' was true without creating all its objects.

5.13 When the truth of one proposition follows from the truth of others, we can see this from the structure of the propositions.

5.131 If the truth of one proposition follows from the truth of others, this finds expression in relations in which the forms of the propositions stand to one another: nor is it necessary for us to set up these relations between them, by combining them with one another in a single proposition; on the contrary, the relations are internal, and their existence is an immediate result of the existence of the propositions.

5.132 If p follows from q, I can make an inference from q to p, deduce p from q.
          The nature of the inference can be gathered only from the two propositions.
          They themselves are the only possible justification of the inference.
          'Laws of inference', which are supposed to justify inferences, as in the works of Frege and Russell, have no sense, and would be superfluous.

5.133 All deductions are made a priori.

5.134 One elementary proposition cannot be deduced from another.

5.135 There is no possible way of making an inference from the existence of one situation to the existence of another, entirely different situation.

5.136 There is no causal nexus to justify such an inference.

5.1361 We cannot infer the events of the future from those of the present.             Superstition is nothing but belief in the causal nexus.

5.1362 The freedom of the will consists in the impossibility of knowing actions that still lie in the future. We could know them only if causality were an inner necessity like that of logical inference. The connexion between knowledge and what is known is that of logical necessity.
             ('A knows that p is the case', has no sense if p is a tautology.)

5.15 If T_r is the number of the truth-grounds of a proposition 'r', and if Trs is the number of the truth-grounds of a proposition 's' that are at the same time truth-grounds of 'r', then we call the ratio Trs : Tr the degree of probability that the proposition 'r' gives to the proposition s.

5.1511 There is no special object peculiar to probability propositions.

5.152 When propositions have no truth-arguments in common with one another, we call them independent of one another.
           Two elementary propositions give one another the probability ¹/₂.
           If p follows from q, then the proposition 'q' gives to the proposition p' the probability 1. The certainty of logical inference is a limiting case of probability.
           (Application of this to tautology and contradiction.)

5.153 In itself, a proposition is neither probable nor improbable. Either an event occurs or it does not: there is no middle way.

5.154 Suppose that an urn contains black and white balls in equal numbers (and none of any other kind). I draw one ball after another, putting them back into the urn. By this experiment I can establish that the number of black balls drawn and the number of white balls drawn approximate to one another as the draw continues.
           So this is not a mathematical truth.
           Now, if I say, 'The probability of my drawing a white ball is equal to the probability of my drawing a black one', this means that all the circumstances that I know of (including the laws of nature assumed as hypotheses) give no more probability to the occurrence of the one event than to that of the other. That is to say, they give each the probability ¹/₂, as can easily be gathered from the above 2 definitions.
           What I confirm by the experiment is that the occurrence of the two events is independent of the circumstances of which I have no more detailed knowledge.

"What is good is also divine. Queer as it sounds, that sums up my ethics", Monk, p.278)