Tractatus Logico-Philosophicus (6.5) - Tractatus 3-7

Tractatus 3-7

• 3 "The logical picture of the facts is the thought.
• 4 "The thought is the significant proposition.
• 5 "Propositions are truth-functions of elementary propositions.

In this case, the elementary propositions, say a. stand for ordinary sentences in ordinary language. They are not meant to be further analyzed, but are taken as givens.

• 5.2522

"The general term of the formal series a, O' a, O' O' a, ... I write thus: "". This expression in brackets is a variable. ...

Wittgenstein thus gives a notation which expresses an inductive form.

• 6 "The most general form of proposition is .

In this notation, ξ expresses the set of the arguments of truth function ξ, and N( ξ ) is the power set of ξ.

• 6.241 proves 2*2=4 in one sentence, a feat which took Russell hundreds of pages to prove 2+2=4, as his demonstration that he believes his method is more powerful.

• 6.33 "We do not believe a priori in a law of conservation, but we know a priori the possibility of a logical form.

The conservation laws of physics stand as a statement of belief, in contrast with the a priori character of the logical form in 6.

Historically, the statements from 6.4 onward were ignored by the Vienna Circle and the other proponents of logical empiricism, as they simply did not know what to make of them. Wittgenstein was not present to bolster his case, as he was a schoolteacher and gardener at the moment that Tractatus was published. Afterward, he did not help his case by reciting the pacifist poems of Rabindranath Tagore to them, in place of analytic discussion. Indeed, 6.41 below seems to have a different character from the chain of thought stated above.

• 6.41 "The sense of the world must lie outside of the world. ... In it, there is no value, - and if there were, it would be of no value. ...

• 6.42 "Hence also there can be no ethical propositions. ...

• 6.421 "... Ethics are transcendental. ...

• 6.423 "Of the will as the bearer of the ethical we cannot speak.

• 6.5 "For an answer which cannot be expressed, the question too cannot be expressed.

• 7 "Whereof one cannot speak, thereof one must be silent".

But 6.41 needs to be re-examined in this chain of justification. Statement 6.41 appears to be an appeal; the word must shows up in striking contrast to the rest of Tractatus, which consist of declarative statements. His usual economy in words is replaced by repetition. 6.41 is revisited below.

Wittgenstein himself was an exemplar of 7, by acting instead of speaking, an ethical position. What actually impelled Wittgenstein, according to Janik and Toulmin, was the role models of a few men like Fritz Mauthner, as Wittgenstein himself set out to live the example of 7, as an engineer, a soldier, a schoolteacher, an architect, a gardener, a professor, a hospital orderly. As a professor, he attempted to follow up on Tractatus, with his posthumous Philosophical Investigations.

There is an ominous side-note to this action; at the same time that this Viennese was living his ideals, the forces of fascism were also acting to destroy the existing world order. These forces appeared not to be based on existing ethical principles, but on rather different ones based solely on might; the poetry of Rabindranath Tagore meant nothing to them, either.