Tractatus Logico-Philosophicus (6.5)

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In the Tractatus Logico-Philosophicus of Ludwig Wittgenstein, Proposition 6.5 seeks to ground his philosophy of action (Proposition 7: "Whereof one cannot speak, thereof one must be silent").

  • 6.5 "For an answer which cannot be expressed, the question too cannot be expressed.
"The riddle does not exist.
"If a question can be put at all, then it can also be answered.

Although the historical significance of Tractatus is for its influence on the philosophers of logical empiricism, by providing them with a framework for a philosophy of science, and hence engineering, Wittgenstein actually wrote it as a work on ethics.[citation needed] See his propositions 6.4 onward.

But his motivation for writing, and the style of presentation, follow Frege and Russell, below.

Tractatus 1-2[edit]

  • 1 "The world is all that is the case.
  • 1.1 "The world is the totality of facts, not of things.

These famous propositions, starting from 1, and ending at 7, are striking for their simplicity and ambition.

Proposition 6.5 (and its consequence) can not be understood until one realizes that Wittgenstein was a son of a family at the apex of Viennese culture, the capital of an empire (now vanished)[1]. In today's terms, the answer 6.5 is that from a man who some might view as possessed of the highest intellect, moral discrimination, and worldly wealth. He literally could do anything he wished. But his father, Karl, thought him untalented, in comparison to the rest of the family, which included musicians, and artists. He was schooled at home until age 14 (he later imposed his ideals on his hapless students after he had completed Tractatus, and had undertaken training as a schoolteacher (1920)). He was assigned to study engineering and undertook the curriculum of a mechanical engineer at Berlin Technische Hochschule (1906).

Frege and Russell[edit]

He later attended the University of Manchester in England as a doctoral student in aeronautical engineering (1908). Thus Wittgenstein undertook the study of the foundation of mathematics, when he began to design jet propellers. But he refused to accept the propositions he encountered and brought his questions to Frege, who had undertaken a program to base mathematics on logic (1878). Frege, unable to counter his questions, referred him to Russell. Russell, by this time, had completed a work on Frege's program (1903), and was collaborating with Whitehead on Principia Mathematica. He duly appeared at Cambridge (1911), where Russell assigned him a tutor, K.E. Johnson, for logic. After one hour, Johnson reported that Wittgenstein was teaching him. But Russell had discovered some antinomies in logic, seriously calling into question Frege's program. Frege's program for logic as the basis of mathematics was now in shambles. Wittgenstein thus retired to Norway to work out his ideas (1913), and perhaps rescue Frege's program. This was the basis for his Tractatus.

While in Norway, his father Karl died (1913), leaving him heir to a fortune, which he attempted to give away (much of it to his surviving siblings, on the condition that they not give any back to him). By 1914, the Austro-Hungarian Empire was at war with Russell's British Empire, and Wittgenstein volunteered to fight for the Empire of Habsburg Vienna.

Hertz' theory of models and Russell's theory of meaning[edit]

While a soldier, before the serious fighting, he found a magazine article about a lawsuit involving a baby carriage and a truck. The court case re-enacted the incident with models. It was this event which made him realize that the subject of this process could be described by pictures as well as in words -- the genesis of his picture theory of language (Tractatus 2.*). But this idea was already endemic in Viennese thought[2].

Tractatus 3-7[edit]

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: "[a, x, O' x]". 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 [p, ξ, N( ξ )].

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.

6.41 revisited[edit]

Because 6.41 is different in character from the other propositions, a review is appropriate. Here we use the machinery of deontic modal logic, with the following conventions, but tag 6.41's statements with the type of statement:

  • ¬\Box contingency is not necessarily so but which is actually so, and which could have been otherwise.
  • \Box necessary if it must be so
  • 6.41 \Box"The sense of the world must lie outside of the world. ¬\BoxIn the world everything is as it is and happens as it does happen. In it, there is no value, - and if there were, it would be of no value.
  • \Box"If there is a value which is of value, it must lie outside all happening and being-so. ¬\Box For all happening and being-so is accidental.
  • Not ¬\Box"What makes it non-accidental cannot lie in the world, for otherwise this would then again be accidental.
  • \Box "It must lie outside the world.

6.41 is an example of deontic modal logic. Wittgenstein is making statements of necessity of ethical action, rather than basing actions on contingent or accidental results, which he equates with the world. The doubling of the phrase no value is an indication that the statements are being made for different modalities.

  • From a humanist point of view, his actions taken, were to negate the accidental parts of his life:
    • the accident of his wealth, which he attempted to negate by giving away;
    • the accident of his position in society, which he attempted to negate by volunteering for the ranks in the army, rather than accepting a commission in the army;
    • the accident of being a professor in wartime, which he attempted to negate by becoming a hospital orderly.
    • Even his last words "tell them I've had a wonderful life" bespeak someone who was evaluating the sense of his life (and must have been so doing in the other examples just stated).


  • ^ Allan Janik and Stephen Toulmin (1973, 1996), Wittgenstein's Vienna ISBN 1-56663-132-7. Includes Notes, Index, 314 pp. Over 260 books and articles cited in the bibliography. Toulmin was a student of Wittgenstein up to the time of his resignation from Cambridge.
They cite Fritz Mauthner's Critique of Language (Sprachkritik). Beiträge zu einer Kritik der Sprache, 3 vols, Stuttgart: J.G. Cotta (1901-3), Wittgenstein cites this as 4.0031 with a claim his view is different. Janik and Toulmin note that his view began to converge with Mauthner's upon his re-entry into philosophy in 1928.
They cite the Brenner Circle as the pathway for Wittgenstein's donations to Rilke. For more, see Richard Detsch (1990) Georg Trakl and the Brenner Circle (American University Studies. Series I, Germanic Languages and Literature, Vol 91)
  • Jaakko Hintikka (2000) On Wittgenstein ISBN 0-534-57594-3 p. 55 cites W's accus. of Carnap upon receiving a 1932 preprint.
  • Hans Sluga and David G. Stern, eds. (1996). Cambridge Companion to Wittgenstein ISBN 0-521-46591-5
  • P. M. S. Hacker (1999), Wittgenstein 99pp. ISBN 0-415-92376-X
  • Marie McGinn (1997) Wittgenstein and the Philosophical Investigations ISBN 0-415-11191-9
  • Ludwig Wittgenstein (1939) Remarks on the Foundations of Mathematics, Revised Edition. G. H. von Wright, R. Rhees (eds.), G. E. M. Anscombe (trans.) ISBN 0-262-73067-7
  • Ludwig Wittgenstein, Vermischte Bemerkungen (his personal notes taken 1914-1944) packaged as Culture and Value (1977), Peter Winch, trans. ISBN 0-226-90435-0
  • Ludwig Wittgenstein, Lectures and Conversations on Aesthetics, Psychology, and Religious Belief Cyril Barrett, ed. ISBN 0-520-01354-9