We can use a mathematical function to calculate that n elemental propositions produce L(n) groups of truth values. These can be ordered in a row (or added as a column to the truth table).
Among all the possible groups of truth values there are two extreme cases. The first case agrees with all combinations of truth values and we call the proposition a tautology. The second case agrees with none and we call it a contradiction.
A proposition shows what it has to say; tautologies and contradictions show that they have nothing to say. Because a tautology is unconditionally true, it has no truthconditions; and a contradiction has none because it is never true.
Tautologies and contradictions have no sense; just as a point from which arrows go out in two directions. (For example, I know nothing about the weather when I know that it is either raining or not raining.) Tautologies and contradictions are not, however, absurd. They belong to symbolism; much as zero to the symbolism of arithmetic.
Tautologies and contradictions are not images of reality. They do not represent possible situations, for the former admit all situations, and latter none. In a tautology the conditions of agreement with the world  the embodying relations  cancel one another, so that it does not express reality.
The truthconditions of a proposition determine the range of the facts. (Interpreted in the negative sense, a proposition, a picture, or a model is like a solid body that restricts the freedom of movement of others. Interpreted in the positive sense, it is like a space bounded by solid substance in which there is room for a body.) A tautology leaves the infinite whole of logical space open to reality. A contradiction fills it, leaving no point of it for reality. Thus neither of them can determine reality in any way.
A tautology is certainly true, a proposition possibly, and a contradiction certainly not. (We have the scale that we need in the theory of probability.) The logical product of a tautology and a proposition says the same thing as the proposition and is therefore identical with the proposition because one cannot change the essence of a symbol without changing its sense.
A particular logical combination of signs corresponds to a particular logical combination of their meanings. Absolutely any combination corresponds to uncombined signs, but only to them. In other words, propositions that are true for every situation cannot be sign combinations at all, for if they were, only particular combinations of objects could correspond to them. (And what is not a logical combination has no combination of objects corresponding to it.)
Tautology and contradiction are the limiting cases of sign combinations  their dissolution. Admittedly the signs are still combined with one another even in tautologies and contradictions. That is, they relate to one another. But these relations have no meaning, they are not essential to the symbol.
This log was inspired by "How to Read Wittgenstein" and "Ludwig Wittgenstein: the duty of genius" by Ray Monk. It is based on reading Tractatus LogicoPhilosophicus by Ludwig Wittgenstein translated by D. F. Pears & B. F. McGuinness (Routledge and Kegan Paul:1963)
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 Tractatus LogicoPhilosophicus 1
 Tractatus LogicoPhilosophicus 2
 Tractatus LogicoPhilosophicus 2.01
 Tractatus LogicoPhilosophicus 2.02
 Tractatus LogicoPhilosophicus 2.03 to 2.063
 Tractatus LogicoPhilosophicus 2.1
 Tractatus LogicoPhilosophicus 2.2
 Tractatus LogicoPhilosophicus 3
 Tractatus LogicoPhilosophicus 3.0
 Tractatus LogicoPhilosophicus 3.1
 Tractatus LogicoPhilosophicus 3.2
 Tractatus LogicoPhilosophicus 3.3
 Tractatus LogicoPhilosophicus 3.32
 Tractatus LogicoPhilosophicus 3.33
 Tractatus LogicoPhilosophicus 3.34
 Tractatus LogicoPhilosophicus 3.4 to 3.5
 Tractatus LogicoPhilosophicus 4
 Tractatus LogicoPhilosophicus 4.00
 Tractatus LogicoPhilosophicus 4.01 to 4.022
 Tractatus LogicoPhilosophicus 4.023 to 4.027
 Tractatus LogicoPhilosophicus 4.03
 Tractatus LogicoPhilosophicus 4.04
 Tractatus LogicoPhilosophicus 4.05 to 4.0621
 Tractatus LogicoPhilosophicus 4.1
 Tractatus LogicoPhilosophicus 4.12 to 4.1213
 Tractatus LogicoPhilosophicus 4.122 to 4.1252
 Tractatus LogicoPhilosophicus 4.126 to 4.128
 Tractatus LogicoPhilosophicus 4.2 to 4.28
 Tractatus LogicoPhilosophicus 4.3 to 4.442
 Tractatus LogicoPhilosophicus 4.45 TO 4.4661
 Tractatus LogicoPhilosophicus 4.5 to 4.53
 Tractatus LogicoPhilosophicus 5
 Tractatus LogicoPhilosophicus 5 to 5.101
 Tractatus LogicoPhilosophicus 5.05 to 5.156
 Tractatus LogicoPhilosophicus 5.11 to 5.132
 Tractatus LogicoPhilosophicus 5.133 to 5.143
 Tractatus LogicoPhilosophicus 5.2 to 5.254
 Tractatus LogicoPhilosophicus 5.3
 Tractatus LogicoPhilosophicus 5.4 to 5.44
 Tractatus LogicoPhilosophicus 5.45
 Tractatus LogicoPhilosophicus 5.46 to 5.472
 Tractatus LogicoPhilosophicus 5.473 to5.476
 Tractatus LogicoPhilosophicus 5.5 to 5.503
 Tractatus LogicoPhilosophicus 5.51
 Tractatus LogicoPhilosophicus 5.52
 Tractatus LogicoPhilosophicus 5.53 to 5.535
 Tractatus LogicoPhilosophicus 5.5351 to 5.5352
 Tractatus LogicoPhilosophicus 5.55 to 5.5571
 Tractatus LogicoPhilosophicus 5.6 to 5.621
 Tractatus LogicoPhilosophicus 5.63 to 5.641
 Tractatus LogicoPhilosophicus 6
 Tractatus LogicoPhilosophicus 6 to 6.01
 Tractatus LogicoPhilosophicus 6.1 to 6.1202
 Tractatus LogicoPhilosophicus 6.1203
 Tractatus LogicoPhilosophicus 6.121 to 6.124
 Tractatus LogicoPhilosophicus 6.125 to 6.1271
 Tractatus LogicoPhilosophicus 6.13 to 6.2331
 Tractatus LogicoPhilosophicus 6.234 to 6.3432
 Tractatus LogicoPhilosophicus 6.342 to 6.372
 Tractatus LogicoPhilosophicus 6.373 to 6.3751
 Tractatus LogicoPhilosophicus 6.5
 Tractatus LogicoPhilosophicus 7
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 The world does not depend on me.
 The relative position of logic and science.
 Mathematics is a method of logic.
 Logic is transcendental.
 One can describe all true logical propositions in ...
 We can do without logical propositions.
 Recognizing a Tautology.
 The propositions of logic are tautologies.
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 The microcosm.
 The boundary of my language represents the boundar...
 Elemental Propositions.
 Propositions occur in each other only as bases of ...
 Expressions.
 Identity.
 Truth Functions do not Include the Concept All.
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 Logical Inference.
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 Logical Form  What can be shown, cannot be said.
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