)
4.46211 Tautologies and contradictions are not, however, nonsensical. They
are part of the symbolism, much as '0' is part of the symbolism of
arithmetic.
4.462 Tautologies and contradictions are not pictures of reality. They do
not represent any possible situations. For the former admit all possible
situations, and latter none . In a tautology the conditions of agreement
with the world--the representational relations--cancel one another, so that
it does not stand in any representational relation to reality.
4.463 The truth-conditions of a proposition determine the range that it
leaves open to the facts. (A proposition, a picture, or a model is, in the
negative sense, like a solid body that restricts the freedom of movement of
others, and in the positive sense, like a space bounded by solid substance
in which there is room for a body.) A tautology leaves open to reality the
whole--the infinite whole--of logical space: a contradiction fills the
whole of logical space leaving no point of it for reality. Thus neither of
them can determine reality in any way.
4.464 A tautology's truth is certain, a proposition's possible, a
contradiction's impossible. (Certain, possible, impossible: here we have
the first indication of the scale that we need in the theory of
probability.)
4.465 The logical product of a tautology and a proposition says the same
thing as the proposition.
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