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. This product, therefore, is identical with the
proposition. For it is impossible to alter what is essential to a symbol
without altering its sense.


4.466 What corresponds to a determinate logical combination of signs is a
determinate logical combination of their meanings. It is only to the
uncombined signs that absolutely any combination corresponds. In other
words, propositions that are true for every situation cannot be
combinations of signs at all, since, if they were, only determinate
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--indeed the
disintegration--of the combination of signs.