th-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. 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.

4.4661 Admittedly the signs are still combined with one another even in
tautologies and contradictions--i.e. they stand in certain relations to
one another: but these relations have no meaning, they are not essential
to the symbol.

4.5 It now seems possible to give the most general propositional form:
that is, to give a description of the propositions of any sign-language
whatsoever in such a way that every possible sense can be expressed by
a symbol satisfying the description, and every symbol satisfying the
description can express a sense, provided that the meanings of the names
are suitably chosen. It is clear that only what is essential to the
most general propositional form may be included in its description--for
otherwise it would not be the most general form. The existence of a
general propositional form is proved by the