eference of a proposition from
the meanings of its component words or images.

Just as a word has meaning, so a proposition has an objective reference.
The objective reference of a proposition is a function (in the
mathematical sense) of the meanings of its component words. But the
objective reference differs from the meaning of a word through the
duality of truth and falsehood. You may believe the proposition "to-day
is Tuesday" both when, in fact, to-day is Tuesday, and when to-day is
not Tuesday. If to-day is not Tuesday, this fact is the objective of
your belief that to-day is Tuesday. But obviously the relation of your
belief to the fact is different in this case from what it is in the case
when to-day is Tuesday. We may say, metaphorically, that when to-day is
Tuesday, your belief that it is Tuesday points TOWARDS the fact, whereas
when to-day is not Tuesday your belief points AWAY FROM the fact. Thus
the objective reference of a belief is not determined by the fact alone,
but by the direction of the belief towards or away from the fact.* If,
on a Tuesday, one man believes that it is Tuesday while another believes
that it is not Tuesday, their beliefs have the same objective, namely
the fact that it is Tuesday but the true belief points towards the fact
while the false one points away from it. Thus, in order to define the
reference of a proposition we have to take account not only of the
objective, but also of the direction of pointing, towards the objective
in the case of a true proposition and away from it in the case of a
false one.

* I owe this way of looking at the matter to my friend
Ludwig Wittgenstein.

This mode of stating the nature of the objective reference of a
proposition is necessitated by the circumstance that there are true and
false propositions, but not true and false facts. If to-day is Tuesday,
there is not a false objective "to-day is not Tuesday," which could be
the objective of the false belief "to-day is not Tuesday." This is the
reason why two beliefs which are each other's contradictories have the
same objective. There is, however, a practical inconvenience, namely
that we cannot determine the objective reference of a proposition,
according to this definition, unless we know whether the proposition
is true or false. To avoid this inconvenience, it is better to adopt
a slightly different phraseology, and say: The "meaning" of the
proposition "to-day is Tuesday" consists in p