Bertrand Russell: The Analysis of Mind

13. LECTURE XIII. TRUTH AND FALSEHOOD (continued)

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 pointing to the fact "to-day is Tuesday" if that is a fact, or away from the fact "to-day is not Tuesday" if that is a fact. The "meaning" of the proposition "to-day is not Tuesday" will be exactly the opposite. By this hypothetical form we are able to speak of the meaning of a proposition without knowing whether it is true or false. According to this definition, we know the meaning of a proposition when we know what would make it true and what would make it false, even if we do not know whether it is in fact true or false.