ARGUMENTS FOR MONOTHEISM 171Types of propositions
Something has truth value if and only if it is either true or false. Anything
that has truth value is a proposition. Declarative sentences, typically used,
express propositions; the same proposition can be expressed by various
sentences in the same language or by various sentences in different
languages. Thus “The man is old and asleep, and the woman is reading” and
“The old man is asleep, and the woman is reading” are different sentences
that typically express the same proposition. A proposition is either:
1 necessarily true (P is a necessary truth if and only if not-P is a
contradiction – e.g., Nothing has logically incompatible properties is
a necessary truth.)
2 necessarily false (P is necessarily false if and only if P is a
contradiction – e.g., Bill Russell is exactly 6’9? tall, and is not exactly
6’9? tall is a necessary truth.)^4
3 logically contingent (P is logically contingent if and only if it is
neither necessarily true nor necessarily false; a logically contingent
proposition may be true or it may be false – e.g., Bill Russell is
exactly 6’9? tall is a logically contingent proposition.)
Further:
4 A proposition P is possibly true if and only if P is not a necessary
falsehood – every necessary truth, and every logically contingent
proposition, is possibly true.
Logical necessity
There are different views about logical necessity, and different meaning
assigned to the words “logically necessary proposition.” A brief
explanation is in order as to how logical necessity is understood here.^5
Logical necessity is a feature of propositions, not sentences. It is not an
artifact of our language or thought. Coming to see that a proposition is
necessarily true is a discovery, not an invention or a discovery about our
inventions. The reason for this is that necessary truths are not possibly
false. Anything whose truth depends on our language or our conventions is
possibly false, for our language and our conventions might never have
existed at all. So neither the necessity nor the truth of necessary truths