Logic: A Very Short Introduction (Very Short Introductions)

Sentences may be true, false, both, or neither.

the account of descriptions that I have explained is itself problematic in certain ways. According to this account, if δP is a sentence where δ is a description that does not refer to anything, it is false. But this does not always seem to be right.

To put it tendentiously, there are truths about non-existent objects, after all.

Russell’s paradox. Like the liar paradox, it has a cousin. What about the set of all sets that are members of themselves. Is this a member of itself, or is it not? Well, if it is, it is; and if it is not, it is not. Again, there would seem to be nothing to determine the matter either way.

the thing satisfying such and such a condition, satisfies that very condition. This is often called the Characterization Principle

description is something of the form ixcx, where cx is some condition containing occurrences of x.

descriptions have the form: the thing satisfying such and such a condition.

definite descriptions, or sometimes just descriptions

The sentence nP is true in a situation if the object referred to by n has the property expressed by P in that situation.

(Compare: Everyone has a mother; it does not follow that there is someone who is the mother of everyone.)