Possibility
Possibility
According to distinctions of modality (q. v.), a proposition is possible if its negation is not necessary. The word possible is also used in reference to a state of knowledge rather than to modality, as a speaker might say, “It is possible that 486763 is a prime number,” meaning that he had no information to the contrary (although this proposition is impossible in the sense of modality).
A propositional function F may also be said to be possible. In this case the meaning may be either simply (Ex)F(x); or that (Ex)F(x) is possible in one of the senses just described; or that F(x) is permitted under some particulai system of conventions or code of laws. As an example of the last we may take “It is possible for a woman to be President of the United States.” Here F is ?x[x is a woman and x is a President of the United States], and the code of laws in question is the Constitution of the United States. — A.C.