Opposition

One of the fundamental parts of philosophy is the four forms of opposition in predication. These have traditionally been expressed in the square of opposition. The following diagram is courtesy of The Oxford Dictionary of Philosophy.
The vowels A,E,I, and O are used as abbreviations for the four kinds of predications. A is the universal affirmative: all S are P. E is the universal negative: no S is P. I is the particular affirmative: some S is P. O is the particular negative: some S is not P. These kinds of predications form four kinds of oppositions. I won't uses these vowel abbreviations in what follows, but I may use them in future posts. S and P stand for subject and predicate, respectively.

The first kind of opposition is that of contraries: all S is P, no S is P. Only one of the contraries can be true at a given time. It is not possible for all S to be P and for no S to be P at the same time and in the same respect. However, it is possible for them to both be false. If some S is P and some other S is not P then neither of the contraries is true. It can both be false that all coffee is served black and that no coffee is served black; however, if all coffee is served black, then it is false to say that no coffee is served black.

Additionally, intermediates exist between the extremes of any genus. In this way, black and white are opposed. Between the extremes lies numerous intermediates. The extremes cannot be exactly reduced to the first meaning of contrary given above, viz., contrary predications. Rather, what they are is contrary.

The second kind of opposition is that of contradictories. Two sets of contradictories exist in the diagram above. The first is the opposition between all S is P and some S is not P. The second is the opposition between no S is P and some S is P.In each of these oppositions, one of the predications must be true and the other must be false. If it is true that some coffee is served black, then it cannot be true that no coffee is served black.

The third kind of opposition is the subcontrary. Both of these can be true at the same time. It is possible for some S to be P and for some other S to not be P. The same S cannot both be P and not P, but the group of subjects can be varied. If it is true that some coffee is served black, it can also be true that some coffee is not served black.

The fourth kind of opposition is that of subalternates. The subalternates are true if the universal predication is true, but the universal predication is not necessarily true if the particular is true. However, if the particular is false, then the universal must likewise be false. Thus, if it is false to say that some coffee is served black then it is also false to say that all coffee is served black.