An elementary precept of logic says that where there are two propositions, P and Q, there are four possible "truth values," P~Q, Q~P, P&Q, ~P~Q, where ~ means "not."
Do people ever apply this to pairs of philosophy propositions? For example, has anyone applied it to positive and negative liberty, or to equality of opportunity and equality of condition, or to just process and just outcome? On these topics I can find treatments of the first two truth values but none of the second two.
If this precept of logic is not applied, has anyone set out the reasons?
I'm not entirely sure I
I'm not entirely sure I follow, but perhaps this will be of some use. Whether two propositions really have four possible combinations of truth values depends on the propositions. Non-philosophical examples make the point easier to follow. Suppose P is "Paula is Canadian" and Q is "Quincy is Australian." In this case, the two propositions are logically independent, and all four combinations P&Q, P&~Q, ~P&Q and ~P&~Q represent genuine possibilities. But not all propositions are independent in this way; it depends on their content. P and Q might be contradictories, that is, one might be the denial of the other. (If P means that Paula is Canadian and Q means that she is not Canadian, then we have this situation.) In that case, the only two possibilities are P&~Q and ~P&Q. Or P and Q might be contraries, meaning that they can't both be true though they could both be false. For example: if P is "Paula is over 6 feet tall" and Q is "Paula is under 5 feet tall," then we only have three...
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