Search results
Results From The WOW.Com Content Network
For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P. (Equivalently, it is impossible to have P without Q , or the falsity of Q ensures the falsity of P .) [ 1 ] Similarly, P is sufficient for Q , because P being true always implies that Q is true, but P not being ...
If a statement is true in all possible worlds, then it is a necessary truth. If a statement happens to be true in our world, but is not true in all possible worlds, then it is a contingent truth. A statement that is true in some possible world (not necessarily our own) is called a possible truth.
So the idea that a statement might ever be false and yet remain an unrealized possibility is entirely reserved to contingent statements alone. While all contingent statements are possible, not all possible statements are contingent. [3] The truth of a contingent statement is consistent with all other truths in a given world, but not necessarily so.
Future contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are contingent: neither necessarily true nor necessarily false. The problem of future contingents seems to have been first discussed by Aristotle in chapter 9 of his On Interpretation ( De Interpretatione ), using the famous ...
A truth is necessary if it is true in all possible worlds. By contrast, if a statement happens to be true in our world, but is false in another world, then it is a contingent truth. A statement that is true in some world (not necessarily our own) is called a possible truth.
[11] The sufficient reason for a necessary truth is that its negation is a contradiction. [4] Leibniz admitted contingent truths, that is, facts in the world that are not necessarily true, but that are nonetheless true. Even these contingent truths, according to Leibniz, can only exist on the basis of sufficient reasons.
Each row of the truth table contains one possible configuration of the input variables (for instance, A=true, B=false), and the result of the operation for those values. A proposition's truth table is a graphical representation of its truth function. The truth function can be more useful for mathematical purposes, although the same information ...
One statement logically implies another when it is logically incompatible with the negation of the other. A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth.