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The commonly employed system S5 simply makes all modal truths necessary. For example, if p is possible, then it is "necessary" that p is possible. Also, if p is necessary, then it is necessary that p is necessary. Other systems of modal logic have been formulated, in part because S5 does not describe every kind of modality of interest.
Contingency is one of three basic modes alongside necessity and possibility. In modal logic, a contingent statement stands in the modal realm between what is necessary and what is impossible, never crossing into the territory of either status. Contingent and necessary statements form the complete set of possible statements.
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 ...
But all past truths are necessary truths. Therefore, it is not possible that the battle will be fought. 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.
[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.
Hamilton opines that thought comes in two forms: "necessary" and "contingent" (Hamilton 1860:17). With regards the "necessary" form he defines its study as "logic": "Logic is the science of the necessary forms of thought" (Hamilton 1860:17). To define "necessary" he asserts that it implies the following four "qualities": [12]
Treating logical truths, analytic truths, and necessary truths as equivalent, logical truths can be contrasted with facts (which can also be called contingent claims or synthetic claims). Contingent truths are true in this world, but could have turned out otherwise (in other words, they are false in at least one possible world).
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.