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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 ...
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.
This means that even though a future contingent will occur, it may not have done so according to present contingent facts; as such, the truth value of a proposition concerning that future contingent is true, but true in a contingent way. al-Farabi uses the following example; if we argue truly that Zayd will take a trip tomorrow, then he will ...
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) P is a priori iff P is necessary. (b) P is a posteriori iff P is contingent. Hilary Putnam comments on the significance of Kripke's counter-examples: "Since Kant there has been a big split between philosophers who thought that all necessary truths were analytic and philosophers who thought that some necessary truths were synthetic a priori.
A chart of accounts (COA) is a list of financial accounts and reference numbers, grouped into categories, such as assets, liabilities, equity, revenue and expenses, and used for recording transactions in the organization's general ledger. Accounts may be associated with an identifier (account number) and a caption or header and are coded by ...
[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.