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A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic.
In the most common interpretation of modal logic, one considers "logically possible worlds". 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.
The term goes back to Leibniz's theory of possible worlds, [2] used to analyse necessity, possibility, and similar modal notions.In short, the actual world is regarded as merely one among an infinite set of logically possible worlds, some "nearer" to the actual world and some more remote.
Under multimodal logic, e.g., "X is possibly (in epistemic modality, per one's data) necessary (in alethic modality)," it no longer follows that X being necessary in at least one epistemically possible world means it is necessary in all epistemically possible worlds. This aligns with the intuition that proposing a certain necessary entity does ...
In these approaches, modal expressions such as must and can are analyzed as quantifiers over a set of possible worlds. In classical modal logic, this set is identified as the set of worlds accessible from the world of evaluation. Since the seminal work of Angelika Kratzer, formal semanticists have adopted a more finely grained notion of this ...
In deontic modal logic, one can say that iff is a morally ideal world given the moral standards of . In application of modal logic to computer science, the so-called possible worlds can be understood as representing possible states and the accessibility relation can be understood as a program.
In modal logic, a logical proposition is possible if it is true in some possible world. The universe of "possible worlds" depends upon the axioms and rules of the logical system in which one is working, but given some logical system, any logically consistent collection of statements is a possible world.
Given the existence of a Godlike object in one world, proven above, we may conclude that there is a Godlike object in every possible world, as required (theorem 4). Besides axiom 1-5 and definition 1–3, a few other axioms from modal logic [ clarification needed ] were tacitly used in the proof.