A logically possible proposition is one that can be asserted without implying a logical contradiction. This is to say that a proposition is logically possible if there is some coherent way for the world to be, under which the proposition would be true. Thus, "the sky is blue" (and all other actually true propositions) is logically possible: there exists some logically coherent way for the world to be such that it is true, viz., the way that the world actually is. But this "way for the world to be" need not be the way the world actually is; it need only be logically coherent. So, for example, the false proposition the sky is green is also logically possible, so long as we are able (as we indeed seem to be) to conceive of some logically coherent world in which the sky is green. Philosophers generally consider logical possibility to be the broadest sort of subjunctive possibility in modal logic.
Logical possibility should be distinguished from other sorts of subjunctive possibilities. For example, it may be logically possible for the universe's physical laws to be different from what they actually are. If it is, then many things that we would normally consider to be demonstrably impossible can be logically possible: for example, that travel might be possible at speeds faster-than-light or that escape from black holes is not impossible. Many philosophers, then, have held that these scenarios are logically possible but nomologically impossible (impossible under the actual laws of nature).
These propositions are also to be contrasted with logically impossible propositions, i.e., propositions which could not possibly be true under any circumstances in any universe because they are formal contradictions. While it is logically possible for the sky to be green, it is not logically possible for a square to be circular in shape. Some combinations of physical laws are also known to result in contradictions. For instance, if a given universe's physical laws are invariant through time, then the law of conservation of energy holds in that universe. This is a consequence of Noether's theorem, which can be proven mathematically. Thus, a universe whose physical laws do not vary with time and which does not exhibit conservation of energy is not logically possible.
With this understanding of logical possibility in mind, other logical modalities may be defined in terms of it: a proposition is logically necessary if it is not logically possible for it to be false, logically impossible if it is not logically possible for it to be true, and logically contingent if it is logically possible for it to be true and also logically possible for it to be false.
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- Do Modal Claims Imply the Existence of Possible Worlds?, paper criticizing David Lewis' theory of possibility.