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I have come across the idea of possible worlds in high school and my first year of undergrad studies.

Assuming that the concept of possible worlds or possibility is useful for philosophical analysis, how do we actually establish whether something is possible?

Aside from examining what we see in our actual world, and claiming these things are possible, how can we jump and make the claim that things we have never seen before are possible?

I know some people used conceivability as a guide to possibility, but is this a good one? It seems that there is no way to verify that our process of claiming that world's are possible is correct, as we have very little data to work with (only 1 actual world Vs infinite possible worlds).

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    Good question, approaches include modal intuition, imaginability, conceivability analysis based on what is permitted by a set of laws (logical, physical, etc.), similarity/analogy analysis, etc. SEP has a long article discussing them, Epistemology of Modality. – Conifold Feb 13 '18 at 20:40
  • Very simple: we do not. Actually, being the Multiverse potentially infinite, "everything exists". – Rodrigo Feb 18 '18 at 0:37
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The SEP articles mentioned in the comments outline everything that can be reasonably said on the topic. But they are rather technical, so there is perhaps room for a more intuitive presentation.

The gist of the problem appears to be the coordination of two pairs of opposites, e.g.: un/real and im/possible. Traditionally the first is assumed to be the most general and known while the second is subordinated. It is contradictory to say that the real is impossible and, at least ontologically, it makes little sense to say that it is possible, so both are seen rather as species of the unreal. In this way there is graduated ontology: real, possible, impossible which is actually a genus-species mix. But this is the view most commonly associated with Leibniz who proposed that god gives reality only to the best of possible worlds.

In later times, especially after the discovery of non-euclidean geometries, logic and epistemology acquired a superiority and the pair im/possible came to be accepted as the major one with un/real as species of possibility. As the older view saw the possibility of the real as a tautology, now the unreality of the impossibility is even more obvious (unless we accept miracles).

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1 Something is possible if it is actual. In this sense the actual world is a possible world.

2 By contrast something is also possible if it is not actual but (not 'imaginable' - too psychological a notion and too vague) but maximally consistently describable. If we posit a conjunction of states of affairs, objects, properties, and laws of nature or randomness, and whatever else you want to include in your ontology, of the totality of which a non-self-contradictory set of descriptions can given, then we have a possible world. I would locate the key to possibility, at least in regard to possible worlds, in maximal and non-self-contradictory (i.e. consistent) description.

3 I don't understand what a possible world would be like if its maximal description involved self-contradiction. I do not rule it out entirely but I exclude it until persuaded how such a world would be possible.

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