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Philosophers, especially in analytic metaphysics, often talk about the conceivability of things. Here are some examples:

I can conceive a perfect being, therefore, a perfect being is possible.

I can conceive a junk world, therefore, priority monism is false.

I can't conceive a round square, therefore, round squares are impossible.

When can we truly say of something to be conceivable? What are its necessary and sufficient conditions? Is it like imagining? Is it just being consistent with everything we know? How many people have to conceive something in order for it to be conceivable?

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This is an important and difficult question and there isn't a settled 'right answer' about it.

One thing that is clear is that conceivability should be distinguished from "imaginability". I can conceive of what a thousand sided regular polygon would be quite clearly. I know exactly what that phrase would refer to and I could use my geometrical knowledge to prove things about such a figure. However, I can't really clearly imagine what it looks like. It'd look a lot like a circle form some distance, but I can't picture in my mind the difference between the regular 1000-gon and the regular 999-gon or the regular 1001-gon.

Another thing that is clear is the conceivability should be something like being able to understand or grasp some concept. The things that are supposed to be inconceivable are contradictions like "round square." And that much seems right--every contradiction is inconceivable. The harder question is whether every conceivable situation isn't contradictory. Is it conceivable that Goldbach's conjecture is true, or that it is false? It's an arithmetic conjecture, so it is either necessarily true or necessarily false. And if it's necessarily false, then it's a contradiction in terms, like a round square.

People who are skeptical about the use of conceivability as a guide to logical possibility think that examples like the goldbach conjecture show that "conceivability" is just lack of knowledge of the contradiction. Maybe people before modern geometry would have found it "inconceivable" that there be triangles whose interior angles added up to more than 180 degrees. But they were wrong about what is actually logically possible, because we can clearly see now that there are hyperbolic geometries, and so forth.

People who do like to use conceivability as a guide to logical possibility, on the other hand, agree that such cases point to a difficulty for their theory--because it means that people pre-Riemann only thought that something was inconceivable when in fact it wasn't. However, they say, there simply isn't any other alternative. What else is the guide to logical possibility, if not conceivability?

That's roughly the state of play today.

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Awesome answer :). Are there paradigm cases of someone who is a skeptic and of someone who thinks that conceivability is a guide to possibility? I currently read Yablo (1993) and Chalmers (2002), can you recommend others? –  Lukas Apr 18 at 18:11
    
I'm not really up on this literature, but you might check out Roy Sorensen's awesome paper "The Art of the Impossible" in Gendler's anthology on conceivability. –  shane Apr 18 at 18:42

Descartes uses this concievability-property as an argument for God, but Descartes definition isn't of that much help in the issue; he adds perceives "clear and distinct", by the light of his consciousness. Descartes idea of "clear and distinct" influenced many writers after him.

Plato seems to have his own idea (pun intended) of what "concieve" must mean, so your question is sort of related to a context - in my experience, "concievable" can mean a whole lot, dependning on who wrote it.

Sidenote: the 1001 polygon would look like a circle, more so if it is an even polygon. This is actually how circles are generated on a computer monitor/TV - it's just indisguinshable from a perfect circle due to the small scale.

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Thanks for your answer :). I guess my context is contemporary analytic metaphysics (authors like Schaffer, Sider, Tallant, Chalmers, Fine, van Inwagen, and so on) –  Lukas Apr 20 at 11:50

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