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There are several arguments in metaphysics which are based on "conceivability":

In each of these arguments, the starting point is the conceivability of a entity or property, and then a step is made from conceivability to possibility.

What I don't understand is the following: It is intuitive in several fields of inquiry that conceivability doesn't entail possibility in any way. So why is that step valid in the above examples? One could never build physical or metaphysical statements on the premise that faster than light speed is conceivable or that dragons exist.

My question: From a formal logic, what is exactly the difference between "XYZ water substitute is conceivable, therefore XYZ is possible" or "A difference between mental states and physical states is conceivable therefore Mental states are not the same as physical states" vs "Faster than light speed is conceivable therefore faster than light speed is possible" or "Fire regurgitating reptiles are conceivable therefore fire regurgitating reptiles are possible"? What is the logical principle behind the validity of the first two arguments but not the second two?

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  • In the realm of concepts conceivability does actually produce possibility in the sense that as soon as it is conceivable without contradiction, it is possible. In the realm of nature possibility is defined by nature itself. Every other position is some crude constructivism or something like this. The interesting part is therefore what this tells us about the ontology implicit in the positions you mentioned.
    – Philip Klöcking ♦
    Commented Dec 14, 2015 at 20:54
  • @Philip Klöcking What is "conceivable without contradiction"? Contradiction, if there is any, is discovered by subsequent reflection, sometimes very long one, and who is to say that it was long enough to be sure that there is no contradiction. And why exclude contradictions? We conceive of round squares and time travel enough to reason about them, we conceive of (what turns out to be) a contradiction at the start of every reductio, and who is to say that it won't turn out the same for set theory or Peano arithmetic? If the latter are "conceptually possible" so are the former.
    – Conifold
    Commented Dec 14, 2015 at 21:16
  • @Conifold I just used the classical thought of Aristotle here, it is logic ;)
    – Philip Klöcking ♦
    Commented Dec 14, 2015 at 21:22
  • I would answer, but it would come out as a variant of this old answer philosophy.stackexchange.com/a/36300/9166 Fictional representability lies between conceivability and possibility. So you can sneak up on possibility by starting there and adding structure.
    – user9166
    Commented Jun 20, 2017 at 17:23
  • It's worth noting the VERY different meanings of "possible". You use 'possible' to mean, that it is physically possible as a matter of fact, whereas you should use possible to mean 'We haven't yet ruled it out.' By that definition everything is possible, whether you conceive of it or not. I.e. I can conceive of FTL travel therefore it is possible.' vs 'I can conceive of FTL Travel therefore its possibility is a possibility.' Those arguments segue from one meaning to the other using careful sleight of hand.
    – JeffUK
    Commented Oct 6, 2017 at 11:04

2 Answers 2

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Conceivability and possibility arguments became fashionable after Kripke made modal logic respectable by providing semantics for it in terms of possible worlds. However, to make it applicable to anything real one needs a way to decide what is possible. This gave rise to "imaginability" and "conceivability" as "guides" to possibility. The game is to argue that in some circumstances our sense of possibility is refined enough so that what we can imagine or conceive turns out to be possible. This usually concerns the traditional epistemic possibility. But in counterfactual reasoning we often "restrain" our imagination to what Kripke calls "metaphysical possibility" with closer ties to the actual world, so Nixon could possibly lose the 1968 election, but could not possibly be an alien.

As for your examples, generally speaking there is no difference, the move from conceivability to possibility is either accepted or not accepted, and depending on that all four will be valid or invalid. Swinburne does think that Kripke's mind-body dualism argument can succeed even if one generally rejects this move however, because imagination is usually mistaken about issues we have no direct acquaintance with, and our mind is an exception to that, see SEP.

But modal arguments that end with a mere possibility of something are not very interesting. Under different physical laws faster than light travel is possible. Perhaps it is even "metaphysically" possible for a mind to be disembodied. But so what? It is when possibility is used as a premise to draw conclusions about the actual that they show real bite, e.g. that mind and body are separate entities because they are possibly so because we can imagine them so. And as van Inwagen points out thereby lies the problem:

"I know of no case in which a possibility argument has changed any philosopher's mind about anything. No one (I think) would now dispute the logical validity... but a philosopher who rejects the conclusion of any of them will simply - I know of no exceptions to this generalization - reject (or at least refuse to accept) the crucial modal premise of the argument that has the unwelcome conclusion... it is always possible to replace the crucial modal premise of a possibility argument with the denial of its conclusion and to replace its conclusion with the denial of its crucial modal premise. The resulting argument will, of course, be valid if the original argument was valid, and those who reject the conclusion of the original argument will invariably claim to find the resulting "contrapositive" argument at least as plausible as the original argument".

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  • Great answer. Deliciously pragmatic. To be fussy, do our current physical laws not allow for faster than light travel. I seem to recall reading something about "tachyons" - theoretical particles permanently in a state of superlight speed travel. Maybe I misread it.
    – nwr
    Commented Dec 14, 2015 at 22:40
  • @Nick R I forgot about them :) But Tipler-Llewellyn write that tachyons "would present relativity with serious... problems of infinite creation energies and causality paradoxes", so I guess they are out of luck. en.wikipedia.org/wiki/Tachyon#cite_note-Randall-3
    – Conifold
    Commented Dec 15, 2015 at 0:59
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    Conceivability/Possibility arguments are much older than Kripke. They're present in Descartes, Locke, Hume, and most of the modern philosophers and something like the principle seems to be invoked occasionally even in medieval arguments. Also, imaginability isn't conceivability. The reason is that imagination involves something like being able to form a mental picture of the issue at question, whereas conceivability is just the ability to grasp that the concepts in question aren't contradictory. I can clearly conceive that a 999-gon != a 1000-gon, but I can't picture the difference.
    – user5172
    Commented Dec 15, 2015 at 3:43
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    That said, I actually am on Van Inwagen's side here. Conceivability/Possiblity arguments don't seem to me to be very good evidence of any substantive metaphysical theses.
    – user5172
    Commented Dec 15, 2015 at 3:46
  • @shane Modal arguments go even further back, Avicenna's Floating Man is the earliest version of the modal argument for dualism, and Molina and Suarez had possible worlds even before Leibniz. They went out of fashion after Kant however, along with rational intuition, even when Lewis, Carnap, etc. developed modal logic. Until Kripke. But what is a mental picture of a disembodied mind or "how you feel"?
    – Conifold
    Commented Dec 15, 2015 at 19:23
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The answer is that there are different notions of possibility. Conceivability only entails the very weakest kind, which is logical possibility.

To introduce the idea of different kinds of possibility, consider the difference between what is humanly possibly and what is technologically possible. It is not possible for a human, by simply moving their limbs, to travel 100 miles per hour. But given some automobile technology, this becomes possible. In other words, traveling a hundred miles an hour is prohibited by the limitations of the stronger sense of what is "humanly possible," but permitted by the weaker sense of what is "possible with the aid of technology."

The kind of possibility which is supposed to be guaranteed by conceivability is mere logical possibility. This is the weakest kind of possibility of all, because it says that something isn't prohibited by the laws of logic. So, the mere fact that something is conceivable just means it isn't prohibited by the laws of logic, although it could still be prohibited, by the laws of physics, say.

Is this weak form of possibility at all useful? It turns out that it is. Identity, for instance, seems to be a necessary relation, which means that if two things are identical, they have to be identical. Which means that if it is logically possible for one to exist without the other, then they must be distinct. If that's right, then all we need to do to show that A != B is that one can conceive of A existing without B existing.

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    Conceivability does not entail even that. Time travel is logically impossible, but Star Trek demonstrates just how conceivable it is.
    – Conifold
    Commented Dec 14, 2015 at 21:20
  • Definitely agree with the point about different kinds of possibility. This is often overlooked: when people say something is possible we must always ask what kind of possibility is in view. As a minimum there is logical possibility (desn't entail a contradiction), physical possibility (doesn't violate known laws of nature), actual possibility (physically possible plus agrees with a set of boundary conditions that describes our world at some point in time), epistemically possible (consistent with what I know to be true) and this more mysterious metaphysical possibility that Kripke is fond of.
    – Bumble
    Commented Dec 15, 2015 at 0:32
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    @Conifold Why think time travel is logically impossible?
    – user5172
    Commented Dec 15, 2015 at 3:38
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    Nobody who thinks conceivability entail possibility would agree that Pythagoras had managed to conceive of the square root of 2 being rational. Chalmers goes to great lengths trying to make this clear. Further, there are lots of responses to the grandfather paradox by people who believe in backwards time travel in the literature as well. Further, your position has the difficulty that you seem to require something like the conceivability/possibility principle yourself---you are arguing that if I travelled back in time I could kill my grandfather because we could conceive of my doing so, no?
    – user5172
    Commented Dec 16, 2015 at 0:50
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    @Conifold What do you think about Chalmer's account of ideal positive conceivability? His account of this kind of conceivability is supposed to rule out precisely the sort of things you're worried about. ("Does Conceivability Entail Possibility" in Conceivability and Possibility, OUP 2002). Do you have a substantive criticism of him to make?
    – user5172
    Commented Dec 16, 2015 at 18:46

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