Kripke on Unicorns: Some Thoughts

Saul Kripke makes, in passing, a rather surprising claim: Necessarily, unicorns do not exist. The surprising part, of course, is the model operator. Everyone (or almost everyone?!?) will agree that actually unicorns do not exist. But if it is the case that necessarily unicorns do not exist, then it follows (trivially) that unicorns couldn’t have existed. And, at least initially, many find that hard to believe. I do, at any rate.

More specifically, Kripke claims both

  • The Metaphysical Thesis (MT): “no counterfactual situation is properly describable as one in which there would have been unicorns.”[1]


  • The Epistemological Thesis (ET): “an archeological discovery that there were animals with all the features attributed to unicorns in the appropriate myths would not in and of itself constitute proof that there were unicorns.”[2]

Here’s Kripke’s argument for MT:

  1. Unicorns are (members of) a mythical species. (Explicit statement)
  2. If X is a member of a mythical species, then there is no fact of the matter about what the sort of species an X is. (More or less explicit statement)
  3. There is no fact of the matter about what the sort of species a unicorn is. (Modus ponens on 1 and 2)
  4. If there is no act of the matter about what the sort of species a X is, then necessarily it does actually exist. (More or less explicit statement)
  5. Therefore, necessarily unicorns do not exist. (Explicit statement)

A few comments:

  • It’s not perfectly clear to me how generalizable the principle behind premise 2 is supposed to be, but I think we should expect us to get very far. I doubt that Kripke means that for any X such that X is not an actual species, there is no fact of the matter about what the sort of species an X is. That would mean that only the species that had actually exist could exist! What’s important here, I believe, is not just that the thing in question is not actual; what’s important is that the concept that is supposed to pick out a natural kind is so poorly developed that couldn’t distinguish between various possible but highly different way that the thing in question could be. Hence Kripke’s remark that “one cannot say which of these distinct mystical species would have been the unicorns”[3, emphasis in the original].
  • In light of the considerations just above, we might need to revise premise 1: Unicorns are supposed to be members of a mystical species. That’s probably nitpicking though.
  • Kripke’s thinking here puts me in mind of W.V.O. Quine’s possible (but non-existent) man in the doorway in his article “On What There Is” [4]. Don’t get me wrong: Quine and Kripke disagreed a lot – a lot – about modality. But much as Quine’s possible man in the doorway remains too indeterminate (Is he fat? Is he tall?) to allow for identity conditions, so too unicorns remain too indeterminate to count as even possibly existing.
  • There’s another echo of another philosopher here too, one who is a bit closer to Kripke’s peer group. In “It Ain’t Necessarily So,” Hilary Putnam entertains the possibility that cats (an example chosen more or less at random” aren’t necessarily mammals, since the term we use to designate cats would continue to pick these creatures out even if – bizarrely – we later learned they were robots from Mars. Now, cats – unlike unicorns – are actual, and the name “cat,” in Kripke’s idiom, rigidly designates all and only cats because “cat” is causally connected (in ways that can be somewhat difficult to pin down) cats. But unicorns are not actual, so the name “unicorns” can’t be causally connected to unicorns. “Unicorns” doesn’t rigidly designate anything, and, as a result, nothing in any world would count as being a unicorn. Hence, it’s metaphysically necessary that unicorns don’t exist.
  • But if that’s the right story, then I’m left a little puzzled about how any possible but non-actual natural kind name can denote. One can’t be causally connected with things in other possible worlds, so, if rigid designation of names depends on causal interaction, then no name of a possible but not actual species is a rigid designator. And that can’t be right! Let the name “shmonkey” denote a possible but not actual species that looks and acts just like a Capuchin monkey but that is more closely related to rodents than to chimpanzees. It would seem a little bizarre to insist that, necessarily, shmonkies don’t exist, but if that’s true of unicorns, then why isn’t it true of shmonkies as well?

Let’s move on to ET. Here is my take on Kripke’s argument for it:

  1. Names rigidly designate that which they name.
  2. So something, P, counts as proof that N exists only if E has the (superficial) properties of N and E can be connected appropriately to N.
  3. Therefore, the discovery that there once existed some species that has the (superficial) properties of a unicorn (horse-like qualities, say, but with a spiral horn between its eyes) does not count as evidence that unicorns existed unless the discovery could also be tied to the unicorns of mythology.

Again, a few comments on ET:

  • Kripke gets premise 1 for free, I think, since he has the modern progenitor of the idea of a rigid designator.
  • One obvious response is that the term “proof” is ambiguous. It has a strong sense in which if there is proof that P then P is true, and it has a weak sense in which there might be a proof that P even though P is false. Hence, we say things like “She refuted my proof” or “There is a fatal flaw in your proof.” Kripke’s argument works only for the weak sense of “proof,” as far as I can see. But how much do we care about the strong sense of proof when it comes to the existence of mythical creatures? I would be damn interested to know if there was evidence that unicorns exist, but proof (in the strong sense) is probably more than I’d expect. I suppose it’s correct to say that we have proof (in the strong sense) that sabertooth tigers existed. But we could learn that some elaborate hoax has taken place, and that there’s really no such thing. It’s enough for me to know that there’s a lot of evidence. And the discovery of horse-like beings with spiral horns betwixt their eyes looks like that. Nothing that I can see in Kripke’s argument should cause me to back away from this claim, though I certainly take seriously his point that this evidence is far from conclusive.
  • I don’t think that ET is meant to presuppose MT, though I think that if MT is true than ET follows. Here’s how the argument would go:
  1. Necessarily, nothing counts as a proof of a false proposition.
  2. Necessarily, there are no unicorns.
  3. So, necessarily, the proposition that unicorns exist is a false proposition.
  4. Therefore, necessarily, nothing counts as a proof unicorns exist.


[1] Saul Kripke, Naming and Necessity, p. 156.

[2] Ibid., p. 156.

[3] Ibid., p. 157.

[4] W.V.O. Quine, “On What There Is.”

[5] Hilary Putnam, “It Ain’t Necessarily So.”


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