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I have just read Angelika Kratzer's paper "Conditionals". In this paper Kratzer rejects the traditional account of the "if-then" construction in English as a two-place material implication operator, in favor of a new interpretation of "if" as a modal scope modifier.

It seems to me that this account might provide an alternative resolution to Hempel's raven paradox. It appears to me that this paradox arises precisely because of a confusion between quantifiers and material implication: the statement "all ravens are black" is taken to be equivalent to "for each x, if x is a raven, then x is black"; then by the contrapositive to "for each x, if x is not black, then x is not a raven". The paradox is that in this form, observing a green apple becomes evidence for the original claim about ravens.

I think Kratzer's account would have something to say about the first transformation, in which the quantifier is recast as an if-then form which is then interpreted as a material implication.

I am most interested in references to the literature, but I would also be glad to see a summary discussion.

  • It would be good if you could say more of how you think Kratzer's paper bears on the raven's paradox. As I read her, "If p then q" is true in those possible worlds in which all accessible p-worlds are also q-worlds. There is, that I can see, no suggestion that "All ravens are black" should not be analyzed as meaning "If something is a raven then it is black". – Schiphol Jun 29 '12 at 15:22
  • And you have me backwards :) As I wrote above, I don't find any reason to think that Kratzer would object to the treatment of that quantified sentence in terms of conditionals. Letting that pass, if you do interpret it that way, Kratzer's analysis does not seem to help: "If something is a raven, it is black" is true because in all (accessible) possible worlds in which something is a raven, it is black. By the same token, "If something is not black then it's not a raven" is true in K's analysis because in all accessible pos. worlds if something is not black it's not a raven. – Schiphol Jun 29 '12 at 15:38
  • Note that any theory that interprets conditions using one of the strict implications will interpret it as having modal scope, since you can express strict implication using material implication and modalities. – Charles Stewart Nov 8 '12 at 8:46
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After a quick scan of Kratzer's paper, I can't actually see a logical difference between the modal and implicational forms of any of the examples. It seems to me only a different way to feel about the statement if you want to not offend your notions of causality.

As detailed on the Wikipedia page, the raven paradox isn't paradoxical at all (just surprising); in fact, by examining a non-raven you do gain information about whether all ravens are black because you can only verify that statement by checking every extant object and independently assessing both whether it is a raven and whether it is black.

If you recast the raven statement modally as [Always: x is a raven] x is black, then to test the truth of it you still need to check everything, and you end up with the same "paradox" that observing a green apple tells you something (namely, that this green apple part of the universe is not a counter example to the blackness of ravens, in this case because you do not fall into the "is a raven" category). Since you have asserted that you're testing the raven-ness first, the greenness of the apple is irrelevant, but there's no logical reason why you have to test the mode first to find a counterexample; if [condition]: p and p is true for all conditions, you don't need to check whether you're in the right condition to rule this out as a counterexample.

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If it is not black and not a raven then one thing in the universe has shown to be among a diminishing(?) set of things we have experience of which is not of the class of ravens. If it were black and not of the raven class it would still eliminate that item. A ratio of things not raven to raven declines shifting probabilities. Infinities might alter this.

  • What language is this answer written in? It seems to some sort of terse shorthand that's incomprehensible to your readers. – virmaior Apr 4 '14 at 7:44

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