Wolfgang Schwarz

In Defense of the Impossibility Hypothesis

My wrists still don't feel quite fine, in particular after writing such a long piece as this one. So this will probably be the last entry for another couple of days.

I want to defend the Impossibility Hypothesis about Imaginative Resistance. The hypothesis is that when we find ourselves unwilling to accept that some statement explicitly made in a fiction is true in the fiction, this is (always) because what the statement says is in some sense conceptually impossible.

The main positive argument for the Impossibility Hypothesis is that it fits nicely in my preferred general picture of belief and language: By uttering (certain) sentences, people express possible ways things might be. If I believe what people say, I believe that the way things in fact are is one of the ways their sentences express or represent them as being. So the representational content of a sentence selects a region in "logical space", the region containing those possibilities that are compatible with the sentence being true. The same holds for beliefs. The content of my beliefs is (or can be represented by) the region in logical space containing those possibilities that are compatible with what I believe. That region doesn't have precise borders. It is more like a very fuzzy set: Certain possibilities may be definitely inside, others definitely outside, but most are somewhere in between, reflecting my degrees of belief. For example, I am pretty certain, though not entirely certain, that the sun will rise tomorrow. That is, possibilities in which the sun doesn't rise tomorrow belong to my belief space only to a very diminished degree. Or, to change the metaphor, they belong only to very remote parts of my belief space

Entertaining a hypothesis means focussing on those subregions of ones belief space in which the hypothesis is true, without however committing oneself to its truth (that is, without really conditionalizing all ones beliefs on it). For example, in solving a murder case, Hercule Poirot might consider two rather sophisticated hypotheses, hypothesis A and hypothesis B. Hypothesis A is that things were more or less as the butler said they were, whereas hypothesis B involves that the butler lied because things were quite different. After a while, Poirot finds evidence strongly suggesting that hypothesis B is true. So hypothesis A, the butler's story, gets the status of fiction: a detailed and maybe entertaining, but very remote possibility.

Reading fiction is entertaining a hypothesis. That is, accepting the sentences in a novel means hypothetically conditionalizing ones belief space on their representional content. That is, it means focussing on those subregions selected by the content. (Probably not only by the explicit content of the fiction, but also partly by the background beliefs of the author's community, by general rules of the genre, etc.)

If there is no such subregion the fictional sentences are conceptually impossible and we get imaginative resistance.

In defense of this view, I have to explain away alleged cases of (1) imaginative resistance without conceptual impossibility, and (2) conceptual impossibility without imaginative resistance.

(1). Some examples. In the Sherlock Holmes Stories, Watson's war wound is at one time said to be in his arm, and at another time in his leg. In Titanic, (the terrible 1997 movie) one of the people getting on the life boats is wearing a digital watch. In The Matrix, the Oracle takes 4 cookies out of the oven and brings them to the table, but when she offers a cookie to Neo there are 6 cookies on the plate. (I would use more examples from literature if there was something like movie-mistakes.com for literature.)

None of these are impossible. It is perfectly possible that in 1912 some unknown genius had created the first digital watch and took it to the life boat, or that he was handed over the watch from an alien zivilisation. Yet I believe that none of this is true in the Titanic story. In fact, I believe that in this story, nobody is wearing a digital watch. Similarly, there is no magic cookie creation in the Matrix story, and no magic war wound movement in the Holmes story. So I don't believe what is explicitly told in the stories (via the ordinary conventions). So here we have imaginative resistance without impossibility.

I have two replies. One is that the alleged possibilities are not really possibilities after all. Of course the isolated claim that some person wore a digital watch in 1912 is not impossible. But all the possibilities where it is true might be outside the possibilities selected by the (rest of the) Titanic story. So if we hypothetically conditionalize on the Titanic story, the claim becomes impossible.

If this doesn't work, I have a second reply, which is to weaken the Impossibility Hypothesis: We get imaginative resistance not only if a fictional statement is conceptually impossible but also if it is conceptually remote. That is, after hypothetically conditionalizing ones belief system on the fiction, the statement is assigned a very low degree of belief.

Tamar Gendler suggests in "The Puzzle of Imaginative Resistance" (JoP 2000) that we get imaginative resistance when accepting a fictional claim would imply taking a "perspective" on the actual world we don't want to take. There is something true about this, and the Impossibility Hypothesis can explain it. Consider

In killing her baby, Giselda did the right thing; after all, it was a girl.

For those of us who believe that killing babies because of their sex is morally wrong, this statement will provoke imaginative resistance when it occurs in a certain kind of story. Not in any story. I, for one, can perfectly well imagine a story in which the statement is acceptable, for example if in that story Giselda knows that any daughter she had will, when grown up, become an evil terrorist, or suffer unbearably. But if the statement occurs in a story where there is no mention of any such peculiar knowledge, I would resist. The case is then exactly like the cases mentioned above: For the statement to be true would require that certain extraordinary further facts were true in the fiction, of which there is no mention at all in the story.

Accepting the statement (in a normal story) would mean that one doesn't believe that very extraordinary circumstances are required for it to be right to kill a baby because of its sex. And this would mean taking a certain "perspective" on the actual world.

(2). What about cases of alleged impossibilities that we nevertheless accept in fictions?

First, we must be sure to track the right kind of impossibility, that is, conceptual impossibility in the sense explained above. A statement is impossible in this sense if conditionalising on it would result in an empty (or unduly remote) belief space.

This kind of impossibility is considerably stronger than "metaphysical impossibility". Notoriously, even though "water is not H2O" and "Hesperus is not Phosophorus" are metaphysically impossible, the representational content of these sentences is not empty. In other words, there is something you convey by uttering "astronomers were wrong all the time: Hesperus is not Phosophorus". And it makes sense to conditionalize on this information. It is different with conceptual impossibilities. You can't convey much by uttering "philosophers were wrong all the time: there are married bachelors", except perhaps that you are confused. And it doesn't make sense to conditionalize on this information.

Similarly, though much more controversially, the representational content of "Fermat's theorem is false" differs from the representational content of "there are married bachelors". Given sufficient evidence, I would be willing to accept the former, whereas it wouldn't even make sense to think about accepting the latter.

The fact that conceptual possibility is both weaker and more fine-grained than metaphysical possibility poses some difficult problems for the possible worlds account of conceptual possibility (and thereby of representational content). I believe these problems can be solved -- even in the mathematical case --, but even if they couldn't, this would merely show that there is something wrong with the possible worlds account. It won't do to argue against the Impossibility Hypothesis by riding piggyback on these independent problems for the possible worlds account.

Another important feature of conceptual possibility is that it is to a certain degree subjective. Some statements about elms are conceptually possible for me but impossible -- or at least very unlikely -- for an elm expert. Similarly, I once actually believed that there are only finitely many primes, but now I take this to be a very remote possibility. This subjectivity raises some difficult problems for the conceptual possibility account of linguistic meaning, but again I believe that these can be solved, and that at any rate they are irrelevant for the Impossibility Hypothesis.

Now the stage is set. Let's look at the examples. Tamar Gendler mentions impossible stories "where characters travel back in time, where space-ships go faster than the speed of light, where wizards turn straw into gold, and where lonely geniuses prove the continuum hypothesis". It is clear that these impossibilities are not clearly conceptual impossibilities, sometimes they are not even metaphysical, but mereley physical impossibilities.

Later, she discusses more interesting examples. What about Frosty the singing Snowman, or the knave of hearts in Alice in Wonderland? Is it conceptually possible that a snowman sings, and that a playing card talks? Well, it is certainly conceptually very remote. But not as remote as the married bachelors. Recall: The region of possibility selected by a statement is roughly the region of possibilities such that the statement would be true (true-in-English) if it were uttered there. And I can rather easily imagine possible situations in which it would be true (true-in-English) to say "there is a singing snowman". And it is only slightly more difficult to imagine a situation in which it would be true to say "there is a speaking playing card". Whereas I simply can't imagine a situation in which it would be true to say "there are married bachelors".

This has nothing in particular to do with "one-criterion concepts". I also can't imagine a possible situation in which it would be true to say "there is a snowman who sings and behaves like an ordinary human being, who even has a human body and does not consist of snow". I also can't imagine a possible situation in which the story told in Brian Weatherson's A Quixotic Victory is true.

In her paper, Tamar Gendler tells an even stranger story, The Tower of Goldbach, in which it is claimed that 7+5 is not 12, and even that 7+5 both is and is not 12. I must admit that I find this story completely unintelligible. Here is a typical passage:

In one town [the mathematicians] found seven who were righteous. In another, they found five. They tried to bring them together to make twelve, but because twelve was no longer the sum of [5 and 7], they could not.

I, for one, have no idea what bringing together people from different towns has to do with addition. On my understanding, once you've found seven righteous men in one town and 5 in another, and none of the seven is one of the five, you have ipso facto found 12 righteous men. For me, this passage is conceptually impossible, and this means that I can't make any sense of it. My feeling of imaginative resistance is not very strong here because the entire story is full of such passages, so that I can hardly identify anything as being true in the story.

I must admit that I'm slightly worried that Tamar Gendler and Brian Weatherson apparently can make sense of The Tower of Goldbach. This shows that they have a rather different understanding of "12", "5", "7", or "sum" than I have. It also shows that for them, the story is not conceptually impossible.

So do I save the Impossibility Hypothesis by effectively redefining "conceptually impossible" as "provoking imaginative resistance"? Well, sort of. But the trick is not quite that cheap because, I have argued, this fine-grained notion of possibility is precisely the one we need anyway for an adequate theory of representational content. That is, if you believe in conceptual possibility at all (as opposed to metaphysical or physical possibility), you should individuate it in such a way that it saves the Impossibility Hypthesis.