The revenge of inconsistent fictions





s⁺_F(p), if p6∈D s⁻_F(p), otherwise.

3.3.4 The revenge of inconsistent fictions

Essentially vs accidentally inconsistent fictions

The above definition of fictional “truth” arguably runs into trouble when it comes to essentially inconsistent fictions. Indeed, it is useful to distinguish between acci-dentally inconsistent fictions and essentially inconsistent fictions. The Adventures

CHAPTER 3. INDIRECT ARGUMENTS AGAINST THE MODAL ACCOUNT

Back totable of content Page 68 of369

of Sherlock Holmes are accidentally inconsistent, in the sense that Conan Doyle ob-viously forgot about Watson’s war wound when he wrote about it in two places.

In some other fictions, authors write inconsistencies on purpose. These essentially inconsistent fictions are usually taken to force one to accept the hot-head strategy.

Priest’s reading test

[Priest1997] is the classic example of such a fiction.¹⁶ Graham Priest tells the story of his visiting Richard Routley-Sylvan’s house soon after he died in 1996 with Nick Griffin who was Routley-Sylvan’s literary executor. In putting some order in the house, Priest finds “Sylvan’s box” which is an impossible object. Here is the first description of the box:

At first, I thought that it must be a trick of the light, but more careful inspection certified that it was no illusion. The box was absolutely empty, but also had something in it.¹⁷

Later on Priest adds:

Looking in the box was something like that: the experience was one of occupied emptiness. [...] The box was really empty and occupied at the same time. The sense of touch confirmed this.¹⁸

Priest then claims that the modeling of such a story requires that we add impossible worlds to the picture. See his fifth moral:

There are, in some undeniable sense, logically impossible situations or worlds. The story describes (or at least, partially describes) one such.¹⁹ In my opinion, Priest’s conclusion is a little hasty. Indeed, it seems that we can handle Sylvan’s box with subvaluation. Take Priest’s own rendering of what is “true”

in the story, before he draws any conclusion:

[...] let us take an old-fashioned comprehension test on the story.

Question 1: In which country did the meeting take place? Answer: Australia.

16There are many other examples. In §12.2, I give many other examples created by real authors, not by a hoot-headed philosopher.

17[Priest1997], p. 575.

18[Priest1997], p. 576.

19[Priest1997], p. 580.

Question 2: Was Richard at the farmhouse? Answer: No.

Question 3: Was the box empty? Answer: Yes and no.

Question 4: How many times did Nick leave the property? Answer: Once.

Question 5: Was the box shot off to the moon at the end of the story? Answer: No.

Other answers are wrong, or in the case of Question 3, at least incom-plete.²⁰

Interestingly,F T gets all the answers right.

Despite this fact, Priest asserts in his fourth moral:

Nor can we simply break the information up into (maybe maximally) consistent chunks and infer from each of these. If we could, we would have to infer that the character were astonished by the fact that the box was empty and/or by the fact that it had a figurine in it, which they most certainly were not.²¹

I simply deny this, for the following reasons:

• The characters were astonished (supertrue, hence fictionally true) because the box was full and empty (subtrue, hence fictionally true).

• The characters were astonished because the box was full (subtrue, but not fictionally true).

• The characters were astonished because the box was empty (subtrue, but not fictionally true).

Inconsistent fictions as double-binds

I think the disagreement with Priest points towards a very interesting phenomenon which I will try to explain.

One very intuitive interpretation of what is happening withF T is that it models inconsistent stories as double-bind phenomena. This view is, I think, very appeal-ing.²² It says that whenever a contradiction is fictionally “true”, one can break up

20[Priest1997], p. 579.

21p. 580.

22Note that double binds happen in many places: in legal systems as well as in computer programs.

In such cases, one might also refrain from accepting true contradictions into the picture without trying something else.

CHAPTER 3. INDIRECT ARGUMENTS AGAINST THE MODAL ACCOUNT

Back totable of content Page 70 of369

the contradiction into two prescriptions to imagine. It fits nicely with the functional account to be discussed for which a proposition p is fictionally “true” iff there is a work of fiction which prescribes to imagine p. As for impossibilities, as Walton remarks:

Can one imagine impossibilities? Not, presumably, if imaginability is a good test for possibility. But then can contradictory or metaphysically impossible propositions be fictional, on our account? I am inclined to think that even contradictions can be imagined in the relevant sense. But our understanding of fictionality is safe even if they cannot be. There can be prescriptions to imagine a contradiction even if doing so is not possible. (A badly drafted law might require one to do something and also to refrain from doing it.) There may also be separate prescriptions to imaginep and to imagine not-p, without a prescription to imagine their conjunction. The set of propositions fictional in a given world might be inconsistent even if no contradiction is fictional.²³

The cool-head can thus use this idea to defend that, in practice, all inconsistent stories imply distinct contradictory injunctions.

This idea is naturally formalised so as to yield a adjunctive logic. A non-adjunctive logic is a logic in which the following rule fails:

A, B `A∧B

F T, because it is has a subvaluationist feature, is non-adjunctive.²⁴

Therefore, in the case of Watson’s wound, indeed,F T predicts that both (9) and (10) are fictionally “true” without (9 ∧ 10) being true. In the case of Sylvan’s box, F T has it that the box is full and it is empty, but it is not fictionally the case that the box is full and empty.

Sylvan’s fempty box

I think Priest is precisely denying that fictional inconcistencies should be modeled as a double-bind phenomenon. But his reading test does not do the trick.

It is arguably possible to think of a fictional inconsistency which resists being deleted and cut into consistent fragments. What if Sylvan’s box was full-and-empty as a single requirement? Using an elegant neologism from [Badura and Berto2019],

23[Walton1990], pp. 65-6.

24A logical consequence relation based on subvaluations is non-adjunctive. See [Hyde 1997] on this.

let us call this “being fempty”. One would argue that Sylvan’s box prescribes imag-ining that Sylvan’s box is fempty.

Fempty is a simple, contradictory predicate. As such, it cannot be deleted.

Indeed, there is no way of extracting a contradiction of the form p ∧ ¬p from

“Fempty(b)”. Moreover, there is no possible world in which “Fempty(b)” is true.

Therefore, truth in this story cannot be modeled by F T.

The argument is indeed valid, although I want to question the truth of the premise which says that the story Sylvan’s box requires the reader to imagine that Sylvan’s box is fempty. If that is the case, then Sylvan’s box is even stranger than it seems.

Indeed, it introduces a new predicate, namely “fempty”, which means the same as

“both full and empty” without being a complex predicate.²⁵ My intuition is that nothing like this is going on in reading Sylvan’s box. This requirement is indeed barely comprehensible, whereas Sylvan’s box is a perfectly comprehensible story, albeit inconsistent. I suggest we should rather think of the inconsistency as a double-bind phenomenon as explained above.

At this point, I think we can appreciate Lewis’s remark that:

[...] where we have an inconsistent fiction, there also we have several consistent fictions that may be extracted from it. (Perhaps not in the very hardest cases—but I think those cases are meant to defy our efforts to figure out what’s true in the story.)²⁶

This shows that one can go much further than expected using the cool-headed attitude towards fictional inconsistencies.