A diagonal argument against the unrestricted non- non-normal world accountnon-normal world account

The argument

I think the discussion around “fempty” can be generalised into what may be called a “diagonal argument”. The basic idea is the following: each time one restricts the non-normal worlds so as to have enough structure to define a consequence relation, one can devise a fiction in which the minimal logical structure is violated. As a result, there is no way of defining a consequence relation of all stories within the unrestricted non-normal framework.

Interestingly, this argument can be found in two places in the philosophical lit-erature. First Routley:

Given that the logic of a fictional world may be any logic, it follows that there is no general uniform logic of fiction. For the intersections of all logics is a null logic, no logic, as each purported logical principle is

31[Berto2017], pp. 1287-8.

cancelled out by a logic where it does not hold good. Consider, to illus-trate, one of the more promising principles for a logic of fiction, formed by introducing a fictional functor O (Woods’ olim operator) read, say,

“it holds in fiction that”, namely the principleO(A∧B)→OA. Spelled out semantically the principle has it that if A∧B holds in the world of an arbitrary workN then so doesA. But consider now a novel where the principles of connexive logic govern, and where hence A∧ ¬A may hold thoughA does not. The world of such a novel repudiatesO(A∧B)→A.

In claiming that there is no uniform logic of fiction, it is not implied that fiction has no logic, far less that it is illogical. In general,each work will have its own internal logic: it is simply that the emerging set of common logical principles will be zero. The semantical structure will reflect this situation.³²

Proudfoot made the same argument quite independently. Her formulation of it is also quite nice, since she explicitly compares the possible-world attempt with the impossible-world attempt:

Both the possible world semanticist and the impossible world seman-ticist are caught by the diversity of fiction. Just as there are more fictions than the possible, so the class of “impossible fictions” includes more cases than the impossible worlds semanticist can deal with. [...] As a striking and simple example, consider a logician’s in which both A and its nega-tion as defined by the familiar truth-tables are true (and true only). Even impossible worlds semanticists agree that there are no worlds in which A and its truth-table negation are true simpliciter (for by the truth-table if A is true then its negation is false).³³

The unrestricted non-normal framework is thus inert. It is arguably possible to express all “possible” fictional truths in this framework, even the die-hard incon-sistencies. But it is impossible to define a consequence relation to model fictional inferences in general. So the distinction between explicit and implicit fictional truths which was at the core of the problem is lost: there is no solution to the problem of fictional “truth”.

32[Routley1979], p. 10-11.

33[Proudfoot2006], p. 31.

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The end of a dialogue

I think this argument settles the matter, although it is not, strictly speaking, a knock-down argument. I think we simply reach an impasse.

In order explain what I mean, consider the following dialogue. On part is the functional theorist (F) who has been raising indirect arguments against the modal account all along. The other is the heroic saviour of the modal account (M) who has been led to defend the unrestricted non-normal account in the face of die-hard inconsistent stories.

F: All right, let’s take non-normal worlds on board. The whole lot of them, even the wild ones. But the natural question is: howdo we get the fictional “truths”?

And the natural answer is: by reading the text.

M: True. But my job was not to give a theory of interpretation. I gave you what you asked for, namely a theory of truth in fiction. Interpretation, I take it, is a completely different problem.

The last move of the modal theorist thus consists in distinguishing between truth and interpretation, when it comes to fiction. I think this is a move for the hopeless.

On the contrary, we will see that the functional account of fictional “truth” artic-ulates interpretation and “truth”, explaining the latter by the former. As I suggested in the cool-head last defence, I think this basic tenet of functionalism can be com-bined with the modeling of fictional worlds as sets of possible worlds. This may suggest that, if functionalism is correct, one could use its notion of (fictional) inter-pretation so as to revitalise non-normal world semantics by providing the missing fiction-relative notion of consequence that it lacks.³⁴

3.5 Conclusions

This section focused on two indirect arguments against the modal account: the argument from incompleteness and inconsistency. They consist in denying that the set of fictional worlds is a subset of the possible worlds of possible-world semantics.

The observation that fictional worlds, if there are such things, are often incomplete and sometimes inconsistent shows that the possible-world framework is too strong for modelling fictional worlds. Hence, it is not adequate for modelling fictional “truth”.

34I imagine that this is what Berto is trying to do, since he calls for our intuitions about fiction at crucial moments of his exposition. Perhaps one can see the functionalist account developed below as a way of fleshing out these important intuitions so that they can, eventually, be built into impossible world semantics.

There are two ways of responding to these indirect arguments. The first way (that of the hot-head) is to extend the set of possible worlds so that some worlds are incomplete and inconsistent. Consequently, the set of fictional worlds is indeed a subset of the worlds of the extended semantic apparatus which contains both possible (or normal) and impossible (or non-normal) worlds. The second way (that of the cool-head) accepts the claim the set of fictional worlds is not a subset of the set of possible worlds, but makes a counterproposal according to which the set of fictional worlds is a subset of the power set of the set of possible worlds. In other words, according to the cool-head, a fictional world is thought of as a set of possible world.

As can be seen, both ways involve a substantial revision of the central tenet of the modal account, according to which fictional worlds are possible worlds. But they are still modal accounts of fictional “truth”, for they both claim that fictional sentences are one kind of modal sentences among others and so they give a theory of fictional “truth” in a general semantic framework for all modal sentences. In this sense, against the functional account, they treat fictional “truth” as a kind of truth.

I showed that the cool-head strategy was interesting to investigate for at least two philosophical reasons. First, it recognises that the two problems are actually two sides of the same coin and tries to provide dual solutions to dual problems. It is thus elegant. Second, the subvaluation strategy, which is one side of the coin, induces a very natural interpretation of what a fictional inconsistency is: it is a double-bind phenomenon. I gave an argument that shows that this idea was more robust than it first seems, based on a distinction between contradictions which are logically complex and contradictions which are logical simples. I explained why I am sceptic about the existence of the second kind of contradiction when it comes to fiction, for it seems to me that the alleged examples of fictions which require to imagine a logically simple contradiction do not keep their promises, the paradigmatic example being Priest’s short story Sylvan’s box. But I acknowledge that if contradictions can be logical simples and if these can appear in fiction, then the cool-head strategy should give way to the hot-head strategy.

Impossible possible worlds are strange entities which one might want to avoid if possible. If accepting non-normal world is like climbing a mountain up to the summit, then I think one can see the cool-head strategy as a base camp one should stay in for a few days in order to get used to the lack of oxygen up there. What I tried to show is that this base camp was higher than one might have guessed from the normal ground.

The last part of this section was thus concerned with the non-normal world ac-count of fictional “truth”, in order to acac-count for die-hard inconsistent stories, if there are such things. The paradigmatic case being Sylvan’s box rewritten so as to

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involve a fempty box. I presented Berto’s non-normal framework for two reasons.

First, he presents the most unrestricted framework, which contains the worlds in which a box can be fempty, without being either full or empty. Second, he claims that this framework is adequate for the modelling of all imaginative acts, soa fortiori he should be able to model acts of fictional imagination.

I showed that this unrestricted non-normal framework meets a diagonal argument, when it comes to defining a notion of logical consequence. This argument was already present in the literature, in the independent works of Routley and Proudfoot. It says that any way of defining a general consequence relation for fictional imagination will meet ad hoc counter-examples in the form of a fiction in which the definition fails.

Sylvan’s box interpreted as involving a fempty box is, for instance, a counterexample to the rule of adjunction, which Berto takes as a good candidate for defining a minimal consequence relation for all imaginative acts. Consequently, the argument shows that non-normal-world semantics is bound to fail to model fictionalinferences if it can model all fictional “truths”.

I suggested that, quite surprisingly, the functional account could come to the rescue here by providing systematic reasons to put constraints of the acts of fictional imaginationviaa proper analysis of what counts as aninferencein a fictional context.

This bridge between functionalism about fictional “truth” and impossible-world se-mantics is rather tentative and cannot be thoroughly discussed until I presented the functional account in detail. However, as will be seen when I discuss the functional account, the formalism is far less mature than that of non-normal world semantics.

So the bridging may be technically difficult if one ever wants to do it. Time will tell.

I think the take-home message of this chapter is that the two indirect arguments are interesting in that they force the possible-world framework to adapt and develop general formal tools which are used for many other purposes than modeling fictional

“truths”. Such adaptation, I tried to show, are also interesting conceptually. I think indirect arguments cast serious doubts on the modal account but they are not knock-down arguments. As such, they should pique the wise philosopher of fiction’s curiosity into considering rival accounts. Direct arguments against the modal account are following and they will, hopefully, end up convincing even the obtuse modally-minded philosopher of fiction.

Direct arguments against the