Empty Fictions

Comments on Nathan Wildman's "The Possibility of Empty Fictions"

Nathan Wildman, “The Possibility of Empty Fictions,” The Journal of Aesthetics and Art Criticism, Vol. 77, No. 1 (Winter 2019), pp. 35-42.

Joris Hoefnagel, “Plate 3: Empty Oval" (16th century), courtesy of The National Gallery of Art Open Access collection.

An empty fiction is a fiction in which there are no ‘fictionally true propositions’. That is to say, if we were to ask, ‘What does this fiction include as being true in the fiction?’, the answer would be that it doesn’t put forward anything as being true in the fiction. For any p, neither p nor its negation, -p, is part of the fiction itself. If there are no empty fictions, then every fiction must make some kind of claim of some sort, in such a way that it is at least treated as if true for the purposes of the fiction. Are empty fictions possible? Wildman argues that the matter has some potential pitfalls and traps, but empty fictions are in fact possible.

To do this, he makes a few distinctions. He distinguishes between a fiction’s primary content and its secondary content. The primary content consists of the propositions that are explicitly put forward in the story. Secondary content is further distinguished into imported content, which consists of propositions contributing the fiction while not being explicitly stated because they are brought in from elsewhere, such as background facts that are just assumed, and entailed content, which consists of propositions that are not explicitly stated but that logically follow from what is explicitly stated.

Because of the flexibility of truth, we have to be careful about how we build a case for empty fiction. If you construct a fiction which explicitly says that nothing is true in it, you don’t have an empty fiction, because your fiction is explicitly saying that ‘Nothing in this fiction is true’ is true. That’s a contradictory thing to say in context, but it is not empty. Contradictory fictions are not empty fictions. (In fact, as noted below, in a classical logic they are the opposite, universal fictions.) So one might try a few other things. One thing you might do is suggest that there is a null fiction, that is a fiction with no propositions at all. But the difficulty is to say how one would actually construct a null fiction in this way; we’d have to distinguish something’s being fictional from any content that it might have, and thus we’d already need to know that we can make a fiction without any propositional content.

A further attempt might be made by using zero-length literary works. A zero-length literary work is a literary work that has in itself no words, symbols, or letters suitable for explicit propositions. An example would be Paul Fournel’s Banlieue, “a ‘novel’ that includes title and copyright pages, dedication, table of contents, introduction, footnotes, index, and list of errata, but lacks any body of text” (p. 36). This Oulipian exercise in paratext gives us everything that belongs to a novel except the actual novelistic text. However, zero-length literary works are not automatically empty fictions. Their secondary content may still be quite proposition-rich.

Some accounts of fiction take fiction to be based on prescriptions to imagine, so one might try to think of a fiction that tells us only not to imagine things. But, since the fiction has to be, on such a view, something more than just a bare non-imagining, it seems like this just gets us a contradictory fiction.

This might seem to suggest that empty fictions are impossible, but Wildman thinks there is another way to argue for their possibility. In fictional works, complementation is characterizing something by characterizing something else. For instance, we might learn what somebody is like by learning about someone who is their exact opposite in some way. We can, however, have other rules in play other than mere opposition. These rules can even cross fictional works, for inter-fictional complementation; you can write a work in which the main character is contrasted with Sam Spade. On the basis of this, Wildman considers whether you could have a text whose entire content was constructed by inter-fictional complementation. If you had a zero-length literary work with no sentences, Vacuum, you could construct by inter-fictional complementation another literary work, Plenum, which is prefaced by saying that whatever is not primarily fictionally true in Vacuum is true in itself. If Vacuum has no propositions to be true, Plenum is a universal fiction, in which every proposition is true. Thus, from any universal fiction we can get an empty fiction by inter-fictional complementation.

What kind of fiction could be a universal fiction? If we are assuming classical logic, any fiction with a contradiction. By the logical principle of contradiction explosion, it would then follow that every proposition is part of the fiction’s entailed content. (Contradictions only lead to explosion if we are assuming that from a contradiction everything follows, though; in another logic, a story with a contradiction is not necessarily a universal fiction.) Nathan Wildman and Christian Folde had in a previous paper considered an example, called Ohle’s Amazing Adventure:

One day, Ohle the wonder dog set out on a wander through Explodiberg, a land governed by the principle of explosion (which, as we all know, states that from a contradiction, anything follows). During his adventure, Ohle ate exactly three treats and not exactly three treats (rather,exactly four). Doing so,he brought about the greatest calamity Explodiberg ever saw,since everything followed in his wake.¹

Call this OAA. Then by inter-fictional complementation, we can identify the complementary empty fiction, which can call Comp-OAA. Comp-OAA could itself be constructed by prefacing it or externally indicating that in it nothing is true except what is not true in OAA. Thus Comp-OAA would by, by inter-fictional complementation, an empty fiction.

This is an interesting argument, but there are some complications here which, while not necessarily refuting Wildman’s argument, nonetheless highlight its dependence on background principles. For instance, at one point in considering another argument for empty fictions, Wildman notes that according to some positions, fictions involve a reality principle, which says that everything true in reality is true in a fiction unless the fiction excludes it. This means that all true propositions are found in the imported content unless the primary content and (presumably) the entailed content excludes it. We are not convinced that the reality principle is correct, but let’s assume that it is. Do empty fictions exclude anything? For instance, Comp-OAA is prefaced by a construction-rule, but does Comp-OAA itself exclude anything? It might seem that it does so only if the preface is included in Comp-OAA. But the preface does put forward something as true – that nothing in Comp-OAA is true except what is not true in OAA. This seems to suggest that, if the reality principle is accepted, Comp-OAA is not an empty fiction but a contradictory fiction (if we include the preface) or else is not an empty fiction but includes every proposition that is true in reality (if we don’t include the preface). If the latter ended up being the case, then Comp-OAA would (interestingly) be a fiction in which everything true in the fiction was true in reality. So what we need is a better sense of what it means for a fiction to exclude something, particularly when we are dealing with inter-fictional complementation.

We seem to get the result that Comp-OAA is not an empty fiction but a contradictory one another way, namely, if we consider that the principle of explosion tells us that a contradiction gives us not just all truths but all falsehoods as well. Everything is true in OAA, but everything is also not true. The complementation-rule then seems just to reverse: Everything is not true in Comp-OAA, but everything is also true. Wildman assumes that, since OAA includes every proposition as true that Comp-OAA would include none as true; but if the complementation-rule is “Nothing is true except what is not true in OAA”, one could also interpret this as getting us the result that Comp-OAA has all the same propositions, but just has the truth-values flipped – for every proposition identified as not-true in OAA, there would be a true proposition in Comp-OAA. On this view, OAA and Comp-OAA be equivalent as far as the propositions true in them goes, since in one p is true and p is false and not-p is true and not-p is false, and on the other, p is false and p is true and not-p is false and not-p is true. Everything is true (and not true) in both OAA and Comp-OAA.² (However, as noted in footnote 1, they would not be equivalent in every way.)

Presumably this could be handled by more precision about how exactly complementation-rules work; we get this result by taking each proposition one by one, and we suspect that Wildman gets his results because he is assuming that the complementation-rule somehow takes all the propositions of OAA together. Perhaps “Taking the set of all propositions from OAA as mapped to their truth values, Comp-OAA includes as true only those propositions that are never in that set mapped to ‘true’”?

All of this, of course, is assuming the principle of contradiction explosion, which brings us to another facet of this argument. If we change the logical system from a classical logic to a basic paraconsistent logic in which contradiction implosion rather than contradiction explosion is true (that is, contradictions imply nothing rather than everything), then OAA stops being a universal fiction and Comp-OAA could therefore not be an empty fiction. In such a system, contradictions are the end of the road in reasoning, so it seems that OAA as a contradictory fiction would have no entailed content (if we take the whole story as the unit) or it would only have entailed content that followed directly from the first (and only non-contradictory) sentence (if we take the propositions one by one). There would be no way to get from OAA to an empty fiction by any obvious complementation-rule. It is perhaps not surprising but nonetheless seems strange, or at least notable, that whether or not any fiction would count as an empty fiction would depend on the logical system we were assuming. And it seems that this suggests we should allow there to be fictions that are empty in different ways, and thus allow there to be fictions that are empty in one way and not empty in another.

If this is the case, then many zero-length literary works might as well be counted as empty fictions. We do not have to assume the reality principle (which is in fact quite controversial), and if we assume another principle, zero-length literary works might have no imported content. If Banlieue has no imported content, and if it is taken not to have any primary content, then it’s not at all clear that it has entailed content. This would seem to make it a genuine empty fiction.

There is perhaps another way to get empty fictions. All of Wildman’s definitions are in terms of propositions. But could we have fictions with no propositions at all? Wildman passed over null fictions quite quickly, but perhaps he should not have done so. If they have no propositions, they have no propositions that are true in the fiction. If we accept the reality principle, or something functionally similar, they might have imported content, which would complicate things – but again, we could have a different conception of imported content. A possible candidate for a fiction with no proposition is Lewis Carroll’s “Jabberwocky”, which has the following first stanza:

‘Twas brillig, and the slithy toves
     Did gyre and gimbal in the wabe:
All mimsy were the borogoves,
     And the mome raths outgrabe.

Or in Hassard Dodgson’s Latin translation, “Gaberbocchus”:

Hora aderat briligi. Nunc et Slythia Tova
Plurima gyrabant gymbolitare vabo;
Et Borogovorum mimzebant undique formae,
Momiferique omnes exgrabuere Rathi.

This is arguably fiction, but as every sentence has essential words with no actual meaning, neither the first stanza nor the poem as a whole seems to have any propositions at all in its primary content. Thus it would seem to have no entailed content, if (as would often be assumed) one takes it to be the case that only propositions have entailments.

“Jabberwocky” has sentences but functional words in the sentences lack meaning in a way that seems to suggest that we have no propositions. We could perhaps also have a fiction in which there are no sentences, and thus no propositions from sentences. A possible example is our fictional experiment, The Catastrophic Age, which is a fictional table of contents. One might hold that there were propositions in the entailed content, but for there to be entailed content, one would have to know exactly what the chapter and section headings meant, and there is no way to do this just with chapter and section headings, any one of which might be taken either literally or figuratively. The headings suggest meanings, but they suggest a plurality, and there is nothing to specify which is the ‘correct’ meaning.

We have therefore seen that getting empty fictions can depend on the following things:

1. Whether the primary content of a text has any propositions.

2. The principle of import that governs what ends up in our imported content.

3. The logical system governing the entailed content.

4. How the fiction is constructed (e.g., whether it is constructed by complementation-rules).

Perhaps we should also include a point that has just been assumed from the beginning:

5. The theory of true-in-a-fiction that is being used.

If we were to count as ‘empty fiction’ any fiction that lets us say that it has no true-in-fiction propositions under any combination of its primary content with a principle of import, a logical system, a construction method, and a theory of true-in-a-fiction, then it seems that there would probably be a lot of empty fictions. We would in fact suggest that contradictory fictions, null fictions, indeterminate fictions, zero-length literary works, and more all have a claim to being empty fictions by this way of thinking. That is, it seems very likely that you could get, for each, some variation on (1) through (5) that would make it an empty fiction with respect to that variation. (Indeed, given (5), it might well be the case that every fiction would count as an empty fiction under some variation.) On the other hand, if we restrict any of this (e.g., by assuming the reality principle or classical logic) then this would limit what would count as an empty fiction. All of this is worth considering if you are interested in the logic of fictions and fictional entities, and the logic of fictions and fictional entities has implications for broader logical fields.

1. Nathan Wildman and Christian Folde, “Fiction Unlimited,” The Journal of Aesthetics and Art Criticism, Vol. 75, No. 1 (Winter 2017), p. 76. We hope to talk about universal fictions at some point, but the subject has its own particular quirks, and is if anything more complicated than that of empty fictions.

2. It’s worth pointing out, however, that the distinction between primary and secondary content means that these universal stories are not equivalent to each other in every way — while they all contain all propositions, the propositions are partitioned differently into primary and secondary content. This is a good example of why this topic is of logical interest, such as if we are interested in exploring the possible implications of Trivialism. (Trivialism is the mostly hypothetical philosophical position that takes all statements whatsoever to be true.) Philosophers often assume that all cases where we reach triviality are necessarily equivalent, simply speaking, but we see here that this is not true, if there are differences in how they are organized. That is, it can in fact matter where and how the explosion arises, and we can distinguish cases according to this.