Literary Inconsistency and Paraconsistent Logic
19 November 2007 – 7:09 am byA while ago Philosophiocal Pontifications posted about dialetheism, the notion that certain contradictions are OK and our logic should be able to handle them. More recently Robert Seddon of The Face of the Moon and I have been thinking about “fictional facts“. I suspect there’s a connection here.
One trouble with fictional narratives is they can be inconsistent; at one moment p, at another ¬p. Robert talks about this in terms of continuity errors and multiple narrators; cases where the text gives us two possible “facts” that are in contradiction and refuses to resolve them.
Very old-fashioned literary criticism thought it was its job to “fix” these inconsistencies, and it’s certainly known even today for editors to suggest changes of this sort. Yet much modern criticism finds such inconsistencies telling and interesting, treating them as valuable because they add to the complexity and hence the richness of the meanings in the work.
Let’s construct a very simple test case. Here’s a complete literary text:
Stuart is a dog. Stuart is a cat. Stuart is not a cat and a dog.
We are inclined to say that at least one of the three sentences that make up the text must be false. There are a few ways of dealing with this interpretatively. Perhaps the narrator is unreliable, or mad. Perhaps “Stuart” isn’t what we think he is; perhaps he’s a metaphor for something else, and “is” here has a weaker meaning than identity. Perhaps the three instances of the word “Stuart” in the sentence don’t all refer to the same thing; there’s more than one Stuart.
But on what grounds are we making such suggestions? On the grounds that the “reality” of this text is similar to our own. Yet the text contains no information to that effect. Why can’t all three statements be “true”, inasmuch as any statement in a work of fiction is “true”? If they can’t then how can we, on the basis of the text alone, determine which of the three sentences is false?
It’s tempting to say that the work asserts both p and ¬p; a contradiction. In classical logic, which is designed for talking about our world, such contradictions are fatal. Assuming a contradiction allows any absurdity to be derived, and not assuming one means no contradiction can be arrived at; this is the very point of having a consistent logical system.
But it seems that, at least for talking about some fictional works, such a system is too strict; we want to allow certain contradictions to exist in the fictional text so that we can explore them in interpretation. This is where paraconsistent or dialethic logic comes in.
Probably the most promising approach to paraconsistency in this context is to take classical propositional logic and make the negation operator non-truth-functional. In classical logic, if p is true then ¬p is automatically false, and vice versa, which is precisely what it means for the not-sign to be truth-functional.
Removing truth-functionality means that p and ¬p just become names for different propositions. The proposition p might be “Stuart is a dog”; then ¬p is “Stuart is not a dog”. In classical logic, if p is true then ¬p must be false, but in this paraconsistent scheme the truth of falsehood of p has no bearing on the truth or falsehood of ¬p. Cases in which both p and ¬p have the same truth value (whether true or false) are known as dialetheias.
This way, of course, lies madness. In all but the most artificial cases, texts do not support a complete independence of p and ¬p for every proposition p. Indeed, contradictions are rare. So it seems that most texts, when treated paraconsistently, behave just like consistent texts treated classically except at certain points. We could claim that a dialetheia is a local property of a text, not a global one, but that the possibility of dialetheias mandates the use of a paraconsistent logic even if no dialetheia is in evidence.