# The logic of unreliable narrators

In fiction, an unreliable Narrator is a narrator whose credibility is in doubt – in other words, a proper reading of a narrative with an unreliable narrator requires that the audience question the accuracy of the narrator’s representation of the story, and take seriously the idea that what actually happens in the story – what is fictionally true in the narrative – is different from what is being said or shown to them. Unreliable narrators are common in fiction. Notable examples include Agatha Christie’s The Murder of Roger Ackroyd, Ken Kesey’s One Flew Over the Cuckoo’s Nest, Akira Kurosawa’s Rashômon, and Ron Howard’s A Beautiful Mind.

There are all sorts of interesting philosophical questions one might ask about unreliable narrators and how they function as a storytelling device. Here, however, I am going to point out some purely logical features of unreliable narrators.

Presumably, although the full account is no doubt more complex, one of the primary factors that determines whether a narrator is reliable, and to what extent, is the ratio between the number of (fictionally) true claims made by the narrator to the total number of claims made by the author. All else being equal, the higher this ratio, the more reliable the narrator is. Now, consider two stories. The first story – S1 – involves the narrator making n claims for some number n:

S1 = {C1, C2, C3Cn}

And let’s assume that, for some number mn, m of these claims are true. So the relevant ration is m/n. The second story – S2 – is exactly like the first except for the addition of one more claim by the narrator: the claim that he or she is unreliable, which we shall call U:

U = “I am an unreliable narrator”

Hence:

S2 = {C1, C2, C3Cn, U}

Now, there are two possibilities. Either U is true, or U is false. If U is true, then the ratio of truths to falsehoods is (m+1)/(n+1). But, for any positive finite numbers m and n where mn:

(m+1)/(n+1) > m/n

So, although the narrator of S2 might well be unreliable, he or she is more reliable than the narrator of S1 which fails to contain the admission of unreliability U. Note that this also implies that the narrator of S1 must have been unreliable as well.

If U is false, however, then then the ratio of truths to falsehoods is (m)/(n+1). But, for any positive finite numbers m and n where mn:

m/n > (m)/(n+1)

So, although the narrator of S2 might well be reliable, he or she is less reliable than the narrator of S1 which fails to contain the admission of unreliability U.

The latter fact – that a reliable narrator claiming to be unreliable in fact makes them less reliable – is perhaps unsurprising and uninteresting, the fact that an unreliable narrator admitting their unreliability makes them more reliable is more interesting. Before examining this fact further, however, it is worth noting that there is a Truth-teller like phenomenon in the vicinity as well.

Consider a story where the narrator, in addition to narrating the story, also claims to be a reliable narrator (perhaps, along time-honored traditions, by beginning the story with “Everything I am about to tell you is true”). Via computations similar to the above, if the narrator of a story not containing a claim to reliability of this sort is generally reliable then the narrator of a story otherwise identical but supplemented with such a claim to reliability is even more reliable, and if the narrator of a story not containing a claim to reliability of this sort is generally unreliable, then the narrator of a story otherwise identical but supplemented with such a claim is even less reliable.

Now, although it involves fictional truth (i.e. what claims we ought to make-believe to be true when consuming a fiction) rather than actual truth, at this point this puzzle looks like nothing more than a variant of the Liar paradox and the Truth Teller. But there is a secondary puzzle that arises once we have noted the Liar-like behavior of “I am an unreliable narrator.”

Whether or not a narrator is reliable, and more generally, the extent to which a narrator is reliable, is typically not something the author of a work announces at a press conference or prints on the cover of a book or DVD, but is instead something that the reader or viewer of a work has to decipher for him-or-herself from clues included in the story. On the face of it, one piece of evidence that we might think to be definitive in this regard is an admission of unreliability by the narrator him-or-herself. But, as we have seen, such an admission in fact makes the narrator more reliable, rather than less, if the narrator is in fact generally unreliable. In short, the sort of claim that we might, on the face of it, take to be good evidence of the presence of an unreliable narrator turns out to be much less useful than we might have first thought.

On the other hand, the results given above do suggest a sort of informal decision procedure for determining whether or not the narrator of a work is generally reliable or not. When confronted with a story where the evidence seems indeterminate with regard to whether, and to what extent, we should “believe” the narrator, we can just imagine a story that is similar except that the narrator claims to be reliable. If the narrator of the original story was generally reliable, the narrator of this new story will be even more reliable, and if the narrator of the original story was generally unreliable, then the narrator of this new story will be even more unreliable. Presumably, the more pronounced reliability, or unreliability, in the new story will be easier to detect than the original degree of reliability or unreliability in the original story was. If there still isn’t enough evidence to decide, then simply add another claim to reliability on the part of the narrator. And if this isn’t enough, add another one. Presumably at some point the reliability, or unreliability, of the narrator will become so extreme that it will be impossible not to spot, in which case the narrator of the original story will be generally reliable or generally unreliable if and only if the narrator of this new expanded story is (although not, of course, to the same degree).

Now, clearly the recipe just given is absurd – this algorithm for detecting whether or not a narrator is reliable or not just won’t work. But it strikes me as a little bit difficult to say exactly where it has gone wrong.

Featured image: Book by Kaboompics // Karolina, Public Domain via Pexels.

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The logic of unreliable narrators

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