24. Fake or Not Fake?

The Liar’s Paradox

The Question:

In the times of fake news, one never knows what to believe. Most reports from respectable news outlets are true; some stories, however, disseminated mainly via dubious websites, are fake. But there is (hopefully, by the time you read this book: was) an American president who, faced with overwhelmigly negative coverage, wants to make you believe via Twitter that all news is fake news. Like so many of his declarations, these tweets are also not really thought out.

Well, I for one, at least admit it in the title of my work: This Book Contains Nothing but Lies. But if anything in the book is true, then the title lies. But that means that not everything in the book is untrue. So, does the title correctly reflect the truth? Or does it lie?

The Paradox:

Yes and yes! Or no and no! Or yes and no! Or no and yes!

Here’s the problem: since the President’s own utterances and tweets obviously constitute news, and since he is known for spouting untruths (read: lies) at any occasion, the question must be asked: are his tweets true or false? If all news is fake then his tweets are true. But if his tweets are true then not all news is fake. Hence, his tweets are false. It is confusing…as confusing as his foreign policy. And his interior policy. And his economic policy.

Concerning this book, if the entire text indeed contained nothing but lies, the title would be appropriate. But in that case the book would contain at least one true sentence, namely the title itself. Hence, the title lies. But if the title lies, then – as the title asserts – everything in the book is a lie, hence the title reflects the truth.

Background:

Widely discussed in Ancient Greece, the Liar’s Paradox was also known by scholars in India and in the Islamic world. It was first recorded in the seventh century BCE, if not earlier. The prophet and philosopher Epimenedes is supposed to have stated to an interlocutor that “all Cretans lie.” As a Cretan himself, he must have known what he was talking about. So, since all Cretans lie, he was telling the truth. But if he told the truth, not all Cretans lie.

The poet and grammarian Philetus of Cos (c. 330–c. 270 BCE) is said to have worried so much over the Liar Paradox that he could no longer sleep and eventually died of insomnia. The Roman statesman and orator Cicero (1st centuty BCE) was so frustrated with it that he included it among the inexplicabilia, questions that have no answer. Some philosphers believed that the underlying reason for the paradox was a problem with the Greek and Latin languages themselves.

In the late Middle Ages, the Liar’s Paradox was included by the Oxford cleric and scholar Thomas Bradwardine (c. 1300–1349) among the insolubilia, questions that have no solution.

Dénouement:

Since Epimenedes was a Cretan, since the President’s tweets are part of the news, and since the title is an element of the book, we again have the vexing situations of self-reference. (See chapters /// and ///.)[1]

There are several copouts from the problem like, for instance, that the truth cannot be decided, that there are several levels of ‘true’, that the statement falls into a gap between true and false, that it is not a real statement because it violates some semantic rule. These suggestions do not really satisfy.

A more compelling solution to the paradox goes as follows:[2] whenever a statement is uttered it is implicit that it is true. This does not need to be justified or explicitly stated. Hence, there is no need to precede a statement with “It is true that…”. For example, the statement “Paris is the capital of France” could be enhanced, as in “it is true that Paris is the capital of France.” But one does not need to enhance it since the former clause is implicit in the latter.

Hence, “Epimenedes says all Cretans lie” is, by implication, equivalent to the ‘enhanced’ statement “Epimenedes states the truth and says all Cretans lie”. So, we have “One Cretan states the truth and says all Cretans lie” which, phrased slightly differently, becomes “One Cretan does not lie and all Cretans lie”.

Now it’s obvious: the fact that one Cretan does not lie contradicts the fact that all Cretans lie. Hence, the sentence is self-contradictory and therefore unambiguously false. Given the context – that Epimenedes, the Cretan, is the speaker – the statement is irrational and unintelligible…a paradox!

The president’s tweet “All news is fake” becomes, by implication, “the president tweets that it is true that all news is false.” Since the president’s tweet is news, this becomes “News is true that all news is fake.” As with all contradictory statements, the two mutually exclusive clauses negate each another, hence we have a logical inconsistency which we mistakenly took for a paradox.

And now to the title of this book: “The title states that the book contains nothing but lies” implies “The title states that it is true that the book contains nothing but lies.” Since the title is part of the book, this is equivalent to “part of the book is true and all of the book is lies.” So, we have a contradiction the title is inappropriate and as far as logic is concerned, the case is again clear: the title unambiguously lies. Sorry about that!

Technical supplement:

One caveat about Epimenedes’s utterance: all Cretans lie may mean that they lie from time to time. It does not preclude that on occasion they tell the truth; thus, there would be no paradox. To really express the paradox, Epimeneds should have said that all Cretans always lie.

* * *

The paradox can also be formulated as a dialogue:

Alice: “Bob’s statement is true.”

Bob: “Alice’s statement is not true.”

What are we to make of this? This is not self-reference since each statement refers to the other statement. We have a circularity. But it’s still self-reference, namely self-reference in a chain. Alice and Bob are sometimes referred to as ‘loop liars’.

* * *

It is amazing that only one word is required for ‘telling a lie’, namely ‘lying’, while one needs three words to express ‘telling the truth’. Why is there no ‘truthing’?

[1] Given the President’s preoccupation with his self-image, self-importance, self-obsession, why not also self-reference?

[2] The argument is based on //// Arthur Prior asserts that there is nothing paradoxical about the liar paradox. His claim (which he attributes to Charles Sanders Peirce and John Buridan) is /// Prior, A. (1958). Epimenides the Cretan. Journal of Symbolic Logic, 23(3), 261-266. doi:10.2307/2964285

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