Solutions to the Liar: Automatic Truth Assertion

C.S. Peirce

For a quick description of the Liar, read this.

Some philosophers, including C.S. Peirce, have argued that the Liar is demonstrably false and not true. The argument is based on the premise that all statements implicitly assert their own truth.

At first glance, this seems plausible. If I tell someone, “I did your laundry,” it carries with it an implied “it is true that I did your laundry.” This would seem to hold for all assertions. So, Peirce argues, the Liar is really saying: “It is true that this sentence is false,” which essentially comes down to saying “this sentence is true and false.” This is no longer a paradox, but a plain contradiction, and so false. It is like saying, “I’m a cat owner that doesn’t own a cat.” That’s not a mystery, just a lie. What makes the Liar a paradox is that what it says is, on the surface of it, coherent. If it just asserts a flat-out contradiction, then it poses no problem.

That a proposition automatically asserts its own truth is an interesting notion, and it is not easy to say whether it is accurate or not. Peirce later in life argued that it was incorrect. Luckily, it is not necessary to determine whether it is accurate or not because, even if it is, it does not resolve the Liar.

It is not true that, if a proposition automatically asserts its own truth, then the Liar really says: “It is true that this sentence is false.” In that sentence, “this sentence” refers to that whole sentence. However, in the original Liar, “this sentence” refers only to “This sentence is false.” “This sentence” has changed what it refers to from one sentence to the other. Therefore, the purported truth-asserting version asserts the truth of a different statement than the Liar. This mistake happens because of how slippery “this sentence” can be if you’re not careful with it.

Consider, for example, the obviously true sentence “This sentence has five words.” If this sentence were really saying, “It is true that this sentence has five words,” it would then be false. But that’s a mistake. If the sentence asserts its own truth, then it says, “It is true that the sentence ‘This sentence has five words’ has five words.” This is still true.

Similarly, the accurate truth-asserting version of the Liar is: “It is true that the sentence ‘This sentence is false’ is false.” This is a sentence that says that some other sentence is true. That other sentence says that it itself is false. Neither sentence expresses a flat-out contradiction. Both still yield contradictions when we try to determine their truth-values. This is because, as we would expect, they really say the exact same thing. Automatic truth-assertion doesn’t add anything to the Liar; it certainly doesn’t solve it.

Other posts in the Solutions to the Liar series:

It’s Meaningless (Part 1)

It’s Meaningless (Part 2)

A Quick Note on the “It’s Meaningless” Solution to the Liar Paradox

2 thoughts on “Solutions to the Liar: Automatic Truth Assertion”

  1. It kind of does, William. If you grant that the liar statement does possess meaning, that it does say something (and I’m happy to see from your earlier posts that you do), and that the liar statement says of itself not only that it is false but also that it is true, doesn’t it follow from logical conjunction that the liar is reliably false? I’m sorry, but I fail to see here a clear refute to this fact.

    1. I do agree that the liar is ‘reliably’ false. But then, precisely because it is, it’s also true (since that’s what it’s saying). So my best guess at the moment is that it is a true contradiction (ie, that it just is both true and false). That means accepting dialetheism (the view that there ARE some true contradictions). I have my doubts about that, so it’s not a settled question for me; but I do think it’s a lot more plausible than people tend to assume. I make a brief defense of dialetheism here: http://williamnava.com/dialetheism-true-contradiction-square-circle/

      There is a stronger argument than the one I raised in this post for the conclusion that the liar is ONLY false (and NOT true). It was originally formulated by Thomas Bradwardine and recently explicated by Stephen Read. You can see it here: http://williamnava.com/thomas-bradwardines-solution-liar/ (that article also includes a link to my two-part interview with Read, where he explains it and more about the liar in a lot more detail). I don’t accept it because I don’t accept the principle that Read calls closure (ie, that every sentence ‘says’ everything that logically follows from the supposition that it is true).

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