How to Respond to the Liar Paradox

One form of the infamous Liar Paradox asks us to consider a person uttering the phrase “I am lying right now” and to determine if they are or are not lying. The paradox is supposed to emerge once one notices that if the person is lying then it follows that they are not lying, and if the person is not lying, then it follows that the person is lying.

I believe this form of the paradox is bogus because it trades on the erroneous assumption that to lie one must say something false. Once one realizes the falsity of this assumption, the paradox can be dissolved as follows:

Person: I am lying right now.

Reply: To be lying you would have to be trying to get me to believe something that you do not believe by presenting yourself as though you believed it. Therefore, (a) if you are trying to get me to believe that you are lying and you do not believe that you are lying, then you are lying. Or, (b) if you are trying to get me to believe that you are lying and you do believe that you are lying, then you are not lying but simply confused about what ‘lying’ means. And, finally, (c) if you are not trying to get me to believe that you are lying then you are not lying whether you believe that you are lying or not.

In short, whether one lies or not is purely a matter of motive and not at all a matter of whether the normal meaning of what one says is true or false.

Another version of the Liar Paradox asks us to consider the sentence: “This sentence is false.” (Why is this considered a version of the “Liar Paradox” when it has nothing to do with lying? Probably because it often comes up in connection with the “I am lying” version.) This is thought to be paradoxical because, allegedly, the sentence is true if false, and false if true, and it must either be true or false.

There are a couple problems with this. The first problem has to do with the sentence’s self-referentiality. Now, self-reference is not necessarily problematic. For example, “This sentence has five words” is clearly meaningful and true, as we can see by replacing the indexical phrase “this sentence” with its referent:

“This sentence has five words” has five words.

This is unproblematic because having five words is an intrinsic property of sentences, so we can determine it’s truth value simply by inspecting the properties of the quoted sentence.

But truth and falsity are not intrinsic properties of sentences. A sentence is true if and only if it expresses a true proposition and false if and only if it expresses a false proposition. So even though sentences can be said to be true or false, they can be so only in a secondary sense by virtue of expressing a proposition that bears the property in a primary sense. This point is significant because when we replace the indexical phrase in “This sentence is false” with its referent, we get:

“This sentence is false” is false.

which is equivalent to:

“This sentence is false” expresses a false proposition.

But now we run into the problem that no sentence-type, simply qua sentence-type, expresses anything at all. A sentence-type is a pattern of words that can be used to express a complete thought, but it does not actually express anything until it is so used, that is, until it is tokened by a speaker in a given context. It is the speaker’s intent that gives a sentence-token its meaning, not the bare pattern of words by itself. For example, suppose that by pure chance the waves and wind formed on a beach a pattern in the sand having the form HELLO WORLD. Would that have a meaning? Of course not. Meaning, in the cognitive sense, comes from minds and only from minds. Thus, it does not follow simply from the fact that “This sentence is false” is a grammatically well-formed English sentence that it expresses any proposition at all, must less a false one.

And even if we assume that the sentence does express a proposition, we still need some way of determining what that proposition is. That this cannot be done in the present case the following dialogue is intended to illustrate:

A: “This sentence is false” expresses a false proposition.
B: What proposition?
A: That “this sentence is false” expresses a false proposition.
B: Yes, but what proposition is that?
A: I already told you, that “this sentence is false” expresses a false proposition.
B: No, you haven’t. What exactly does “a false proposition” refer to?
A: To the proposition that “this sentence is false” expresses a false proposition.
B: That’s unenlightening because circular. What you’re saying is that “This sentence is false” expresses the false proposition that “this sentence is false” expresses a false proposition that “This sentence is false” expresses a false proposition that …. The meaning of the proposition can never be pinned down because the analysis continually gets pushed back another step.
A: So?
B: Not every verbal pattern of the sort that could be used to express a proposition actually expresses a proposition. Why should anyone think this one does? That the meaning of this alleged proposition cannot be articulated in a non-circular way shows that the expression has no definite meaning and thus does not express a proposition.

Another problem with this version of the Liar Paradox is the assumption that every sentence must be either true of false. The principle of bivalence – that every proposition is either true or, if not true, false – applies to propositions, not sentences. And there is no good reason to suppose that it can be extended to sentences. For example, suppose an actor on the stage says “Methinks it is like weasel” (a line from Hamlet). He has uttered a sentence, but has he expressed a proposition? I think not. If it did express a proposition it would have to be something like I, Hamlet, think that yonder cloud is shaped like a weasel. But there is and never has been any Hamlet, hence there is no autobiographical ‘I’ to give a definite meaning to the first-person indexical, and there is and never has been any particular cloud to give a definite meaning to “it”. So here we have a sentence that does not actually express any proposition, even though it could, in other contexts, be used to express a proposition.

I conclude, then, that neither of these two forms of the Liar Paradox is particularly problematic. There are other, more complex versions, such as those involving pairs of sentences with first saying of the second that it is true and the second saying of the first that it is false. But I don’t see that any reason to think that these versions will prove any harder to defang provided we (1) maintain a sharp distinction between sentences and propositions as I have indicated, and (2) insist on pinning down the cognitive meaning of alleged propositions instead of resting content with mere verbal formulas.