Sunday, January 18, 2009

Liar paradox

I am attracted to accounts of the liar paradox on which "This sentence is false" does not express a proposition. Here is one line of thought in that direction. Roughly speaking, speaker meaning is essential to language. Unless a scribble or a noise has speaker meaning, it is just a scribble or a noise, rather than a sentence, even if it looks just like a sentence. Now, for a sentence to have speaker meaning, the speaker must either understand something by it, or else must be referring the words back to an earlier speaker who meant something by them. But nobody really has any idea what they are saying when they utter the liar "sentence". Hence nobody is saying anything in doing so, and hence the liar "sentence" is not a sentence.


Enigman said...

I like such accounts too. Philosophers always reply, to my assertion that they're senseless, by asserting that such sentences seem to be saying something, that the problem may be that they're saying too much, but clearly not too little. They think that your sentence, for example, clearly says that it's false. I think they don't know what they're saying if they think that. They think it's saying that it's false, whence they ought to think that it's saying that it's true, but they often then say, 'why is that? Is it because all sentences implicitly assert their own truth in some scholastic way?' So I agree with you, they don't really know what they're saying.

Alexander R Pruss said...

I've long had the intuition that the problem with the liar paradox is like one way of looking at problem with the Russell paradox. I might say: "Let S be the set that contains all sets that do not contain themselves." But I have no right to say that, because I haven't shown that there is such a set! Likewise, I cannot say: "Let p be the proposition that says of itself that it is false." For there is no such proposition.

When we say something, we are attempting to express a proposition that fits the words and the speaker's intention. Sometimes we are successful, and sometimes we are not. (Thus, a poet may succeed at expressing propositions that I cannot express.) In "saying" the liar "sentence", we are attempt to express a proposition that says of itself that it is false. But we fail, for there is no such proposition to be expressed.