Proclus wrote:

I tend to think that liar sentences are sentences that do not express real propositions.  What would the truth-maker of the proposition even be?

On the other hand, if we're to take the sentence's claim at face value it seems to be a necessary truth that it's false (!), and there are lots of truthmakers for necessary truths.

RomanJoe wrote:

Now paradoxes like the liar's paradox don't refer to any reality. In fact, they're not just false like "the sun revolves around the earth" (which is at least conceivable in some possible word), they're false in all possible worlds, the proposition literally refers to no reality.

I'm not sure this works, the sentence is implicit that we take into account the liar, and refers to itself. The nature of self-reference in the sentence in conjunction with the liar's being is what makes this a paradox.

Last edited by Dennis (5/16/2017 2:23 pm)

I don't think it's an exception to the excluded middle, I do think it's meaningless, I have stated elsewhere that I don't think that everything we (humans) say is translatable into formal logic. 

"This statement is false." 

However, what is the distinguishing trait of this sentence that makes the translation so problematic? I'm still thinking on it. That said, I'm not so sure that we can quickly dismiss the fact that it is not referring to some reality, it is referring to the statement or sentence, wouldn't the question would then be what kind of being do such things have? The argument you've given, could also be taken as a refutation of Truthmaker maximalism (TM, that position which claims that every truth has a truthmaker), so I think that if we want to save TM, we have to go down the line of denying that liar paradox expresses a proposition.

Last edited by Dennis (5/16/2017 3:09 pm)

John West wrote:

A terminological quibble: You can find the idea of truthmaking as far back as Aristotle, but the terms “truthmaker” and “truthmaking” are usually associated with the theory of truth independently developed by Charlie Martin, and Simons, Smith, and Mulligan.*

If we're talking about truthmaking as usually understood, then necessary statements are made true by literally anything—my fridge, your shoes, Edward Feser's nose hair. That, however, doesn't necessarily mean that they refer to anything (e.g. the statement that two plus two is equal to four probably doesn't refer to Ed's nose hair).

Anyway, Joe infers meaninglessness from necessary falsehood. If this inference is right, then by the same argument all necessarily false statements are meaningless. It's, however, probably not the case that “Lewisian possibilia exist”, “God doesn't exist”, and “Platonic objects exist” are meaningless statements.

*Russell had a similar theory, but called truthmakers "verifiers".

Then perhaps I should amend what I said earlier. Something that is meaningless is neither true or false. In order for a proposition to be true or false it has to refer to some reality, be it our own or some other conceivable one. False propositions refer to a conceivable reality that isn't our own--e.g. "the sun revolves around the earth." True propositions refer to our reality--e.g. "the earth revolves around the sun." Meaningless strings of words refer to no reality, making them neither true or false--e.g. "burpuloofy is ihol-ool."

Now Dennis brings up a good point, namely that "This statement is false" is self-referential. It therefore refers to something. Does this mean it refers to some reality? And if it does, is this reality our reality or some conceivable one? If we are to deny that it's a meaningful proposition then, on the view I just summarized, we'll have to say that it refers to no reality. Would this mean we would have to conclude that the statement isn't a reality? What do we mean by reality in the first place?
 

Last edited by RomanJoe (5/16/2017 8:05 pm)