It's not the statement itself you need to deny, but the presupposition. — Srap Tasmaner
Perhaps then it is the combination of mere self-referentiality with a truth claim (which to be coherent requires pointing to something else) that leads to contradiction and/or meaninglessness. — Janus
This sentence is true" is nonsense; it is like saying "This car is true". — Janus
Janus I'm not splitting hairs but I'm not sure that's exactly correct. Saying " this sentence is true" is actually true , I think, because it's a statement about itself. — 3017amen
Socrates: 'What Plato is about to say is false.'
Plato : 'Socrates has just spoken truly.' — 3017amen
"Janus cannot prove this statement to be true." — 3017amen
It basically means that there will always exist certain true statements that cannot be proved to be true. — 3017amen
Which statement and which presupposition? — Banno
(The usual criterion for A being a presupposition of B is if B and its negation both imply A.) — Srap Tasmaner
"(Li) is happy" doesn't cause any such issue. We don't spend hours working out what "This sentence is happy" could possibly mean because sentences aren't the sorts of things which can be happy.
But sentences aren't the sorts of things which can be true either. Beliefs can be true, propositions can be true, mathematical equations can be true...sentences themselves can't. It's like saying "This horse is true", I don't know what it would even mean? — Isaac
The truth predicate applies to sentences (or propositions). It does not apply to any other object. — Kornelius
We often speak this way, but I think what we mean is that the content of a belief is true. And the content of a belief is a proposition — Kornelius
You're right to think along these lines, and indeed Kripke's solution can be understood as a formalisation of that idea. — Banno
This seems to indicate an interesting approach. If the Liar were changed to "This proposition is false" we might ask "which proposition?". There is a sentence there, but is there a proposition? — Janus
Saul Kripke contends that a natural language can in fact contain its own truth predicate without giving rise to contradiction. He showed how to construct one as follows:
Begin with a subset of sentences of a natural language that contains no occurrences of the expression "is true" (or "is false"). So The barn is big is included in the subset, but not " The barn is big is true", nor problematic sentences such as "This sentence is false".
Define truth just for the sentences in that subset.
Then extend the definition of truth to include sentences that predicate truth or falsity of one of the original subset of sentences. So "The barn is big is true" is now included, but not either "This sentence is false" nor "' The barn is big is true' is true".
Next, define truth for all sentences that predicate truth or falsity of a member of the second set. Imagine this process repeated infinitely, so that truth is defined for The barn is big; then for " The barn is big is true"; then for "' The barn is big is true' is true", and so on.
Notice that truth never gets defined for sentences like This sentence is false, since it was not in the original subset and does not predicate truth of any sentence in the original or any subsequent set. In Kripke's terms, these are "ungrounded." Since these sentences are never assigned either truth or falsehood even if the process is carried out infinitely, Kripke's theory implies that some sentences are neither true nor false. This contradicts the Principle of bivalence: every sentence must be either true or false. Since this principle is a key premise in deriving the Liar paradox, the paradox is dissolved.[26]
As has been said - more authoritatively than I put it, the ability to evaluate the truth value of a proposition seems to depend on the nature of the proposition. — Isaac
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.