You are going to get into all sorts of trouble by treating truth as a first-order predicate. — Banno

T(q) ↔ p is the same as “p” is true iff p which is the T-schema which you have previously said is the correct account of truth.

This is a thorny issue... — Pie

I'm not so sure. I suspect it's actually pretty simple, if folk don't confuse themselves. Treat T-sentences as a definition of "...is true" and you won't go far wrong.

For example, beliefs can be true or false, like the belief that "the sky is blue", and their truth value is dependent upon whether the content of the belief is an actual pattern in reality. — Jerry

For me, it's hard not to simplify this into : "the sky is blue" is true if and only if the sky is blue. The temptation is to say more, to explain truth, but it tends to come out as the same tune in another key.

I guess this is just a roundabout way of accepting the correspondence theory of truth, but I think the key idea is that truth isn't a fundamental "thing", like an abstract object that we discover. It simply describes whether our mental models correctly describe reality. — Jerry

I think the deflationary/redundancy view which I endorse is a leaner, cleaner version of correspondence.
Talk of mental models and representation in general seems to want to put two things together side by side, but it seems that only the thing on our side is intelligible. How does 'the sky is blue' match anything ? The language and the world are one, you might say. But it'd make sense to evolve a language like that. (I don't mean that letters or sounds are the same as the world but that meaning is something like the world-for-us, though it's probably safer to just endorse the redundancy theory of truth.)

I'm not so sure. I suspect it's actually pretty simple, if folk don't confuse themselves. Treat T-sentences as a definition of "...is true" and you won't go far wrong. — Banno

:up:

I think we should make it simple in just way (or close enough.)

T(q) ↔ p is the same as “p” is true iff p which is the T-schema which you have previously said is the correct account of truth. — Michael

I'm not sure of that. Your version hides the disquotation in a seperate line. 'q' becomes explicitly the name of a sentence, raising the complex issue of individuating that sentence. Types, tokens, and so on. The quotes make it clear that what is true is an utterance, in a specific circumstance - a quote.

I think we should make it simple in just way (or close enough.) — Pie

That's what this thread might do, for some.

The quotes make it clear that what is true is an utterance, in a specific circumstance - a quote. — Banno

I think the quotes make it clear that what is true is a proposition. Whether or not a proposition is an utterance is open to debate which the rest of my post explains.

That's what this thread might do, for some. — Banno

:up:

I think the quotes make it clear that what is true is a proposition. — Michael

I will go with Davidson and opt for utterance rather than proposition. I understand what an utterance is, not so much a disembodied proposition, floating between "it's raining", "il pluet" and "Sta piovendo"

will go with Davidson and opt for utterance — Banno

My impression was that he used sentences, not utterances. An utterance is the actual sounds or marks used in communication. A sentence is a formal thing. Any number of utterances can convey the same sentence.

OK, p is a sentence. "p" is an utterance.

You're using your own definition, then.

Radical interpretation does not deal in utterances?

Radical interpretation does not deal in utterances? — Banno

I don't think so. Sentences. Tarski used sentences.

Doesn't look right. What is interpreted is a particular utterance, made by a specific speaker, at a given time, in a certain situation. Hence the context that permits triangulation.

Radical interpretation, per the SEP:

"So, for example, when the speaker with whom we are engaged uses a certain sequence of sounds repeatedly in the presence of what we believe to be a rabbit, we can, as a preliminary hypothesis, interpret those sounds as utterances about rabbits or about some particular rabbit. Once we have arrived at a preliminary assignment of meanings for a significant body of utterances, we can test our assignments against further linguistic behaviour on the part of the speaker,".

This is about utterances, yes, but we haven't yet arrived at issues of truth. For that we move on to sentences.

TO get back to the point at hand, do you think that

T(q) ↔ p — Michael

is a T-sentence, as Michale claims?

I think there are important differences. You?

For Tarski, both the quoted and disquoted portions are sentences. The issue of utterances and propositions doesn't come up.

The T-schema is used in other ways, though. In redundancy, we're imagining someone making an assertion, so uttering a sentence. Whether we want to also say they're expressing a proposition by uttering a sentence isn't relevant to the point.

The T-schema has also been used as a rendering of correspondence theory. It just depends on how we want to read it. I gather you're leaning toward correspondence theory.

But do you think

T(q) ↔ p

where

q ≔ the proposition that p — Michael

is the same as

"p" is true ↔ p

And if so, how, and if not, why?

Seems to me the problem stems from treating propositions as individuals.

As is obvious, @Pie wants to know why (the jesting) Pilate didn't wait for an answer to the question "Quid est veritas?" he had posed to Jesus? He was on the right track, Pilate was!

Res, non verba!

Are we in sophist territory? It's baffling, all this.

q ≔ the proposition that p
— Michael
is the same as
"p" is true ↔ p
And if so, how, and if not, why? — Banno

If you're interpreting the t-sentence rule as a rendering of correspondence theory, then yes, the quoted part is a truth bearer, probably a proposition, and the disquoted part is a truth maker.

It just depends on how you want to read it.

Seems to me the problem stems from treating propositions as individuals. — Banno

Why is that problematic?

truth bearer — Tate

Agent Smith notes that down for future reference! Has a religious subtext to it which I find fascinating (re messengers of God).

I don't see what difference it makes. In The Semantic Conception of Truth, Tarski offers this example:

The sentence "snow is white" is true if, and only if, snow is white.

If the sentence "snow is white" is true then the sentence "snow is white" exists. Therefore, given the biconditional, if snow is white then the sentence "snow is white" exists.

I suppose you could amend it to:

If the sentence "snow is white" exists then it is true iff snow is white.

∀q: T(q) ↔ p

Then the conclusion to the argument I gave at the start of this discussion is the tautology:

∀q: ∃x(x=q)

and the disquoted part is a truth maker. — Tate

Not so fast. The sentence in the second part is a truth maker? Or it picks out a truth maker?

Seems to me the problem stems from treating propositions as individuals.
— Banno

Why is that problematic? — Tate

How is it clear? Is such an individual: truth-bearing sentence, truth-making event or relation, or something in between, or (as so often carelessly implied) all at once.

Tarski offers this example:

The sentence "snow is white" is true if, and only if, snow is white. — Michael

Quite. "Sentence" is fine. Drop "proposition". (Everyone!) If not why not?

and the disquoted part is a truth maker.
— Tate

Not so fast. The sentence in the second part is a truth maker? Or it picks out a truth maker? — bongo fury

Yes. :razz: My point was that you need to look for how an author is using the t-sentence rule. Use varies.

Seems to me the problem stems from treating propositions as individuals.
— Banno

Why is that problematic?
— Tate

How is it clear? Is such an individual: truth-bearing sentence, truth-making event, or something in between, or (as so often carelessly insinuated) all at once. — bongo fury

Again, look to use. Propositions are usually the content of uttered sentences, but nothing stops people from using "proposition" to mean pizza.

Tarski offers this example:

The sentence "snow is white" is true if, and only if, snow is white.
— Michael

Quite. "Sentence" is fine. Drop "proposition". If not why not? — bongo fury

Tarski doesn't deal in propositions. It's just sentences from two different languages, one that has a truth predicate and one that doesn't. It's not a definition of truth.

Tarski doesn't deal in propositions. It's just sentences from two different languages, one that has a truth predicate and one that doesn't. It's not a definition of truth. — Tate

He does provide a definition of truth in The Semantic Conception of Truth:

Hence we arrive at a definition of truth and falsehood simply by saying that a sentence is true if it is satisfied by all objects, and false otherwise.

He does provide a definition of truth in The Semantic Conception of Truth:

Hence we arrive at a definition of truth and falsehood simply by saying that a sentence is true if it is satisfied by all objects, and false otherwise. — Michael

I think he eventually admitted that it's not a definition. Since Frege, the standard view is that truth can't be defined. It's too primitive.

"Is truth a property of sentences (which are linguistic entities in some language or other), or is truth a property of propositions (nonlinguistic, abstract and timeless entities)? — Pie

Both, because propositions are in fact a class of sentences.

propositions are in fact a class of sentences. — Olivier5

Sure. But a sentence is already a class: of tokens, or copies. So you don't need another name for the more inclusive class.

Allowing translations into the class won't matter at all if they are parsed and interpreted the same. It's no different to letting symbols stand for the sentence-parts.

If you want a proposition to be a class of differently parsed paraphrases, then, why? And what? Non-linguistic? Abstract? Timeless?

Non-linguistic? Abstract? Timeless? — bongo fury

Meh... Why would propositions be timeless? By definition, someone needs to actually propose a proposition and one can't do that outside of time.

And if a proposition is non-linguistic, what does it say?