You've also got the weirdness that comes from convention T working for factual, declarative language and using it to, generically, set out the meaning of non-factual, non-declarative language through how the sentence somehow 'pictures' the relevant state of affairs. EG, like you can elucidate the speech act of flipping someone off through ""fdrake flipped someone off" is true if and only if fdrake flipped someone off". — fdrake

Just a side note, but Convention T and the T schema are different things.

Convention T. A formally correct definition of the symbol 'Tr', formulated in the metalanguage, will be called an adequate definition of truth if it has the following consequences:

1. all sentences which are obtained from the expression 'x E Tr if and only if p' by substituting for the symbol 'x' a structural-descriptive name of any sentence of the language in question and for the symbol 'p' the expression which forms the translation of this sentence into the metalanguage;
2. the sentence 'for any x, if x E Tr then x E S'.

So Convention T is the claim that an adequate definition of "true" will entail the T-schema for all sentences.

And, as I've mention before, this highlights the fact that Tarski didn't offer the T-schema as a definition of truth, but as a consequence of a correct definition. As I mentioned here, we still need an actual definition of "true".

In On the Concept of Truth in Formal Languages he says:

In § 1 colloquial Ianguage is the object of our investigations. The results are entirely negative. With respect to this language not only does the definition of truth seem to be impossible, but even the consistent use of this concept in conformity with the laws of logic.

...

If these observations are correct, then the very possibility of a consistent use of the expression 'true sentence' which is in harmony with the laws of logic and the spirit of everyday language seems to be very questionable, and consequently the same doubt attaches to the possibility of constructing a correct definition of this expression.

...

For the reasons given in the preceding section I now abandon the attempt to solve our problem for the language of everyday life and restrict myself henceforth entirely to formalized languages.

The object language is a formalized language, specifically the calculus of classes in his example.

1. "p" is X iff p

Does (1) tell us the meaning of "X"? If not then the T-schema doesn't tell us the meaning of "true". It sets out the condition under which "p" is true, but nothing more.

This, perhaps, is the point @Sam26 makes when he says that the T-schema is irrelevant?

Trump team's filing

Movant also agrees that it would be appropriate for the special master to possess a Top Secret/SCI security clearance.

So they accept that these documents haven't been declassified.

I think sometimes we expect more from certain concepts than they give us, or we over analyze certain concepts in search of a some phantom that will answer our intellectual itch. Philosophers have a tendency to take concepts out of their natural habitat, and place them in an unnatural one. — Sam26

I think this is one of the things that Wittgenstein got right in the Philosophical Investigations. I'm not entirely convinced that meaning is as simple as use, but at the very least I think it's a good approach to dissolve some of the problems that philosophers effectively invent by injecting undue significance into a word (like "truth").

Sure, although I don't understand the relevance of this?

And yet, "It's fuzzy" isn't really truth apt until you know the context. At that point, you have an abstract object on your hands. — Tate

What abstract object? All I see there is a sentence with no explicit referent.

Sentences are not favored as truthbearers outside artificial systems. Propositions work better for that purpose, although they're abstract objects. There's no 'aboutness' to a proposition. It's the content of an uttered sentence, which can take many forms: usually speech or writing.

How would you say a proposition corresponds to a truthmaker? Where do we look to see this relation? — Tate

I think you're making things far too complicated. We use speech and writing to talk about/describe the world. If there's nothing mysterious about this then there's nothing mysterious about correspondence.

I just meant we don't have to get our boxers in a bunch over the status of truthbearers, the content of truthmakers, and the mysterious correspondence relation that's supposed to hold between them. — Tate

Is there something mysterious about correspondence?

We have a sentence "the cat is on the mat", we have the cat on the mat, and we say that the former is about or describes the latter. Is that mysterious? I don't really think so. So why would it be mysterious to say that the former corresponds to the latter?

In addition to my reply to Tate above, counterfactuals also imply, right up front, something that is the case, and try to show how that matters, in this world, by imagining that it's not. — Srap Tasmaner

I'm a bit confused. I just don't quite see the connection between "if Hitler had not committed suicide then he would have been executed by the Allies" being true (assuming for the sake of argument that it is) and the truth being "about our world, about where we live, and is thereby also about us, every time", as you say.

It seems to me that the counterfactual says something about some other possible world.

Although if you want to say that counterfactuals like the above are about our world (somehow) then I'm not entirely sure what significance there is in saying that the truth is "about our world". What would it mean for the truth to not be about our world? Are you just saying that "is true" means "is about our world"?

If legal action against ex-presidents becomes a "thing", we are entering a new age of tyranny. — Merkwurdichliebe

Prosecuting people for their crimes is tyranny?

I was thinking about how truth has to be about our world, about where we live, and is thereby also about us, every time, whether it seems to be or not, because every truth says something about what kind of world we live in and that says something about us as its residents, as part of it. — Srap Tasmaner

What about counterfactuals? Are they false (or not truth-apt)?

Proper names behave differently to common nouns.

As another example, assume that you believe that Trump is the President. If you were to claim that the President lives in Mar-a-Lago then you would be wrong because Joe Biden doesn't live in Mar-a-Lago. Regardless of who you believe is the President, the term "the President" refers to Joe Biden.

Yes.

What is a proper name if not a word that means a particular thing? — hypericin

It refers to a particular thing, but whether or not it means something is a contested subject. See the SEP article on names:

As well as having a range of entities to which it applies, the common noun “bachelor” has a meaning; it means man who has never been married. What about names? “Socrates” certainly applies to things. It applies, most obviously, to the founder of Western philosophy. Understood as a generic name (see Section 1), “Socrates” applies to several individuals: to a first approximation, all those who are called “Socrates”. But does “Socrates” also possess a meaning?

Some names have meanings in a sense. I have heard “Merlot” used to summon a child, and once knew of a married couple whose respective names were “Sunshine” and “Moonlight”. These names, we would say, have meanings. “Moonlight”, for instance, means light from the Moon. Something similar goes on when we say that “Theodore” means gift of god, or interpret a Mohawk name as a verb phrase. But this sense of meaning turns out not to be the one we are after.

Consider that for “bachelor” the meaning—man who has never been married—is also what determines the noun’s range of application. When the noun “bachelor” applies to someone, it’s because they are a man who has never been married. And when it fails to apply to someone, it’s because they are not. By contrast, the kind of meaning just canvassed for the names “Merlot” or “Moonlight” places no direct constraint on what they apply to. One may be named “Merlot”, and so fall within the name’s range of application, no matter what relationship one bears to the wine grape variety, Merlot (Mill 1843: 34). Moreover, one’s particular relationship to the grape is not the reason the name applies.

In this long tail of the article on semantics, we will confine ourselves to the question of whether names have a meaning in the sense in which “bachelor” does. Do they have a meaning that determines, or at least restricts, their extension (i.e., either range of application or reference)?

---

The same example can be made without using a proper name. Suppose all the world's water was suddenly replaced with twin water. Until I learned of this replacement, I would still mean water when I said "water". Only when I learned would I mean twin water. While still acknowledging that the people who were naïve to the change still mean water. — hypericin

And in such a scenario if you were to say "this is a glass of water" you would be wrong because it isn't a glass of water, it's a glass of twin-water. The extension of the word "water" isn't just whatever you claim to be water; it's whatever satisfies the intension of the word.

Imagine you were killed and replaced by an evil doppelganger. Your friend George, unaware of this, says "Hi Michael". George doesn't mean the doppelganger, he means to greet Good Michael. Only for those who learned of substitution would "Michael" mean the doppelganger. — hypericin

That's a proper name. "Michael" doesn't really mean anything¹.

¹ Unless you want to address the Hebrew etymology, in which case it means "who is like God?"

Nonetheless, when earthlings and twin earthlings say "water", they mean the exact same thing, for them. — hypericin

By this you mean that the subjects have the same psychological state? The point of Putnam's argument is to show that:

a) the subjects have the same psychological state, and
b) the word "water" means different things (both in the sense of intension and extension, as explained above) in each world

So therefore the subjects' psychological states have nothing to do with the meaning of the word "water", hence his conclusion "meanings just ain't in the head".

In other words, there's no such thing as what I mean by the word "water", there is only what the word "water" means.

Fine, but that has nothing to do with what I was saying so I don't understand why you're bringing it up as a response to my comment.

And I don't understand how Davidson's comment has anything to do with me making a distinction between these two claims:

1. "p" is true iff p
2. "'p' is true" means "p"

So could you actually clarify what it is you are trying to say? Are you saying that, according to Davidson, (1) and (2) are equivalent?

So what are you doing here? — Banno

Check the rest of the comment. You may need to refresh your page as I made some substantial edits about half an hour ago.

The main point is that, prima facie, these are different claims:

1. X is Y iff Z
2. "X is Y" means "Z"

So, prima facie, these are different claims:

3. "p" is true iff p
4. "'p' is true" means "p"

And, as my argument from that original comment shows, (3) has possibly undesirable implications – implications which may not follow from (4) – hence the importance of distinguishing (3) and (4).

1. "the cat is on the mat" is a true sentence written in English iff the cat is on the mat
2. "'the cat is on the mat' is a true sentence written in English" means "the cat is on the mat"

These mean different things. And (1) is true but (2) is false.

Now consider:

3. "the cat is on the mat" is a true sentence iff the cat is on the mat
4. "'the cat is on the mat' is a true sentence" means "the cat is on the mat"

If (3) and (4) also mean different things, with presumably (3) being true and (4) being false, then what of these two?

5. "the cat is on the mat" is a true sentence
6. "the cat is on the mat" is true

Do (5) and (6) mean the same thing? If they do, and if (3) and (4) mean different things, then (7) and (8) mean different things:

7. "the cat is on the mat" is true iff the cat is on the mat
8. "'the cat is on the mat' is true" means "the cat is on the mat"

And I don't understand how your question is related to what I was saying.

I don't understand what that question has to do with the point I'm making. The point I am making is that if for all p, the proposition that p is true iff p, then for all p, the proposition that p exists.

Q(a) already assumes that a exists, so of course it follows - from the definition of ∃x. — Banno

Then the argument is valid. From the premise ∀p: T(q) ↔ p it follows that ∀p: ∃x(x=q). For all p, the proposition that p exists.

And can you remind my why we started on this argument? — Banno

We didn't. This argument was a response to Pie's OP where I wanted to draw a distinction between these two related claims:

1. "p" is true iff p
2. "'p' is true" means "p"

The former has a possibly problematic entailment as my argument shows.

But as I said to Srap, the simple resolution is to specify that the T-schema is saying ∀q: T(q) ↔ p, i.e. for all propositions that p, the proposition that p is true iff p. The conclusion is then the truism that ∀q: ∃x(x=q), i.e. for all propositions that p, the proposition that p exists.

Just that. The argument is ill-formed. — Banno

Did you bother even reading the rest of what was said?

This way you can formalize the sentence "if the cat is on the mat then that cat exists" as

Q(a)→∃x(x=a)

where a is that cat, and Q(y) means that "y is on the mat".

It's not ill-formed.

And, to use ordinary English language, are you saying that the below is false?

If the cat is on the mat then that cat exists

Again, this is ill-formed, mixing predicate and propositional terms with abandon. — Banno

I asked a related question elsewhere and got this as the answer by someone more knowledgeable than me:

This way you can formalize the sentence "if the cat is on the mat then that cat exists" as

Q(a)→∃x(x=a)

where a is that cat, and Q(y) means that "y is on the mat".

But if you prefer, perhaps address the English language translation:

1. for all p, the proposition that p is true if and only if p
2. for all p, if the proposition that p is true then the proposition that p exists
3. for all p, if p then the proposition that p exists (from 1 and 2)
4. for all p, the proposition that p is false if and only if not p (from 1)
5. for all p, if the proposition that p is false then the proposition that p exists
6. for all p, if not p then the proposition that p exists (from 4 and 5)
7. for all p, the proposition that p exists (from 3 and 6)

Are you saying that 2 and 6 are false?

But you can't get to "q exists". That'd be an instance of the existential fallacy. That a set has a particular attribute does not imply that the set has members.

The more precise form of my argument takes as a premise ∀p: T(q) ↔ p and so concludes ∀p: ∃x(x=q). It doesn't conclude ∃p: ∃x(x=q), and so there is no existential fallacy.

The relevant parts are these:

(II) That the meaning of a term (in the sense of "intension") determines its extension (in the sense that sameness of intension entails sameness of extension).

...

Let A and B be any two terms which differ in extension. By assumption (II) they must differ in meaning (in the sense of "intension").

Given that "water" on Earth and "water" on Twin Earth have a different extension (i.e. refer to different things), and given that two words with the same intension have the same extension, it then follows that "water" on Earth and "water" on Twin Earth have a different intension (i.e. mean different things).

So he's not conflating meaning and reference, rather pointing out that if they have a different referent then they have a different meaning. Two words that mean the same thing don't refer to different things.

That doesn’t make it gibberish, it makes it trivial, much like p → p.

The pertinent point is that given the premise ∀p: T(q) ↔ p, the conclusion ∀p: ∃x(x=q) follows, which suggests either that the world is exhausted by our descriptions of it or that expression-independent propositions exist.

The simple resolution is to specify the T-schema as saying that for all propositions that p, the proposition that p is true iff p.

Yes, I made a similar point at the very start of this discussion. And here which includes a translation into ordinary English.

Maybe use an actual example.

“John is a bachelor” is true iff John is a bachelor

“John is a bachelor” is true iff John is an unmarried man

This shows us the meaning of “bachelor”.

But with the caveat of the liars paradox, right? I said it just because it seemed like the most obvious thing that would break the logic. — Moliere

Another consideration; what if we drop the use of the word "false" and replace it with some substantial notion of falsity?

1. This sentence does not correspond to a fact

We can then say:

2. "This sentence does not correspond to a fact" does not correspond to a fact

Is (2) a contradiction that entails that (1) does correspond to a fact? Perhaps you might say that it corresponds to the fact that it doesn't correspond to a fact? But it would seem that that reasoning would have to be said of every sentence that doesn't correspond to a fact, and so falsity itself would be self-defeating according to the correspondence theory of truth. Or if (2) isn't a contradiction then the liar paradox is solved: liar-like sentences do not correspond to a fact. Rather than being contradictions they're redundant, as (2) appears to show.

(And in fact the above applies to the stronger "this sentence is not true" form of the paradox).

Or if we don't like the correspondence theory of truth:

3. "This sentence does not cohere with some specified set of sentences" does not cohere with some specified set of sentences
4. "This sentence has not been proved" has not been proved
5. "This sentence does not warrant assertion" does not warrant assertion
etc.

But your point continues to escape me. — Banno

My point is only to show you what Tarski said, which is that, to quote him again:

(5) for all p, 'p' is a true sentence if and only if p.

But the above sentence could not serve as a general definition of the expression 'x is a true sentence' because the totality of possible substitutions for the symbol 'x' is here restricted to quotation-mark names.

And later:

For the reasons given in the preceding section I now abandon the attempt to solve our problem for the language of everyday life and restrict myself henceforth entirely to formalized languages.

He quite literally says that the T-schema isn’t a definition of truth and that a definition of truth for our everyday language is impossible. Maybe you and other authors disagree with him, but I’m not here to defend Tarski’s position, only to present it.

The only contribution of my own that I’ve added is that the sentence “this sentence has thirty one letters” appears to be an exception to the rule that “p” is true iff p, and so this disquotational account of truth is deficient. Tarski does pre-empt this, saying in Truth and Proof that, of his formalized language, "demonstrative pronouns and adverbs such as 'this' and 'here' should not occur in the vocabulary of the language", but I'm unsure how other authors who adopt the disquotational account for everyday language resolve the issue.

And in fact earlier you seemed to agree with me on this, saying "it always was [ 'p' is true iff q ]. Putting p on both sides is a special case", showing that "'p' is true iff p" isn't the definition of truth but something which (most of the time, at least) follows from whatever the actual definition is.

In English, which sentences can we not turn onto quotation-mark names? — Banno

It's not that we can't turn sentences into quotation-mark names, it's that such a proposed definition only applies to quotation-mark names, which is insufficient. The correct definition should apply to all true sentences. Again, from his 1933 paper, continuing immediately from the prior quote:

In-order to remove this restriction we must have recourse to the well-known fact that to every true sentence (and generally speaking to every sentence) there corresponds a quotation-mark name which denotes just that sentence. With this fact in mind we could try to generalize the formulation (5), for example, in the following way:

(6) for all x, x is a true sentence if and only if, for a certain p, x is identical with 'p' and p.

At first sight we should perhaps be inclined to regard (6) as a correct semantical definition of 'true sentence', which realizes in a precise way the intention of the formulation (1) and therefore to accept it as a satisfactory solution of our problem. Nevertheless the matter is not quite so simple. As soon as we begin to analyse the significance of the quotation-mark names which occur in (5) and (6) we encounter a series of difficulties and dangers.

I suggest you read that section of the paper rather than have me quote it piecemeal to you.

And my reply is that for Tarski, that is correct. But it has been used as such since his work. — Banno

Then you should probably mention that in your exegesis as it currently reads as if this was Tarski's position and so is misrepresentative.

That's besides the point. — Banno

The only point I am making is that the T-schema isn't a definition of truth. From his 1969 paper:

In fact, according to our stipulations, an adequate definition of truth will imply as consequences all partial definitions of this notion, that is, all equivalences of form (3):

“p” is true if and only if p,

where “p” is to be replaced (on both sides of the equivalence) by an arbitrary sentence of the object language.

...

If all the above conditions are satisfied, the construction of the desired definition of truth presents no essential difficulties. Technically, however, it is too involved to be explained here in detail. For any given sentence of the object-language one can easily formulate the corresponding partial definition of form (3). Since, however, the set of all sentences in the object-language is as a rule infinite, whereas every sentence of the metalanguage is a finite string of signs, we cannot arrive at a general definition simply by forming the logical conjunction of all partial definitions. Nevertheless, what we eventually obtain is in some intuitive sense equivalent to the imaginary infinite conjunction.

That "imaginary infinite conjunction" (extended from his earlier example of a finite language) which is the definition of truth being:

For every sentence x (in the language L), x is true if and only if either
s₁, and x is identical to “s₁”,
or
s₂, and x is identical to “s₂”,
. . .
or finally,
s_∞, and x is identical to “s_∞"

Although, again, this only applies to formal languages.

This seems to be the only definition of truth that Tarski offers in that paper:

If the language investigated only contained a finite number of sentences fixed from the beginning, and if we could enumerate all these sentences, then the problem of the construction of a correct definition of truth would present no difficulties. For this purpose it would suffice to complete the following scheme: x E Tr if and only if either x = x₁ and p₁, or x = x₂ and p₂, ... or x = x_n and p_n, the symbols 'x₁', 'x₂', ... , 'x_n' being replaced by structural descriptive names of all the sentences of the language investigated and 'p₁', 'p₂', ... , 'p_n' by the corresponding translation of these sentences into the metalanguage.

He makes it clear that a definition of truth is impossible for colloquial language and a formal language with an infinite number of sentences, only offering the above for a formal language with a finite number of sentences.

He's right, since he is talking about formal languages. — Banno

He's not. That quote is from the section "The Concept of True Sentences in Everyday or Colloquial Language". Later on in that section he says:

The attempt to set up a structural definition of the term 'true sentence' - applicable
to colloquial language is confronted with insuperable difficulties.

...

If these observations are correct, then the very possibility of a consistent use of the expression 'true sentence' which is in harmony with the laws of logic and the spirit of everyday language seems to be very questionable, and consequently the same doubt attaches to the possibility of constructing a correct definition of this expression.

And again, from the 1933 paper:

(5) for all p, 'p' is a true sentence if and only if p.

But the above sentence could not serve as a general definition of the expression 'x is a true sentence' because the totality of possible substitutions for the symbol 'x' is here restricted to quotation-mark names.

Tarski does what you say only he makes it clear that this doesn't count as the definition of truth:

(T) X is true if, and only if, p.

We shall call any such equivalence (with 'p' replaced by any sentence of the language to which the word "true" refers, and 'X' replaced by a name of this sentence) an "equivalence of the form (T)."

Now at last we are able to put into a precise form the conditions under which we will consider the usage and the definition of the term "true" as adequate from the material point of view: we wish to use the term "true" in such a way that all equivalences of the form (T) can be asserted, and we shall call a definition of truth "adequate" if all these equivalences follow from it.

It should be emphasized that neither the expression (T) itself (which is not a sentence, but only a schema of a sentence) nor any particular instance of the form (T) can be regarded as a definition of truth. We can only say that every equivalence of the form (T) obtained by replacing 'p' by a particular sentence, and 'X' by a name of this sentence, may be considered a partial definition of truth, which explains wherein the truth of this one individual sentence consists. The general definition has to be, in a certain sense, a logical conjunction of all these partial definitions. — The Semantic Conception of Truth

Which authors disagree with Tarski?