Michael,

The disquotational schema as you are using it is simply false, and your whole notion of how these things works seems to be predicated on it. So it would be best to return to why it's false.

The proposal:

"X" is true iff X.

Let's show that neither direction holds. First, left to right:

If "X" is true, then X.

Suppose that in an alternate state of the language in the future, "X" means the same as "not X" means now; that is, "X" means that not X. Suppose that further, in this situation, not X. In such a situation, "X" (that sentence) is true, yet it is not the case that X. In fact, the truth of that sentence guarantees just the contrary, that not X. So this conditional is false.

Now the right to left direction:

If X, then "X" is true.

Take the case of a time before there is languages, and let X be that there are dinosaurs. In this case, there are dinosaurs, yet it is not the case that "there are dinosaurs" is true, since no such sentence exists ex hypothesi, and a fortiori no such sentence is true. So this conditional is not true either.

So the disquotational schema is false, since neither of its conditional directions holds. Without it, this entire line of thought is fruitless.

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I think, in the end, you confuse claiming that X with something like saying "X," which is the only way I can make sense of your line of thought -- but this is fallacious, as shown above. Sentences do not in any way talk about themselves and claim themselves to be true -- that would require a mention of the sentence in order to predicate truth of it. Yet when sentences are used, they talk about the things they talk about, like horses and rabbits. The truth of a sentence, and the obtaining of the state of affairs that a sentence describes, are simply not the same thing; your philosophy of language is basically and fundamentally wrong and hinges on a use-mention error.

↪Sapientia What? The following two are equivalent:

It is the case that my name is Michael
"My name is Michael" is true — Michael

They are not equivalent; one is about a sentence, the other about a name. The properties of the sentence might change, while the name stays the same, or vice-versa.

1) It is the case that my name is Michael and My name is Michael are equivalent.
2) My name is Michael and "My name is Michael" is true are equivalent.
3) It is the case that my name is Michael and "My name is Michael" is true are equivalent. — Michael

Look, none of those are equivalent in meaning, no matter how determined you are in your attempt to make them so. If you can't see the admittedly subtle differences, then that is not my problem. They are all similar and related, but that does not make them equivalent.

The closest in meaning are the two sentences in 1), but even those two sentences do not have exactly the same meaning. Although, if the latter is asserted, then the "It is the case that..." would be implicit. In that sense, and in that sense only, are the two equivalent.

The first premise should be self-evident. The second premise follows from a) "My name is Michael" is true if my name is Michael and b) "My name is Michael" is not true if my name is not Michael. The conclusion applies a straightforward transitive relation. — Michael

No, that doesn't follow. That one logically implies the other does not mean that they're equivalent in meaning. That is your arbitrary interpretation. They aren't equivalent in meaning for the reason that I stated.

They are not equivalent; one is about a sentence, the other about a name. — The Great Whatever

I thought that you'd notice the difference, too. I'm glad that I'm not the only one to object to Michael's attempt to conflate the two.

I'd add that one is about that which is true (a sentence which satisfies certain truth conditions; language), whereas the other is about that which is the case (a fact or state of affairs; the world).

It follows from this that in all cases where "Smokey the cat is on the mat" (in English) is (or would be) true, Smokey the cat is (or would be) on the mat, and in all cases where "Smokey the cat is on the mat" (in English) is (or would be) false, Smokey the cat isn't (or wouldn't) be on the mat. — Michael

That's exactly right. But notice that it doesn't follow that in all cases where "Smokey the cat is on the mat" is (or would be) true in some other language than English, in 'New English', say, Smokey the cat is (or would be) on the mat. And yet this is what you were saying. Even though you actually meant your claim to be interpreted as if you were expressing the consequent in 'New English', this use isn't warranted by the normal interpretation of the T-shema.

(On edit: I had missed the second part of your comment, so I responded to that below)

I knew that is what you would say, that you would pick the second option. I was interested to hear what Pierre would say. — John

Yes, I agree with Michael. Judgments that are true at the time when they are judged or expressed are true at all times. If one correctly judges at one time that Smokey the cat is (at that time) on the mat, then this judgment remains true at a later time when Smokey has wandered off the mat. The very same judgment (the content, not the speech act) then can be re-expressed with the use of a different 'situational sentence' that includes a verb in the past tense.

I thought that you'd notice the difference, too. I'm glad that I'm not the only one to object to Michael's attempt to conflate the two.

I'd add that one is about that which is true (a sentence which satisfies certain truth conditions; language), whereas the other is about that which is the case (a fact or state of affairs; the world). — Sapientia

It seems to me that you and TGW may be making too much of that. Even though one sentence has an English expression as its grammatical subject, it mentions it (and refers to its meaning) as an indirect means of making a claim about what is the case in the world, whereas the other sentence makes that very same claim directly. Michael is right to point out that they are logically equivalent in that respect -- in that they logically imply one another -- assuming only that the meaning of the mentioned sentence is held fixed and taken to be its ordinary meaning in English. It is through forgetting this necessary assumption (in counterfactual contexts) that Michael sometimes run into trouble, it seems to me.

... we can consider the case of how given the worldly circumstances some dessert ought to be evaluated as a red velvet cake (or not):

This is a red velvet cake iff this recipe was successfully followed.

If the above is true then the below is true.

This recipe was successfully followed iff this is a red velvet cake.

So it doesn't matter whether you explain it in terms of material or subjunctive equivalence or in terms of instructions for evaluation; it can be read in either direction. — Michael

There is a crucial disanalogy that you are overlooking. Correctly following the recipe for a velvet cake ensures the production of a velvet cake, let us assume. However, correctly following the semantic rules of a language doesn't ensure that "Smokey the cat is on the mat", when correctly evaluated to be true according to those rules, implies that Smokey the cat is on the mat. That's only guaranteed to be the case when the semantic rules are those of the English language. If they are the semantic rules for another language, then it may be the case that "Smokey the cat is on the mat" is correctly evaluated to be true according to those rules while Smokey the cat isn't on the mat.

OK, so, that dinosaurs were walking the earth, although true now, was not true at the time. But now that we have judged it to be true that they were walking the earth it will be true for all time, even at some time in the future, when there are no humans?

OK, so, that dinosaurs were walking the earth, although true now, was not true at the time. But now that we have judged it to be true that they were walking the earth it will be true for all time, even at some time in the future, when there are no humans? — John

No, that's not what I meant to imply. That dinosaurs were walking the Earth is both a fact and the content of a true judgment. The content of the judgment is what is shared between different people who judge this content to be true. It also can be the content of other propositional attitudes such as hopes, fears, or it can figure in more complex thought such as, e.g. being the antecedent of a conditional.

All I meant to convey rather is that, if there had been people present at the time when dinosaurs were roaming the Earth, and who would have been in a position to judge this to be the case, and who may or may not have expressed this judgment using whatever language that had sufficient conceptual resources for expressing it, those people would have been entertaining the very same thought content that we now are able to express with a past tense statement. The very same judgment expressed by them, then, can be expressed by us now. So, its being true doesn't depend on them, or us, existing at all. The content of any judgment actually entertained by someone at a specific time (i.e. its truth conditions) necessarily must be ascertained as a function of the concepts employed (reflected in the use of the words that express them) but the truth value of those judgments only depend on what is the case in the world at the relevant time (and not necessarily at the time when the thought is entertained).

I had explained this earlier in rather more details here, here and here.

I don't think that I am making too much of it. Remember that Michael has an underlying agenda, which is to prove my wider position false. He is attempting to show that my position implies a contradiction, and is therefore not only false, but necessarily so. It is on this basis that he rejects the pre-linguistic universe counterexample. So, not only is it important to point out the non-equivalence for it's own sake, my position depends upon it.

I stand by my claims. The two sentences (both in their more generalised and logical form, and in certain specifically worded forms) are not equivalent in important ways: both in terms of meaning and in terms of logical consequence. It is because of this that it is the case that P does not entail that "P" is true (but only if certain conditions are satisfied), and that, therefore, no contradiction is implied by committing to a case in which the former holds, but not the latter. And, because of this, the pre-linguistic universe counterexample stands.

It is because of this that it is the case that P does not entail that "P" is true (although it does so if certain conditions are satisfied), and that therefore, the pre-linguistic universe counterexample stands. — Sapientia

Yes, I think we can agree that in the distant past, when there weren't any language users around, and hence there were no rules governing the use of the words employed in "P", it was still the case that P. That it was the case that P can be expressed by us with the sentence "P", which is true if and only if P, right? Hence it is correct to say that the two sentences (1) "P" and (2) '"P" is true' are logically equivalent, which can be expressed thus:

"P" is true if and only if P

For instance:

"There were triceratops around 68 million years ago" (as expressed by us now) is true if and only if there were triceratops around 68 million years ago.

So, it's not really the disquotational shema in itself that is the source of Michael's trouble. (And indeed, most logicians and philosophers of language don't have any trouble with this schema, though they may disagree on their detailed accounts of truth and meaning.)

That it was the case that P can be expressed by us with the sentence "P", which is true if and only if P, right? Hence it is correct to say that the two sentences (1) "P" and (2) '"P" is true' are logically equivalent, which can be expressed thus: — Pierre-Normand

Again, no. This is the error. Whether a certain sentence or string of words is true or not in a hypothetical situation (not now) does not guarantee that the situation that is described by that string of words in the language as it currently is now, holds in the hypothetical situation. In the hypothetical situation, "P" might very well mean not P, and so the truth of "P" could very well imply not P, rather than P.

Again, no. This is the error. Whether a certain sentence or string of words is true or not in a hypothetical situation (not now) does not guarantee that the situation that is described by that string of words in the language as it currently is now, holds in the hypothetical situation. In the hypothetical situation, "P" might very well mean not P, and so the truth of "P" could very well imply not P, rather than P. — The Great Whatever

Obviously, you overlooked my explicit qualifier "by us". This is always assumed by the logicians and philosophers of language who make use of the disquotational shema. We are not talking about counterfactual situations where the mentioned sentence has a different meaning. We are rather talking about counterfactual circumstances where its truth value varies as a function of the way the world is in those circumstances.

Suppose that in an alternate state of the language in the future, "X" means the same as "not X" means now; that is, "X" means that not X. Suppose that further, in this situation, not X. In such a situation, "X" (that sentence) is true, yet it is not the case that X. In fact, the truth of that sentence guarantees just the contrary, that not X. So this conditional is false. — The Great Whatever

It's implicit in the schema that the sentence mentioned on the one side is the same sentence used on the other side.

So:

"X" is true iff X

The bits in bold are the same sentence.

If X, then "X" is true.

Take the case of a time before there is languages, and let X be that there are dinosaurs. In this case, there are dinosaurs, yet it is not the case that "there are dinosaurs" is true, since no such sentence exists ex hypothesi, and a fortiori no such sentence is true. So this conditional is not true either.

If X then "X" is true follows from if "X" is not true then not X, as per transposition. And given that it's implicit that the sentence mentioned is the sentence used, if "X" is not true then not X must be true to avoid contradiction. Therefore If X then "X" is true must be true to avoid contradiction. Unless you can show that the logic of this fails (and not just that any ontological implications are counterintuitive) then any argument you have against it must be wrong in some respect.

There is a crucial disanalogy that you are overlooking. Correctly following the recipe for a velvet cake ensures the production of a velvet cake, let us assume. However, correctly following the semantic rules of a language doesn't ensure that "Smokey the cat is on the mat", when correctly evaluated to be true according to those rules, implies that Smokey the cat is on the mat. That's only guaranteed to be the case when the semantic rules are those of the English language. If they are the semantic rules for another language, then it may be the case that "Smokey the cat is on the mat" is correctly evaluated to be true according to those rules while Smokey the cat isn't on the mat. — Pierre-Normand

I'm stating the T-schema where the sentence mentioned on the one side is the sentence used on the other side. So whatever language it's in, with this condition the bidirectional equivalence holds.

"X" is true iff X and X iff "X" is true.

No, that doesn't follow. That one logically implies the other does not mean that they're equivalent in meaning. That is your arbitrary interpretation. They aren't equivalent in meaning for the reason that I stated. — Sapientia

They reference the same truth condition. So in that sense they mean the same thing, even if the cognitive content has a different focus. Consider the sentences "you are a parent" and "you have a child". The cognitive content of the first focuses on what you are and the cognitive content of the latter focuses on what you have, and yet they both reference the same truth condition and so amount to the same claim.

I'm stating the T-schema where the sentence mentioned on the one side is the sentence used on the other side. So whatever language it's in, with this condition the bidirectional equivalence holds.

"X" is true iff X and X iff "X" is true. — Michael

Yes, if you settle on a specific language, whatever this language might be, then the material equivalence holds. But then it can't be interpreted as a subjunctive conditional. And you also need to indicate that, when you choose some language L different than English, then you mean your statement of specific shema instanciations to be interpreted in L rather than in English. The default is to interpret sentences that are used as being written in English (on this forum, anyway).

It's implicit in the schema that the sentence mentioned on the one side is the same sentence used on the other side. — Michael

That depends. If it's the disquotational shema (or the homophonic case for the T-shema) that is at issue, then, yes, the sentence mentioned is the same as the sentence used (and both are interpreted in the same language). But in the T-shema derived from a Tarskian truth theory, there is no requirement that the object-language and the meta-language be the same. The meta-language has its own semantic rules fixed and is used to specify truth conditions for the sentences of the object-language. And in both cases (either the simple disquotational schema or the T-schema instanciations of some Tarskian truth theory) the interpretation of the schema instanciations as counterfactual conditionals, where the antecedent specifies some counterfactual semantic rule for the mentioned language, is incorrect.

They reference the same truth condition. So in that sense they mean the same thing, even if the cognitive content has a different focus. Consider the sentences "you are a parent" and "you have a child". The cognitive content of the first focuses on what you are and the cognitive content of the latter focuses on what you have, and yet they both reference the same truth condition and so amount to the same claim. — Michael

Yes, that is quite correct, though I would be tempted to nitpick on behalf of Frege and say that they have the same truth conditions and hence reference the same truth values in all circumstances.

I meant it in the sense that if we think of the cat being on the mat as the truth-condition that makes "the cat is on the mat" true, and if "the cat is on the mat" refers to the cat being on the mat, then "the cat is on the mat" refers to that truth-condition.

Maybe "truth-maker" or even just "referent" is the better term? Although I guess this is largely semantic and makes no significant difference to the issue at hand.

But then it can't be interpreted as a subjunctive conditional. And you also need to indicate that, when you choose some language L different than English, then you mean your statement of specific shema instanciations to be interpreted in L rather than in English.

...

And in both cases (either the simple disquotational schema or the T-schema instanciations of some Tarskian truth theory) the interpretation of the schema instanciations as counterfactual conditionals, where the antecedent specifies some counterfactual semantic rule for the mentioned language, is incorrect.

That's why I clarified the previous example by saying:

Given that in this language "horse" means "rabbit"...

So given that in this language "horse" means "rabbit", 1) horses are rabbits, 2) "horses are rabbits" is true, 3) "horses are rabbits" is true iff horses are rabbits, and 4) horses are rabbits iff "horses are rabbits" is true.

That's why I clarified the previous example by saying:

Given that in this language "horse" means "rabbit"... — Michael

That's not sufficient. You also have to say: "... and given that I've decided to write this post in this language..."

Why? The "this" is meant to be self-referential.

Why? The "this" is self-referential. — Michael

It's unclear because it sounds like "this" is used to single out the language you are making claims about, not to specify the language in which you've decided to write your post, or part of your post, let alone the second part of one single sentence in your post. Also, there are less confusing ways to make your point about meaning being determined by use, it seems to me.

I meant it in the sense that if we think of the cat being on the mat as the truth-condition that makes "the cat is on the mat" true, and if "the cat is on the mat" refers to the cat being on the mat, then "the cat is on the mat" refers to that truth-condition.

Maybe "truth-maker" or even just "referent" is the better term? Although I guess this is largely semantic and makes no significant difference to the issue at hand. — Michael

Yes, it's true that nothing much hangs on the use of "refers to" here. But "refers to" usually is understood as a relation between singular terms and the objects that they refer to, or between concept words and the Fregean concepts (or determinations) that they refer to. In the case of whole sentences, they are said by Frege to refer to truth values, and the thoughts that they express are their senses. Knowledge of the truth conditions of sentences would be equated with knowledge of the senses that they express. One can know the sense of a sentence and not know whether it is true or not. One needs in addition to know the references (Bedeutugnen) of the terms this sentence is composed of. When this is known, then the truth value can be assessed through checking what's up with those Bedeutungen in the world (e.g. does the object referred to by the singular term have the determination referred to by the concept word?). This is why Frege locates the truth value of the sentence at the level of reference, and the meaning of the sentence (its truth conditions) at the level of sense (Fregean Sinn).

Hence it is correct to say that the two sentences (1) "P" and (2) '"P" is true' are logically equivalent, which can be expressed thus:

"P" is true if and only if P

For instance:

"There were triceratops around 68 million years ago" (as expressed by us now) is true if and only if there were triceratops around 68 million years ago. — Pierre-Normand

I do not agree with this part of your post. I don't think that (1) and (2) are logically equivalent, and I find the biconditional in that formulation problematic, because then I couldn't deny the converse, or deny one part of it, without contradiction, right? But I think that it is possible in certain circumstances that P and not "P" is true.

It's also problematic to lose the biconditional, because then I couldn't exclude other possible truth conditions which I'd want to exclude on the basis that they wouldn't make sense.

And given that it's implicit that the sentence mentioned is the sentence used, if "X" is not true then not X must be true to avoid contradiction. — Michael

This is false. The fact that the sentence mentioned is the same as the one used in no way shows that this must be true to avoid contradiction. Perhaps you can show how this is a contradiction?

I can show that it's not, by showing that in a given scenario, one can be true while the other is false:

Suppose X = "there are no more dinosaurs," where we slot in a use of this sentence for the variable "X."

Now, suppose that in Future English, "there are no more dinosaurs" means the same thing that "there are still dinosaurs" means now; that is, it means that there are still dinosaurs.

Now, take a situation in which people speak future English, in which there are no more dinosaurs, since it is the future. In that situation, ex hypothesi," "there are no more dinosaurs" is not true, since it means that there are still dinosaurs, and there aren't. If that sentence were true in the future situation, then there would still be dinosaurs, since that is what the sentence "there are no more dinosaurs" means in this alternate situation. Since there are no more dinosaurs, the sentence is false.

But, ex hypothesi, there are no more dinosaurs in this situation, so X obtains in it, that is, in this situation, X (there are no more dinosaurs).

So this is a situation in which "there are no more dinosaurs" is false, yet there are no more dinosaurs (precisely because "there are no more dinosaurs" means that there are still dinosaurs, and there are not by hypothesis).

There is nothing contradictory about such a situation, and therefore there is no contradiction as you suppose. Somewhere you have gone wrong in your reasoning, and this counterexample demonstrates that: it is another question where you went wrong, and I suspect, as I have said, that you are deeply confusing use and mention.

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I have shown you why this is not a contradiction as you claim. Why do you think it is a contradiction? I've seen no defense of this other than asserting it, but given that (a) this assertion looks absurd on its face, and (b) we can construct a situation to demonstrate that it is wrong, it seems to me that you cannot go on claiming this unless you respond to this situation.

Your example switches languages. You consider the mentioned statement to be in New English but the used statement to be in English proper. As I said before, the sentence mentioned must be the sentence used, such that both the mentioned statement and the used statement are in the same language (and mean the same thing, to account for homonyms).

So given that both the sentence I'm using and the sentences I will mention are to be understood as English proper, if my name is Michael then "My name is Michael" is true and if my name is not Michael then "My name is Michael" is not true. To claim otherwise is to invite contradiction.

So given that both the sentence I'm using and the sentences I will mention are to be understood as English proper, if X then "X" is true and if not X then "X" is false. To claim otherwise is to invite contradiction.

This is false. The fact that the sentence mentioned is the same as the one used in no way shows that this must be true to avoid contradiction. Perhaps you can show how this is a contradiction?

"My name is Michael" is true and my name is not Michael.

How much more evident can a contradiction get?

@Michael, if I understand you correctly, your claim hinges on saying that the same sentence cannot exist in more than one language. Is that correct?

As I see it, a sentence is a certain grammatical object -- a string of morphemes or words, or a syntactic structure, whatever you like -- and that same object can receive different interpretations. It seems for your objection to make sense, you would have to claim this is effectively not possible, which would commit you to a substantial view on the identity conditions of sentences (I'm not sure what they would be, but it looks wrong).

Thus I am not talking about some sentence in English and then some other sentence in the new English, and so I 'switch' nothing. There is just one sentence, namely this one --> "there are no more dinosaurs," and that sentence means one thing now, but could mean something else later.

How much more evident can a contradiction get? — Michael

For me, it's evidently just not a contradiction, and it's puzzling to me why you think it is. You have a claim about a sentence on the one hand, and a claim about a name on the other; presumably, to say these contradict is to say that one side of the conjunction cannot be true while the other is false: but clearly this is possible, as I showed above, so I'm not sure why you think there is any 'evident' contradiction at all.

There is likely a missing premise that you cannot articulate, and I suspect that when that premise is spelled out, the use-mention error will become more clear.