It's never been false. — Michael

It was false at the time of the pre-linguistic universe, but you don't realise that, and want to have your cake and eat it.

It was false at the time of the pre-linguistic universe, but you don't realise that, and want to have your cake and eat it. — Sapientia

It can't be false. It follows from premises which can't be false.

It can't be false. It follows from premises which can't be false. — Michael

The conclusion was false at the time, because it was not the case that there was a corresponding true sentence. The contrary is far too implausible to accept. So, if your argument is valid, then, at the time, at least one of the premises must also have been false.

So, if your argument is valid, then at the time, at least one of the premises must have been false. — Sapientia

They can't be false else we'd have a contradiction.

"P" is true if P
"P" is false if not P

We can't allow that "P" isn't true even if P or that "P" isn't false even if not P.

The contrary is far too implausible to accept.

If logic is inconsistent with intuition then so much the worse for intuition.

They can't be false else we'd have a contradiction.

"P" is true if P
"P" is false if not P. — Michael

No, you're overlooking the circumstances of the scenario under discussion. In a pre-linguistic universe, there is no "P" to be true or false. The concept of truth and falsity requires language.

In a pre-linguistic universe, there is no "P" to be true or false. — Sapientia

Then there is no T-schema to be false. So, as I said, the T-schema must always be true.

The concept of truth and falsity requires language.

As does the concept of cats on mats. ;)

Then there is no T-schema to be false. So, as I said, the T-schema must always be true. — Michael

I didn't say that there would be a T-schema in a pre-linguistic universe. You have claimed or implied that the T-schema would still apply in that circumstance, and I have rejected that. It would've been the case, at the time, that the pre-linguistic universe exists, but there wouldn't have been a corresponding true sentence.

I didn't say that there was a T-schema. — Sapientia

You said "[t]he conclusion [the T-schema] was false at the time" (and "at the time, at least one of the premises must have been false"). How could it (or they) be false if they weren't "there"?

You have claimed or implied that the T-schema would apply at such a time, and I have rejected that.

No I didn't. I have only ever said "X" is true iff X (and X iff "X" is true). I've never said X happened iff "'X' is true iff X" was truthfully said at the time.

It would've been the case that the pre-linguistic universe exists, but there wouldn't have been a corresponding true sentence.

Which is why I said that the pre-linguistic universe existed iff "the pre-linguistic universe existed" is true and not that the pre-linguistic universe existed iff there was a corresponding true sentence at the time.

Also, I think your tense is wrong again. Would have been the case that the pre-linguistic universe exists? Compare with; would have been the case that the Nazis win the war. Does that make sense? I don't think so. Should be; would have been the case that the Nazis won the war, and so; would have been the case that the pre-linguistic universe existed.

You said "[t]he conclusion [the T-schema] was false at the time" (and "at the time, at least one of the premises must have been false"). How could it (or they) be false if they weren't "there"? — Michael

Fine, then I retract that claim. It isn't necessary. I was suspicious when you brought up falsity, and now I realise that I was right to be suspicious.

There would not have been a true conclusion, nor any true premises, at the time. Nor would the latter part of the T-schema apply at such a time, which is to say that there would not have been a corresponding true sentence. This is what I have consistently claimed, with the exception of your successful - albeit shallow - ploy.

No I didn't. I have only ever said "X" is true iff X (and X iff "X" is true). I've never said X iff "'X' is true iff X" is said and is true. — Michael

What? You seem to have reverted back to a misinterpretation that I thought you'd set aside. I have addressed what's in the brackets. It wasn't true in the pre-linguistic universe. There were facts, but no sentences, and therefore no true sentences.

What's the problem?!

Which is why I said that the pre-linguistic universe existed iff "the pre-linguistic universe existed" is true and not that the pre-linguistic universe existed iff there was a corresponding true sentence at the time. — Michael

The former is a separate, nonequivalent claim than the one that I've been addressing, and the latter is more or less what I think you have - perhaps inadvertently - implied.

Also, I think your tense is wrong again. Would it have been the case that the pre-linguistic universe exists? Compare with; would have been the case that the Nazis win the war. Does that make sense? I don't think so. Should be; would have been the case that the Nazis won the war, and so; would have been the case that the pre-linguistic universe existed. — Michael

That's misleading, if not outright incorrect. The pre-linguistic universe existed, and, at the time, it would be the case that the pre-linguistic universe exists. Similarly, the Nazis shot Jews, and, at the time, it would be the case that the Nazis are shooting Jews.

The qualification "at the time" means that you must consider that point in time with regard to what would have been the present state of affairs, and the present state of affairs would have included: the pre-linguistic universe exists.

There were facts, but no sentences, and therefore no true sentences.

What's the problem?! — Sapientia

The problem is that I've never said that there were true sentences, and nor have I implied it. I've simply taken two necessarily true propositions and performed the relevant logical manipulations.

That's misleading. The universe existed, and, at the time, it would be the case that the universe exists. Similarly, the Nazis shot Jews, and, at the time, it would be the case that the Nazis are shooting Jews

The important thing to note is that the following two sentences are equivalent:

It is the case that P
"P" is true

So what you're saying can be re-written, with no change in meaning, into "the universe existed and, at the time, 'the universe exists' would be true".

The problem is that I've never said that there were true sentences, and nor have I implied it. I've simply taken two necessarily true propositions and performed the relevant logical manipulations. — Michael

No, the problem is that you don't realise what you've implied, but how about we just agree to disagree, and leave it at that?

A subjunctive conditional is a counterfactual conditional, and the T-schema doesn't seem to use a counterfactual conditional. If it did (pun intended) it would look like this: — Michael

Rather than focus exclusively on what it looks like, you ought to focus a little more on how it is used. Remember that it is you yourself who introduced explicitly a contentious counterfactual conditional statement, insisted that it be read as such, and invoked Tarski's T-shema in order to justify it. My rejoinder was that you were reading the T-shema in the wrong direction.

The sort of claim that you wish to defend is:

(1) If "Smokey the cat is on the mat" is true, then Smokey the cat is on the map.

And you also insisted that your claims should be understood as counterfactual conditionals (one such claim was concerning horses, rabbits and synonymy).

It is true that (1), interpreted as a material inference, can be validly inferred from

(2) If "Smokey the cat is on the mat" is true if and only if Smokey the cat is on the map.

However, when read as a subjunctive conditional in which '"the cat is on the mat" is true' is the antecedent, (1) becomes a misrepresentation of (2) as it is intended to be read in the context of a Tarskian truth theory.

That's because instanciations of the T-shema (as derived from the meaning assignment axioms of the theory) are meant to be interpreted as a recipe, or instruction manual, that tells you how, given specific worldly circumstances (e.g. circumstances either actual or counterfactual where horses are or aren't rabbits, or where Smokey the cat is or isn't on the mat) sentences in the object language ought to be evaluated as true or false.

This is why (2) must be understood as stating the conditions under which "the cat is on the mat" is correctly evaluated, in whatever object-language is being formalized by the truth theory, rather than as stating what the conditions in the world would be (counterfactually) if the mentioned object-language sentence were true. It can't mean both, for in that case the account would be viciously circular.

The important thing to note is that the following two sentences are equivalent:

It is the case that P
"P" is true — Michael

Not at all.

Of course it is. Which is why "it is the case that P and 'P' is not true" is contradictory.

Where does my logic fail? You say that "the cat is on the mat" would be false if the cat were not on the mat, and so we have ¬C > ¬P (using the subjunctive conditional). As per transposition this is equivalent to P > C, which is that the cat would not be on the mat if 'the cat is on the mat' would be false".

Of course it is. — Michael

Then "of course it is" is equivalent to "of course it isn't".

No, that's a contradiction.

So is yours.

What? The following two are equivalent:

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

But they simply aren't equivalent. The former doesn't mean that a particular sentence is true, whereas the latter does.

Again, they mean the same, which is why the following is contradictory:

"My name is Michael" is true and it is not the case that my name is Michael.

This discourse is not productive. If you say that they're the same, then I'll say that "yes" and "no" are the same. It's just as contradictory, in my view - unless the meanings are changed so that they mean the same thing.

Where does my logic fail? You say that "the cat is on the mat" would be false if the cat were not on the mat, and so we have ¬C > ¬P (using the subjunctive conditional). As per transposition this is equivalent to P > C, which is that the cat would not be on the mat if 'the cat is on the mat' would be false". — Michael

Yes that's correct so long as you hold fixed the range of actual+counterfactual (i.e. 'possible') circumstances in which the implication sign can be interpreted as material implication. Saying that P > C is equivalent to saying that in all possible worlds at which P, it also is the case that C. Hence, relative to this very same range of possible worlds, it also follows that whenever ¬C, it also is the case that ¬P. But this needs not have the same significance as ¬C > ¬P, since the range of possible worlds that ¬C singles out may be a different range. And that is indeed the case where your contentious interpretation of the T-shema is concerned. For the case where the T-shema is correctly interpreted, the relevant range of counterfactual circumstances includes, precisely, worldly circumstances (i.e. ways for things to be) relative to which the truth of object-language sentences are to be evaluated in accordance with their (indirectly) stipulated meanings. There is no ranging over other possible (i.e. non-actual) reference assignments to the object-language terms.

Hence, you are licensed to say, on the basis of the T-shema instanciation previously discussed, that in all cases where Smokey the cat is (or would be) on the mat, "Smokey the cat is on the mat" (in English) is (or would be) true, and in all cases where Smokey the cat isn't (or wouldn't be) on the mat, "Smokey the cat is on the mat" (in English) is (or would be) false. Hence, material equivalence holds relative to a specific range of circumstances. This range of possible circumstances, envisioned by the T-shema instanciation, is a range of circumstances in which Smokey is located at various places, not all of them "on" the mat. But, relative to all the possible worlds in that range, the meanings of the English words used to state the theory, and the meanings of the object-language words (which can be the same language as the meta-language) are held fixed. It's precisely because they are held fixed that the T-shema doesn't licence the ¬C > ¬P subjunctive conditional claim that you want to derive from it, where they would be allowed to vary over circumstance of linguistic use in which meaning assignments to the words of the object-language would be different than those that are intended by the specific truth theory that this T-shema instanciation is a theorem of.

If dinosaurs were roaming the earth (to use Michael's example), does it follow that "dinosaurs roam the earth" was true, or merely that "dinosaurs roamed the earth" is true?

Hence, you are licensed to say, on the basis of the T-shema instanciation previously discussed, that in all cases where Smokey the cat is (or would be) on the mat, "Smokey the cat is on the mat" (in English) is (or would be) true, and in all cases where Smokey the cat isn't (or wouldn't be) on the mat, "Smokey the cat is on the mat" (in English) is (or would be) false. — Pierre-Normand

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.

If we go back to the example you gave earlier...

That's because instanciations of the T-shema (as derived from the meaning assignment axioms of the theory) are meant to be interpreted as a recipe, or instruction manual, that tells you how, given specific worldly circumstances (e.g. circumstances either actual or counterfactual where horses are or aren't rabbits, or where Smokey the cat is or isn't on the mat) sentences in the object language ought to be evaluated as true or false.

... 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.

If dinosaurs were roaming the Earth then "dinosaurs were roaming the Earth" is true.

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

If you say that they're the same, then I'll say that "yes" and "no" are the same. It's just as contradictory, in my view - unless the meanings are changed so that they mean the same thing. — Sapientia

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.

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.

The only way you can reject the conclusion is if you reject either a) or b), but we've already established that that leads to contradictions.

I don't know how much simpler to put it.

If dinosaurs were roaming the earth (to use Michael's example), does it follow that "dinosaurs roam the earth" was true, or merely that "dinosaurs roamed the earth" is true? — John

I know that your question wasn't addressed to me, but that isn't going to stop me from answering. Only the latter follows, or at least it does so if you're talking about the history of Earth, and not some hypothetical Earth which could have an alternative history.