↪Sapientia What? The following two are equivalent:
It is the case that my name is Michael
"My name is Michael" is true — Michael
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
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
They are not equivalent; one is about a sentence, the other about a name. — The Great Whatever
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
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
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
... 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
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
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
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. — The Great Whatever
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
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.
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
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
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
It's implicit in the schema that the sentence mentioned on the one side is the same sentence used on the other side. — Michael
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
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"... — Michael
Why? The "this" is self-referential. — Michael
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
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
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?
How much more evident can a contradiction get? — Michael
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.