The "this sentence" is a recursive reference. — Michael
If I say that "horse" denotes having properties A, B, and C and if I say that this animal is a horse then I am saying that this animal has properties A, B, and C. — Michael
The Great Whatever accepts the first premise, the T-schema shows the second premise, and so the conclusion follows. — Michael
Suppose for example that in a counterfactual situation, "horses are rabbits" means the sky is blue. Then in that situation, if "horses are rabbits" is true (and thus the sky is blue), it is nonetheless not the case that horses are rabbits, which is nonsense anyhow; it is merely the case that the sky is blue. — The Great Whatever
In that situation if "horses are rabbits" is true then horses are rabbits (where the language of the sentence mentioned is the language of the sentence used). — Michael
(where the language of the sentence mentioned is the language of the sentence used). — Michael
In that situation if "horses are rabbits" is true then horses are rabbits
Assertions implicitly assert their own truth, and so to say that X is Y is to say that "X is Y" is true, and vice versa.
Apply the logic to English, where English is both mentioned and used. If "horses" and "equine animals" are synonymous then "horses are equine animals" is true. If "horses are equine animals" is true then horses are equine animals. Therefore if "horses" and "equine animals" are synonymous then horses are equine animals. — Michael
Now inject some Wittgenstein. If we use the words "horses" and "equine animals" in the same way then "horses" and "equine animals" are synonymous. Therefore if we use the words "horses" and "equine animals" in the same way then horses are equine animals.
Your conditional seems to run the wrong way. — Pierre-Normand
If you mean "using in the same way" to imply that referents are identical then in order to know that "horse" and "equine animals" are indeed used in the same way by us, in the case where we already know how to use them, would require that we check that any horse necessarily is an equine animal and vice versa.
Which part? You agreed with 'If "horses" and "equine animals" are synonymous then "horses are equine animals" is true' in your previous post and 'If "horses are equine animals" is true then horses are equine animals' is the T-schema, which you accept. The conclusion 'therefore if "horses" and "equine animals" are synonymous then horses are equine animals' simply applies the transitive relation. — Michael
We need to know that the things we call "horses" are the things we call "equine animals". Which is to say that we need to know that we use the words "horses" and "equine animals" to talk about the same thing. And what does talking about the same thing consist of? What's the metaphysics behind talking about the same thing? I'm loathe to any interpretation that claims there's more to talking about things than behaviour, intention, and the empirical contexts that influence and measure them. How can anything else become a part of language, meaning, and understanding? This was Dummett's point.
The example I gave didn't use a counterfactual meaning. It used ordinary English. If "horses are equine animals" is true then horses are equine animals. — Michael
Even then, that I can state the T-schema in a language other than English, e.g. French, is that I can state the T-schema in a language other than English, e.g. New English.
Also, the T-schema is biconditional so it can be read either way. We can say that "snow is white" is true iff snow is white or we can say that snow is white iff "snow is white" is true. It's an iff, not just an if.
The reason why it's a biconditional simply is because if the T-shema were rather a simple conditional such as:
(1) "The cat is on the mat" is true if the cat is on the mat,
then this would leave the truth value of "the cat is on the mat" undetermined in all cases where the cat isn't on the mat. But we want to stipulate that "the cat is on the mat" is false when the cat isn't on the mat; hence the biconditional. Tarski's intention never was to imply that truth values of object-language sentences determine what can be truly be said in the meta-language. — Pierre-Normand
In that case your example doesn't have anything to do with the T-shemas that occur in a Tarskian truth theory, and so it's unclear why you attempted to rely on this notion. In the context of such a theory, a T-shema states general truth conditions for a sentence expressed in the object-language and hence has the force of a subjunctive conditional where the truth value of the antecedent is defined as true or false in all possible circumstances, accordingly, whether the condition stated in the consequent is satisfied or not in those circumstances.
It might not have been his intention but the logic of a biconditional is such that it can be read in either direction. — Michael
I'm not sure how this makes a difference. You accept that if "X" and "Y" are synonymous then "X is Y" is true and you accept that if "X is Y" is true then X is Y. So it's a straightforward transitive relation to conclude that if "X" and "Y" are synonymous then X is Y. If the premises are true and the conclusion is a valid derivation then the argument is sound. — Michael
For instance, the T-shema instanciation:
(1a) "The cat is on the mat" is true iff (i.e. in all cases and only those cases where) the cat is on the mat
is equivalent to the conjunction:
(1b) "The cat is on the mat" is true if the cat is on the mat and "The cat is on the mat" is false if the cat isn't on the mat. — Pierre-Normand
If "P" means "man" and if you are a man then you are a P.
What's wrong with this? — Michael
1b) is:
(C → P) ∧ (¬C → ¬P)
Using transposition this gives us:
(C → P) ∧ (P → C)
Which is material equivalence. — Michael
According to your claim, with the biconditional, for any sentence "P," if P, then it must be that "P" is true.
Now, it follows from this that before language existed, there was nothing[...] — The Great Whatever
You have agreed that whether a sentence is true or not depends on the way it is used; and since no language exists, a fortiori no language is used, and therefore no sentence is true. So I can take any P, and it will not hold, since nothing can hold unless the corresponding sentence "P" is true. — The Great Whatever
For any sentence "P", if P, then "P" is true for all cases in which "P" can be formed; and for all cases in which "P" can't be formed, then "P" would be true if it was formed. — Sapientia
You don't actually have to tie up the truth of an assertion, or of the linguistic expressions of a thought (that may have a force different than that of assertion or belief) to the circumstances that hold at the time of the utterance. — Pierre-Normand
One can equally say yesterday, or today, or tomorrow, in different manners, that Smokey the cat was on the mat yesterday at 11 o'clock. This very same thought would have been expressed yesterday with the situational sentence "Smokey the cat was (or is, or will be) on the mat today at 11 o'clock" or expressed the day before with the situational sentence "Smokey the cat is going to be on the mat tomorrow at 11 o'clock". This whole system of situational sentences enables one to express the same thought, with the same truth conditions, at different times, while making use of the time of elocution, in addition to the form of the speech act used, to determine the temporal thought being expressed. — Pierre-Normand
(1) "There were/are/will be Triceratops roaming the Earth" is true iff there were/are/will be Triceratops roaming the Earth.
In this case, "were/are/will be" signals the availability of a system of situatonal sentences. This means that the sentence "There are Triceratops roaming the Earth" could (conceivably) have been used to express a truth 68 million years ago. But, more importantly, it also means that whatever thought would have been expressed back then in that way is the very same thought that we can express now with the sentence "There were Triceratops roaming the Earth 68 million years ago". Hence, the statement of the truth conditions of (the thought expressible by) a sentence doesn't require that there actually be anyone able to utter the statement at the time when its truth value is being evaluated, since we still are able to evaluate the truth of the very same thought (concerning past events) as expressed now with the use of a situational sentence that is part of the very same unitary system that allows the expression of this thought at any time. — Pierre-Normand
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