And you claimed that you asked me a question I didn't answer. — TonesInDeepFreeze
If you can show that equality is something other than a human judgement, then you might have a case. Otherwise the charge holds. — Metaphysician Undercover
Formal languages, including the language of identity theory, are more precise than natural languages. But the point I made was not so much about precision but that 'equality of human beings' in the sense of equal rights or whatever is a very different meaning of 'equality' in mathematics. — TonesInDeepFreeze
True, but I don't mean it.
... Nope. I am not bringing the notion of logical necessity into play. — TonesInDeepFreeze
One can stipulate premises and then infer conclusions. That is not question begging. Also, we don't have to stipulate that Henry Fonda is the father of Peter Fonda, since we can arrive at that claim by empirical or historical evidence. — TonesInDeepFreeze
We prove that 2+1 = 3. Then we prove that '2+1' and '3' have the same denotation by the method of models. I've told you that about a half dozen times now. — TonesInDeepFreeze
If you can show that equality is something other than a human judgement, then you might have a case. Otherwise the charge holds. — Metaphysician Undercover
Formal languages, including the language of identity theory, are more precise than natural languages. But the point I made was not so much about precision but that 'equality of human beings' in the sense of equal rights or whatever is a very different meaning of 'equality' in mathematics.
— TonesInDeepFreeze
These two senses utilize the same principle. — Metaphysician Undercover
now you admit that you do not mean that they are "necessarily" the same — Metaphysician Undercover
What good is such a principle? — Metaphysician Undercover
You judge "2+1" as referring to the same thing as "3", because they are equal, but there is no logical necessity there, which proves that they are? — Metaphysician Undercover
One can stipulate premises and then infer conclusions. That is not question begging. Also, we don't have to stipulate that Henry Fonda is the father of Peter Fonda, since we can arrive at that claim by empirical or historical evidence.
— TonesInDeepFreeze
Sure, in that case we can refer to empirical judgement, but in the case of numbers we cannot, because we cannot sense numbers in any way. — Metaphysician Undercover
Can you show me through your "method of models" — Metaphysician Undercover
To say that 2+1 and 3 are equal is saying that 2+1 is 3.
To say that John and Mary are equal (in the sense of equal rights) is not saying that John is Mary. Rather it is saying that the rights of John are the same as the rights of Mary.
These are very different uses of the word 'equal'. — TonesInDeepFreeze
What do you intend the pronoun 'they' refer to there? — TonesInDeepFreeze
(1) So in the empirical context, your objection was refuted. — TonesInDeepFreeze
(2) In the mathematical context, numbers are not physical objects. And over the course of this discussion I said that we arrive at mathematical conclusions by mathematical proof or by performing mathematical procedures. You are not caught up in the discussion because you ignore and skip. — TonesInDeepFreeze
(1) So in the empirical context, your objection was refuted.
— TonesInDeepFreeze
This is incorrect, because there is no empirical object referred to by "2+1", or "3". — Metaphysician Undercover
Now I'm waiting for proof that "2+1" refers to the same object as "3". — Metaphysician Undercover
You need to read a book or other systematic presentation of mathematical logic in which the method of models is explained step by step, including the notions: concatenation functions, formal languages, signatures for formal languages, unique readability of terms and formulas, recursive definitions, mathematical induction, et. al. And prerequisite would be understanding basic mathematical notions, including: sets, tuples, relations, functions, et. al." — TonesInDeepFreeze
I tend to think it is something you made up as a ruse — Metaphysician Undercover
You tend to think irrationally or not at all. — TonesInDeepFreeze
I can't help it if your terminology is a little off the beaten path. You kept referring to a "method of models", and I couldn't even find that on google. — Metaphysician Undercover
[emphases added]You need to read a book or other systematic presentation of mathematical logic in which the method of models is explained step by step — TonesInDeepFreeze
So you opted to suggest that I'm lying about the whole thing instead of just asking "Would you please provide some links?" — TonesInDeepFreeze
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