I didn't say that subset and set align with the mereological notions of part and whole. Agent Smith said that said set theory allows that a part can b...
If part of one's philosophizing about mathematics includes criticisms of certain actual mathematics, then one should know enough about that actual mat...
What you wrote: So I take it that restricting 'object' to refer only to abstractions is not acceptable to you. Thus, indeed you do not agree that abst...
Actually, you could start by just refraining from making claims for which you have no basis. But if you do want to know more about Cantor's life then ...
Cantor doesn't do that. In fact, Cantor proved that that CAN'T be done. It's his MOST famous result. You have it completely backwards. What articles h...
Yeah, you often ditch an exchange with that arch "Good day" sign off, while not ingesting a single bit of the information and explanation given to you...
(1) By what source do you assert that Cantor "lost his mind"? Cantor had collapses and severe depression. I don't know of any source that says he "los...
No. You're just being glib and not even thinking about what I wrote; just pouncing in an ill considered way about it. First, 'finitist' has many diffe...
That's right. In previous threads I've pointed out that in set theory there is not a noun 'infinity'.* Rather there is the adjective 'is infinite'. Th...
The existence of the set of natural numbers is derived axiomatically. Granted, the key axiom is that there exists a successor inductive set, which is ...
As I mentioned, that is not how it is done. You would do yourself a favor by reading a good textbook on the subject so that you would have a basis to ...
Fine. But it's not easy to axiomatize real analysis that way. One can philosophize all day about how one thinks mathematics should be. But other folks...
Consider the sentence: 'Snow is white' is true if and only if snow is white. That sentence is written in a metalanguage. The left side of the bicondit...
First, there are two different notions of 'the continuum'. One is that the continuum is the set of real numbers R. The other is more specifically that...
The adjective 'is infinite' is mathematically defined in the formal theory, set theory. I have seen no formal theory in which the adjective 'is potent...
In Calculus 1 classes, there is not a concern that the subject be axiomatized. But if we are concerned with having the subject axiomatized, then the o...
What do "the domain of the metalanguage" and "the world of that metalanguage" refer to? You're talking about Tarski. It was Tarski who invented the no...
Confusing fundamental concepts is not mere informality. And any outline based on such fundamental confusions cannot be other than itself more confusio...
'trivial' in mathematics, in the context of this discussion, is not a formal notion. What mathematicians mean is that a trivial theorem is one that we...
Consistency follows from soundness. Proving soundness is not deep. We ordinarily just do induction on the length of derivations. 'inconsistent languag...
We need to be careful not to conflate 'language' with 'theory', or with 'a theory and an axiomatization' or 'a logic' or 'logistic system'. These are ...
If the domain is finite, then an existential statement is equivalent to a finite disjunction, and a universal statement is equivalent to a finite conj...
conjunction and disjunction are analogous with: multiplication and addition in Boolean algebra intersection and union in set theory universal quantifi...
Any sentential formula has an equivalent using a combination of 'not' and 'or'. That is only one of the eight cases I mentioned where 'not' with anoth...
For reference: A NATURAL DEDUCTION SYSTEM: Comment: Unlike quantifier logic with predicate symbols of arity greater than 1, sentential logic doesn't r...
For reference: BOOLEAN FUNCTIONS A Boolean function is function* whose domain is, for some natural number k, the set of k-tuples over {0 1} and whose ...
For reference: LANGUAGE symbols: sentence letters P Q R ... connectives ~ v & -> <-> left and right parentheses ( ) formulas: a sentence letter alone ...
The rest doesn't mitigate your contradiction. I've been through this before with you where you shift your position making coherent discussion impossib...
A few posts ago: Now: We should stop right there. But you also put words in my mouth: I haven't said anything about duality. This is yet another insta...
Sure, you can't conceive of an empty set. But lots of people do. But the problem is more fundamental with you. You can't conceive of abstract objects....
For many months you have continued to post disinformation, even repeating items on which you were already corrected or refuted. That is a pattern not ...
I don't know what that emoticon you keep posting means. / I found out more about the -(1/12) thing. It requires taking the infinite sum in a different...
You skipped my previous remarks about that. If I recall, we discussed this at length many months ago. Again, I don't mean a physical object. I mean a ...
There's lot to unpack there. (1) (a minor point) You were responding to a quote of mine about intuitionism. That's the wrong quote, since the subjects...
No derivation of a contradiction has been shown in ZFC. And you write (I'm using plain text): Sum = inf Sum = -(1/12) As far as I can tell, those are ...
For finite cardinals, if ~x = 0, then ~x+x = x. For infinite cardinals, x+x = x and 2x = x. But you cannot infer 2 =1 from 2x = x when x is an infinit...
I have a minor use-mention quibble with the penultimate sentence, but otherwise it seems to me that he or she gave a reasonable explanation of the ide...
x=x ... reflexivity with (x=y & Px) -> Py ... indiscernibility of identicals (aka substitutivity) is a complete axiomatization of identity theory and ...
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