TonesInDeepFreeze

That is not an insult but "ignorant and confused" is?

Did someone say that the axiom of extensionality "states identity"?

See above post.

Of course, you can't deal with the plain fact of the record of posts, which document not only that you've been lying (which itself is insulting) but w...

Again for the crank: There are different orderings on sets. There is no such thing as "THE" ordering for sets with at least two members. There are oft...

Look at the links and my remarks about them.

That is ridiculous. You accused him of exaggeration. That's not simile or metaphor. So you exaggerated, not him.

First, you lied that earlier I began with ad hominems. Second, you skipped my reply about that my arguments are not ad hominem, but rather I give argu...

No, I don't speak on his behalf. I speak on my own behalf to say that it is a plain fact that Banno did not exaggerate by saying 'hundreds' but that y...

I posted the links. That's the evidence. The logic is pretty much inferring that what is posted at the links says just what it says.

Order has nothing to do with this. An ordering is a certain kind of relation on a set. The axiom of extensionality pertains no matter what orderings a...

Any time. Thank you.

The crank is ignorant and confused about identity theory and the axiom of extensionality, so this at least is reference for how they actually work in ...

I really hope you get well soon.

The leap is in the form of axioms. Just to be clear, the logic system itself is not contravened. Rather, we add non-logical axioms. We add axioms that...

Don't know that book, but Ax x*0 = 0 is an axiom of first order PA, so it's easy to prove x*0 = 0 and in set theory, the PA axioms are theorems. / It ...

I read most of 'Fashionable Nonsense' quite a while ago. There were quoted examples from certain writers. If those quotes were in fair context, then i...

Mathematical logic at least explicates symbolic logic, and symbolic logic is useful. We are all typing on computers whose invention and development ar...

Another episode from 'The Adventures of the Crank Metafizzled Blunderbound in the Land of Daily Life': Support Rep: Hello, thank you for calling MetaC...

Still picking up after the crank's daily littering: The axiom of extensionality is not used to prove axioms. Rather, the axiom of extensionality is us...

Which is to say, he cannot do the impossible.

The cranks says, "Tones told you 'don't to listen to that machine it doesn't support me', or something like that." Again, the crank LIES about me. I n...

In mathematics, there are 'points of infinity' (which are not necessarily infinite sets), and the expression 'to infinity' (which is a figure of speec...

Along the lines of "Bad publicity is at least publicity".

The axiom of extensionality is not inconsistent with identity theory. Here is the most trivial model of both the axiom of extensionality and identity ...

In this part of the discussion, as in some recent posts, that is not directly about what mathematics itself in fact says, I am not trying to convince ...

Make an appointment with an ophthalmologist.

Why do you hope that many people want your posts to be monitored by the moderators?

Crank: I want six plus two cans of that delicious abstraction-free metaphysical underground crank juice. Shopkeeper: Here you go, eight cans of crank ...

That's enough for now in reply to the star crank. It's just too laborious to correct every one of his confusions. Several years ago, I moved to an apa...

'1+1' does not equal '2' '1+1' is not '2' the denotation of '1+1' equals the denotation of '2' the denotation of '1+1' is the denotation of '2' 1+1 eq...

He did not say that anyone is wrong merely by the fact of disagreement.

And that quote doesn't support the claim you made that mathematics regards 'infinite' as meaning 'finite'. Though, lately, you say that claim is only ...

The quote above, written to Banno, is exaggeration thus distortion. Banno didn't say that you have made claims by quoting hundreds of philosophers..

That's an interesting idea.

Who are those many people?

Did Banno ever say or imply that he believes that?

You're confused as usual. I didn't say anything about your view of infinity regarding the book. Rather I note that you challenged me to show you a boo...

That is false, since you didn't say that you lied but you did lie. The plain record of the posts in this thread prove that you lied, as I explicitly l...

When you said that you base on philosophy of mathematics and mentioned Putnam in particular, naturally I thought you meant that you base on views of P...

That deserves consideration, though I'm not sure about it while also I don't have an argument in disagreement to give at this time. What is a concrete...

One may discuss its philosophical implications, but the proof itself doesn't require a philosophical interpretation. I am not familiar with the notion...

I have addressed that so many times in so many threads. Maybe earlier in this thread too.

Got it. Thanks. I say that without prejudice to the question of whether the mentioned postmodernist philosophers do or do not understand mathematics a...

How one regards the significance of formal proof and formal theories may be philosophical, but the incompleteness proof itself about formal theories d...

I don't opine on those. Though, of course, certain concepts that are basic to certain areas of mathematics are not even universally known, let alone u...

Is that a rhetorical question meant to convey that Descartes and Leibniz knew little about mathematics? Or is it meant ironically to say that indeed t...

If I recall correctly from my readings about this, Godel did not arrive at realism until long after he proved the incompleteness theorem. In any case,...

Was the axiom of reducibility used in the proof?

Equals, not merely equivalent to. Was it approximately 1000 pages or closer to about 360? Also, the proof is mentioned near the end of the book, but t...