TonesInDeepFreeze

In that context, I don't mean 'system' in the sense of axioms and a theory. I mean it in the sense of a tuple with a carrier set with a distinguished ...

Of course. There is only one set that has no members. That it is called a 'set' is extraneous to the formal theory. The formal theory doesn't even nee...

I'm out of time, probably for a while. But one more tidbit. Some remarks here made my wonder how (using only first order PA (and theorems I already kn...

Of course, one may adopt a thesis that mathematics should only mention what can happen with a computer (call it 'thesis C'). Then, go ahead and tell u...

And one more detail: The von Neumann characterization, which has been standard for a long time now is: The set of natural numbers is the least success...

Here's what we have: A putative description of an imaginary world (which is not a physical world). The description is not coherent, since it posits th...

Ha! I hadn't read this until just now: https://plato.stanford.edu/entries/spacetime-supertasks "Benacerraf (1962) pointed out description of the Thoms...

I just now recognized that it's 'Thomson' not 'Thompson'. It's an important point, since it and the alternating states are what makes Thomson's lamp a...

You tendered the notion that infinite sets are empty. I said that's a contradiction (more exactly, it's inconsistent). Then you replied that if set th...

We both think that, but you're wrong about it and I'm right about it. I have mulled over your remarks a pretty fair amount. I have turned them around ...

You don't know what you're saying. ZFC uses a method of definitions such that no contradictions can be introduced through definitions. ZFC could be in...

Points are not "nothingness". I exactly stated it as regarding Thompson's lamp. There is no geometric series in my writeup. I said nothing whatsoever ...

You have a framework. You don't have a hint of an idea how to make it rigorous, but that doesn't disallow that nevertheless it might suggest an intuit...

Some of your quote links are not going to the posts in which the quotes occur.

You answered the question. You're not serious. You asked me about finitely many points, not about potentially infinitely many points. Be clear. I bet ...

I said that one my choose whatever axioms one wants. That does not imply that there are not many mathematicians who choose axioms on the basis of thei...

And that is misleading. First, at least it is misleading formatting. The items are from very different parts of the paper, and not a list he made, as ...

That's good. You started out in this thread pretty confused. Hopefully some of the comments from posters have helped you. . The details I have mention...

I really appreciate that. It means more to me than you might think. Thank you, jgill.

$ The worst crank on this forum claimed that I lack training in philosophy. (1) I did not say I have not studied philosophy. In philosophy, I am not a...

You have it backwards, and show that you didn't bother to read my previous post about modelling. The realm of the paradox is not a model of the mathem...

No, because mathematics shows how to calculate that Achilles did finish the race. You just keep showing that you don't care about understanding any of...

You asked me about Thompson's lamp. I replied about it, now with rigor. If you then just jump to another subject (and you're incorrect about it also) ...

You're not being reasonable. Do you want to inform and enlighten yourself about the subject, or you just want to raise objections premised in not know...

I think I've said it about two or three times. It is important because it is the very heart of the matter, which is that set theory axiomatizes the ma...

If I understand, your view is that by doing things that are not right, one become habitual in doing things that are not right, thus harming one's char...

One can propose whatever axioms one wants to propose. That doesn't entail that mathematicians propose axioms willy nilly or in an undisciplined way. I...

That's a classic '50s movie, 'Blame It On Bourbaki'. Cary Grant and, if I recall, Anita Ekberg. Grant's character is trying to get Ekberg's character ...

I'll say it again (as this is certainly not a mere "detail"): The schema says that for any sentence P, we have: 'P' is true iff P. He does not say tha...

They are critical details. And I also posted about matters that are not mere details. And you went right past the very critical substantive reply to y...

It's just the ordinary sense here. And that is supported by the fact that it was Tarski himself who specified how symbols of the object language map w...

Thompson's lamp. It's a non-converging sequence. Set theory doesn't have a "final state" with that. But here's what set theory does have: Let N = the ...

I don't know whether platonism and/or variations on platonism are the majority view among those who have a view, but I wouldn't bet against it. In tha...

Cool. The formulas can be about whatever you want them to be. Hilbert's tables, chairs and beer mugs.

Depends on what you mean by 'manipulate'. Set theory, most strictly, is a certain set of formulas. In mathematical logic, when we say 'ZFC' we are ref...

Day one of high school Algebra 1: "Students, we start with the set of real numbers and the real number line." And you don't have to tell me yet again ...

I'm answering very quickly, because I'm out of time now. We proved they are a complete ordered field. I answered that in exact detail in a previous po...

I just now watched this video by Wildberger: https://www.youtube.com/watch?v=U75S_ZvnWNk In that video, he's an intellectually disorganized, sneaky, w...

Just like you can't do very much math without relations. But with just one relation* you can do it all. * membership

What could possibly be more pressing than people getting their satellite dishes on the roof to watch reality TV shows of people eating bugs?

If it is recursively axiomatized and has enough of arithmetic, then if it is consistent then it is incomplete (which is to say that if it is complete ...

Many years ago I was watching the Academy Awards (don't ask me why I would waste my time that way). Whoopi Goldberg was at the microphone, and she sai...

Si. I've told you about a million times already, you can have axioms for whatever you want*, even inconsistency if that's your thing. * 'ceptin someti...

My favorites are cranks who say that mathematical logic, even just sentential logic, is all wrong, as they are typing and reading on computers that ar...

Communication is bad because 'communication' is from the same root as 'communism', which is bad because communism is Marxism, which is bad because Ric...

Couldn't there be something wrong with you?

Mathematicians come up with general formulas, involving pi and other irrational numbers. Isn't it the case that engineers make use of those general fo...

Stick with your earlier theory that irrational numbers are bad because 'irrational' also means illogical. That one is a doozy.

Now that you've explained some of your terminology (I had no way of knowing that, out of the blue, you would be using category theory), I'm going to r...

You seem to be either (1) Using your own made up ways of talking about this or (2) Speaking in a different context from me. If we don't agree on how w...