TonesInDeepFreeze

It doesn't.

You are inference impaired.

I read it. She doesn't say anything on page 4 about set theory not being proven. At an earlier point, she does mention that the continuum hypothesis i...

I didn't write that. I wrote: I don't know what snagging you think there is. You made an unnecessary rally about the matter even after I gave you ampl...

Then you're ridiculous.

It's basically what I said when you first took exception:

Since you stooped to a cheap shot with "Is English not your first language?", I'll do you the favor of correcting your English: it should be 'its' the...

It's a fair paraphrase. If you misunderstood me, then I would have been better just to quote her : "Finally, the whole situation might be interpreted ...

I don't see anything there about set theory being unproven. I don't know what sense of 'unproven' you have in mind. The theorems of set theory are pro...

At that point in the book, she is entertaining the idea that talk about infinite sets is not to be taken seriously. Of course, the book is a presentat...

I didn't say that it is her view that talk about infinite sets is not to be taken seriously. I said that she mentions that the difficulties '"MIGHT" b...

Page 3, last paragraph.

Yes. And other than that, in the Introduction, I don't know what you mean by "It might go the same way it came".

Perhaps you have in mind her idea that difficulties in the question of whether infinite numbers are discovered or invented might be taken as evidence ...

What do you mean by that? And are you referring to her book 'The Philosophy Of Set Theory'? If so, what in particular do you have in mind from that bo...

In ordinary English, we use these senses: (1) A count is an instance of counting. "Do a count of the books." (2) A count is the result of counting. "T...

Those are utterly basic to the subject. If you don't even know what proof is, then you can't very well explain whatever alternative system you have in...

You're lacking not just all the formal details, but even a coherent outline. Again, you can't assume that there is bijection from M onto PM. You are p...

No, let's not say that 1 is the thing counted. The things that are counted are, in this case, the books. '1' is a numeral. 1 is the number denoted by ...

What is the first line in each of the below proofs that is not allowed in layer math?

Note: In my previous posts, anywhere I mistakenly wrote 'level' I meant 'layer', as I guess would be obvious anyway. That stands without your response...

I would guess that layer logic does disprove contradictions. That is, layer logic disproves all formulas of the form 'P & ~P' (where they "reside" (or...

No, neither 'indirect proof' nor 'proof by contradiction' are correctly applied to those proofs, as they are not of the form: Show P. Assume ~P Derive...

Now that you've somewhat clarified that, here's the best I can make of it (I don't claim to represent what you have in mind, but this is the best I ca...

I had said in the very post to which you now replied, "Of course the notion of 'one' is related to that of a unity." So I couldn't possibly be in deni...

If you have in mind the famous proofs regarding a universal set, uncountablity, incompleteness, Tarski's theorem, and the halting problem, then these ...

One can say 'Everything I say is false'. But one can't say it without self-contradiction. (By the way, for purposes of paradox, it's clearer to refer ...

I can't make sense of your essay - from the very start where you begin by flinging around terminology used in a personal way but that you don't define...

So your argument outline is: If someone wants P, he is reminded that P contradicts Q, which he might also want, so we think about a way to adjust so t...

I understood that; I thought you meant that you do want to take '2' and '3' as representing a type of unity, while you think that that is contradicted...

Yes, as I thought, you find that there is a problem with the notion (whatever it means) that 'the numeral "1" represents a basic unity. an individual....

I thought you meant that there is a fundamental problem with: "The numeral "1" represents a basic unity. an individual. The "2" represents two of thos...

The post to which you responded didn't say it. So would you please link to a post or reference anything on the Internet or anywhere else?

What are the primitives of your system? What are the formation rules?

Whose concept is that? Where can I actualy read anyone explaining the concept of numbers that way?

What exactly do you mean by "go towards 0 and infinity"? And who apparently says "oh well" in this context?

1. Set theory does not have, in this context, formal terms 'actual infinity' or 'completed infinity'. So for formal concerns we don't need to vindicat...

Probably the particular formulation of Russell and Whitehead became less used in comparison with the arguably more straightforward approach of axiomat...

Just to be clear, the existence of a set whose members are all and only those sets that are not members of themselves is ruled out by first order logi...

Cantor's diagonal proof is intuitionistically valid.

So you opted to suggest that I'm lying about the whole thing instead of just asking "Would you please provide some links?" Another example of your jej...

You tend to think irrationally or not at all. Below are some articles and a couple of online books. For a more systematic study, if I recall, earlier ...

Those are concepts instrumental to a firm understanding of the method of models.

I think it is eminently helpful to point out to people not familiar with mathematical logic that proof is relative. I mentioned it myself about the Bo...

It seems it wasn't an article but something from a lecture. In any case, I would allow him some liberties when the purpose is to have some rhetorical ...

That Godel was a platonist supports your opinion that Boolos's rhetorical lark is wrong and meaningless?

It is meaningful. People who understand that proof is relative, and who are already familiar with incompleteness, might appreciate that a brief spoken...

One source says that the bit comes from a lecture he gave. It might have been a lecture for logicians and students who would understand that he means ...

Cantor's proof is not a reductio ad absurdum. Cantor's proof can be outlined: Show that there is no enumeration of the naturals onto the reals. Show t...

Boolos says that he means proved by "the aid of the whole of math". My guess is that he means ZFC, which is ordinarily understood to provide an axioma...