TonesInDeepFreeze

Correct that here 'is' is not for equality but for indicating a predicate. I didn't say anything like that.

I'm referring to the fact that set theory proves there exists a complete ordered field and a total ordering of its carrier set. And then I highlighted...

The imaginary hotelier can do that also.

Infinite summation: convergence of an infinite sequence to a limit. I don't conceive of an infinite set of physical rooms. As to sets, I already menti...

Not as a physical object. On the other hand, I know so little of cosmology that I don't know how to dispel my bafflement that the universe could be fi...

You asked, here's my answer: Of course, definitions are crucial. But how demanding we should be must depend on context. Since, for example, this threa...

Adding to my response about the particular paradoxes. Even if we granted that they indicate flaws in the concept of infinitude, then that is a concept...

I wouldn't argue that we can't. I suppose people already have made logic systems with values such as 'uncertain' that can be be applied to a different...

We do prove "sqrt(2) is a number". More exactly: We prove that there is a unique positive real number r such r^2 = 2, and then we prove that r is not ...

Naturally.

Of course. It's important in the study of propositional logic that we understand that 'statement' is considered only in the sense of declarative state...

I said nothing to suggest that I was criticizing you. You mentioned that there are expressions other than declaratives, which is of course true. (And,...

I think I see now. You didn't mean that Cantor claims that we can list the points in the line, but rather Cantor showed that we can't do that? If you ...

Of course, non-infinitistic systematizations for mathematics are interesting and of real mathematical and philosophical import. And there are many sys...

Your phrasing struck me as polemical and misleading by saying "magic" and "leap", which does not do justice to the fact that set theory is axiomatic, ...

My point is that your description is not an accurate or even reasonable simplification of how set theory proves that there is a complete ordered field...

Yes, those are paradoxes. But my point is that they are not contradictions in ZFC* (and I'm not claiming that you claimed that they are contradictions...

I don't know whether a geometric theory can pick out one particular line and definite it as 'the continuum'? I'm too rusty on the subject. Thanks. Hil...

That's interesting. I'd like to understand more about that. This is my guess how (most?) English speakers think (contrary to the material conditional)...

Where do you find that explanation of the material conditional? The material conditional is that the conditional is false when the antecedent is true ...

In propostional logic, we consider only declarative statements.

Your report is quite confused about these notions. I'm afraid that if one wants to properly understand this subject then one has to read a good textbo...

My main point is that I don't accept your argument of posting in terms of what is "productive" or outcomes ("fanned flames"). Evaluation per what is p...

I say he should learn about the subject so that he'll desist from spewing misinformation about it. He fancies himself a critic of classical mathematic...

First, as I've said ad nauseum, (with exceptions of figures of speech) mathematics doesn't have a noun 'infinity' but rather an adjective 'is infinite...

Quine is always quite the pleasure to read. Church too (for me, the intro chapter in 'Introduction To Mathematical Logic' is the definitive primer). T...

This is interesting. Sometimes I encounter people who say symbolic logic is dogmatic because it demands that 'if then' must be taken as the material c...

I hope I say all this right (I'm pretty rusty): Df. A model M is a model of a set of sentences G iff every member of G is true in M. Df. A set of sent...

But there are puzzles I find with infinite sets in certain aspects of mathematical logic. I admit that my framework of understanding hits a wall in th...

Then there is the heuristic question: What practical advantage would there be in throwing out the methods of infinitistic calculus for an ultrafinitis...

Depends on what 'grasps' means. If it means mentally seeing an infinite number of concrete or abstract objects all at once, then probably it can't be ...

The enquiry can be fruitful. But poorly so if the vines are mangled and torn apart by misinformation and unnecessary confusion.

Of course, Monatague is famous for his work in formalizing natural language. It's an interesting question how much that involvement bears on the intro...

That's addressed to Real Gone Cat, but for myself, I don't think he's pretending that. He doesn't even know what the scope of the rubric 'finitism' in...

What do you mean by "ultrafinitism to be an accident"? I think Agent Smith is sincere that he thinks there should be an alternative to infinitistic ma...

Granted, I didn't just say that Wilderberger is an ultrafinitist but that it is quite missing the point to refer to him merely as a finitist. In my po...

Yet again you repeat your false claim that is refuted by content of the posts.

I'm curious about your take on Kalish, Montague and Mar. They don't give as many examples and exercises as most books, but they do give some. What do ...

That was discussed, but I wish also to state for myself: My comments here have not been mere quibbles. They are important considerations, especially f...

It was apokrisis who first mentioned Wilderberger in this context. Then Agent Smith replied that Wilderberger is a finitist. Then I mentioned that, mo...

Stating my own argument about it. Whether you reply to my statement of my argument about your contradiction is entirely your own prerogative. And, sin...

It had a good point. This thread is about a greatest number. Wilderberger is an ultrafinitist. By pointing that out, we see that he's especially relev...

You are just repeating that falsehood, ignoring that there are actual posts in which I discussed your argument in detail, quoting it and analyzing it ...

You wrote: But I did not call on you, or call you back, to defend what you wrote not did I call on you, or call you back, to do anything at all. But m...

I didn't say it was untrue. I said the generality of him being a finitist misses the most salient point about him that he's an ultrafinitist. And I di...

And now you're flat out lying about my posting. I gave specific analysis, quoting you, and arranging my argument about it in conspicuously clear forma...

You took two months to reply to my post. There is no expiration on a poster's prerogative to reply. That is false. I did not ask nor suggest that you ...

You're joking, right? It's pretty much at the basis of this thread you started. And you ask me without even bothering to type it into a search? You're...

So am I. That's why I usually find emoticons inadequate and ugly. Sometimes they're useful, but yours directed to me strike me as mere insouciance.

That is quite missing the point. Wilderberger, as I glean, is an ultrafinitist. Finitism has a broad range. Hilbert was a finitist, yet Hilbert famous...