Ok, I see that I said something that induced you to write in caps. Before responding to the interesting technical points in your following posts, let ...
I can live with that. In fact I've read something along those lines in some of the constructivist references. The decimal representations (modulo dual...
Ok second my replies to your two longer posts of 6 days ago. Ok true confession I haven't had a chance to look at that yet but it's on my reading list...
Ok, first of two responses to your lengthy posts of page 9. I didn't understand this para but you said your point was half of Curry-Howard so I'll tru...
Ok I read the next two of your posts, and they contain a lot of meat. I want to respond to them but not tonight, it's late here. I will just say ahead...
At the moment I haven't bandwidth to engage with the probability topic. So to roll this back, I made the following claim: Claim: Without the axiom of ...
But yes, it is. It's opinion. What math is, how mathematicians think about and practice math, is under constant change. In a trivial sense a propositi...
Hi @"Mephist" I've been percolating on all this a few days. The insight I'm taking away is that constructivists care about Cauchy completeness. I hadn...
I said no such thing and of course believe no such thing. Is this the Curry-Howard correspondence? Ok I believe I've caught up to your series of posts...
Pretty funny. The statement "Every vector space has a basis" is logically equivalent to the full axiom of choice. So every time I give you a vector sp...
I can't comment on this. But if you haven't understood all along what a computable real is, and that there are only countably many of them, and that t...
But I m not choosing to learn constructive math. How we got onto this was that I made the rather trivial point that the standard reals are the Goldilo...
Ah you don't know what are the computable reals! Why didn't you say so about ten or twenty posts ago when I first mentioned them? The definition is du...
I did not say there are any sets that are not computable but computable in ZF. I neither said nor believe such a thing. Are you saying that's true? Yo...
I see your point. I confused that with the fact that there is no computable enumeration of the computable numbers. To enumerate the computable numbers...
You totally missed or ignored my point. You said that (in ZF presumably) we have computable sets and then we can introduce the axiom of choice to get ...
I can't speak to non-pointed set-theoretic probability theory. I know about ETCS (elementary theory of the category of sets) so I understand that sets...
Your markup didn't render but no matter. I'm talking about the Kolmogorov axioms: https://en.wikipedia.org/wiki/Probability_axioms Here's the argument...
Ok let me pick up my reply to your earlier post here so I am one post behind you. I am paddling as fast as I can through these murky (to me) construct...
Still working on my response to the lengthy final part of your earlier post about whether the constructive reals are Cauchy complete. Such an interest...
Great essay and I've read some of his other stuff too. It's not the kind of thing one must vociferously disagree with. It's in the category of "Intere...
I don't want to get sidetracked into all that but every time I take a look at these ideas, I come away thinking that the physicists have a very differ...
Hi @"Mephist", Thanks for your responses. Ok I've satisfied myself on the use of the rate of convergence in the Italian paper. The short answer is tha...
Hi all. I'm a frequent Trump explainer and/or defender, which can certainly appear like, and sometimes actually is, a measure of support. Nobody wonde...
Read this first, don't waste time slogging through my other posts. This is the heart of the matter. Hi @"Mephist". I didn't read your latest posts but...
Ok, here's my detailed response to your post. But I fear we're diverging, since right now I'm 100% focused on understanding the completeness axiom fro...
I just wanted to jump in quickly and tell you that your lengthy post (1) mostly consisted of things I already know; (2) completely failed to address a...
Sure, just like the ordered field axioms in ZF. If you omit completeness you get the rationals. If you toss in completeness you get the reals. I under...
Not sure what you mean. Suppose I have an axiom system that includes axiom X. Then X is a theorem with a one line proof: "X". Any axiom is a theorem w...
\ No worries. Working out if their definition implies Cauchy is something I can take a run at. Math markup's not hard but it does have a bit of a lear...
@"Mephist" I had an insight. A formula in the Italian paper is the link between what I know and what we're trying to understand. That's this paper: ht...
No. Math is not physics. That seems to be a theme today. In fact whenever mathematicians run into infinities, they do NOT say Aha here's an actual inf...
Thanks man I'll get to this later. I am most definitely worn out for the day. What I did learn from all this is that the computable reals are NOT the ...
Yes but first, that in no way invalidates the fact that Cauchy-completeness uniquely characterizes the standard real numbers up to isomorphism; and se...
Wow. I don't know where to start. That couldn't be more false. Not sure what you're getting at, but nothing I relate to. His work on non-Euclidean geo...
You mean besides relativity and quantum physics? The 't' in the Schrödinger equation is a continuous parameter over the real numbers. What math do you...
I didn't know that. But ok. If HOTT is not constructive, what are we talking about? And now after all this: What ARE we talking about? I no longer kno...
Ok, herewith my reply to Part 3. Ok fine. But now you're spinning off into new topics. I can't keep up with this. I've learned a lot from this thread ...
You'll have to take that up with Chaitin and the mathematical logicians. As it happens, the class of real numbers definable in first-order logic is sl...
I have to defer this for now. You already said you're not interested in the proof of B-T and now you've written a lengthy post about it. The proof in ...
Ok herewith my response to your Part 2. I'm buried in mentions again. Working hard to catch up. I posted earlier a proof that the computable reals are...
I have a lot more to say about this second of your posts (of the four that I'm working through) but I wanted to just catch this up first because I alr...
Well I'm three of your posts behind I think so I'm planning to get to them soon. But I'm not sure what you mean that " I am convinced that what I wrot...
Yes Galileo used his heartbeat as a timer. Ah but no. The continuity of the real numbers are the mathematical model of time. But we don't know for sur...
Little late for that. Thanks for your thoughtful comments. I was against the Iraq war at the time and clearly that's colored my take on current events...
Ah. Good point. They are liberal on social issues. On matters of war, they take the establishment line. That's the whole point. The NYT helped Bush li...
A million people marched against the Iraq war. I didn't believe the bullshit about the WMDs. And if Saddam had WMDs it's because we sold them to him w...
Yes, thanks for mentioning it. That's exactly what fake news is. When the establishment lies the country into war. Cheney, Powell, Condi, Rummy, Doug ...
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