I'm afraid I don't follow this at all. I know of no such instance. The axiom of extensionality depends on the law of identity, which is a principle of...
Well there's an answer to that. We distinguish between time, a particular aspect of the universe, and time as modeled in physics. It's traditional to ...
I am not a philosopher. I am not competent to defend anything I wrote in this thread. Consider it just an idle drive-by post, not to be taken as autho...
That's the old mind-body problem. If there's a nonphysical realm of existence where my mind dwells, what exactly is it? And what else lives there? The...
I'm afraid my knowledge of physics is limited to reading Scientific American articles back in the day, and watching Youtube videos lately. My understa...
I suppose so. But even in PA there are infinitely many numbers. There's just no completed set of them. So they are not formally a proper class, but we...
I certainly agree with you that reality is one thing, and our historically contingent scientific models are another. I don't believe that "the univers...
I agree that mathematical infinity is "true" in the abstract realm of math. But that's like saying that the way the knight moves is "true" in chess. B...
I don't know enough physics to serve as an explainer. I couldn't even find a decent explanation online. For ex "The logical consequence of taking thes...
The point isn't that we can talk about when something happens as well as where. The point is that space and time aren't independent. They're not like ...
There's a straightforward and unambiguous mathematical distinction. The inductive axiom of the Peano axioms say that whenever n is a number, n + 1 is ...
You're smart in one area and a delusional bullshit artist when you talk about things you clearly know nothing about. You got busted. Give it a rest. Y...
LOL. One (you, me, anyone) would need a Ph.D. in set theory and several years of specialized postdoc work, and probably more than that, just to read w...
None of that is remotely true. You started talking about set theory here ... https://thephilosophyforum.com/discussion/comment/317954. Note that YOU w...
Ok so in formalism, we have string manipulation rules that have no inherent meaning. But someone can use them by interpreting them; that is, by assign...
https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics) https://plato.stanford.edu/entries/formalism-mathematics/ Hmmm. What does "mathema...
The even natural numbers and the odd natural numbers are both countable but they're not equal as sets. They're cardinally equivalent, but that's not t...
You're repeating them out of context without understanding. I'm always up for a chat about set theory but this ain't it. Without looking it up, what i...
Why not? May I ask if these are technical terms with which you're familar? You mis-stated CH in such a way as to give me the impression you haven't st...
This is true by the definition of the Aleph numbers. It's not a statement of the continuum hypothesis. I hope we can clarify this if we're going to ta...
This is an interesting comment. I could say, suppose the light switch is in the next room and an evil demon electrician is flipping it? There's motion...
The Alephs aren't fields. Finite fields have absolutely nothing at all to do with this. They're apples and rutabagas. One can Google around. A lot of ...
Cantor thought that the limit of that process, essentially the union of all the infinite cardinals, was God. God is the absolute infinity. Cantor's th...
I'm not sure this is sound. If you turn a light in your living room on and off, you have "day and night," but that's not proof of relative motion betw...
Malthus said that 200 years ago and Erlich said it in the 1960's. Both turned out to be wrong. Why should I believe you today? Of course from a numeri...
Sinking boats and earthquakes support the idea of ecological collapse? What are you talking about? People do get hit by city buses, I'll grant you tha...
We should have stayed in caves? I don't follow your point. I've got 200,000 years of human progress on the side of my argument. You've got 200 years o...
Slow day around here? You did NOT talk about fusion. You mentioned cold fusion, a technology that's never been conclusively demonstrated to work at al...
Other sources. I've been reading up on fusion power lately. You're acting like those people in 1995 who said the Internet was a fad. Keeping up with t...
That's silly. Fusion is a technology currently getting a lot of government and private investment. Experimental fusion reactors are already generating...
Regular old fusion is on the 20 year horizon. It runs on seawater. No risk of meltdown or runaway chain reaction. https://www.cbsnews.com/news/ten-ser...
All of Erlich's predictions were wrong. He lost all his resource price bets. I'd say the same will happen in the future. Human ingenuity will defeat d...
I don't mean for this to sound glib or cute. I am trying to understand your use of the term meaningful. Is discussing the upcoming American pro footba...
Your perspective is interesting. I enjoy his books a lot and also his irreverent and "I'm smarter than everyone else" style. On learning that he has s...
I should quit now! I just wanted to say that in the cold light of day I no longer believe what I wrote last night. If you start with classical math an...
https://plato.stanford.edu/entries/mathematics-constructive/ They echoed many of the things you've been saying, such as that there are several (four i...
I don't know much about the guy. I read today that he once said of Hillary Clinton: She’s got dyed blonde hair and pouty lips, and a steely blue stare...
As I think of it, perhaps a new axiom is an oracle. I understand that point of view. So I'm willing to be agreeable on this point, but still no less c...
Hardy was a number theorist. At the time he wrote those words, number theory was regarded as beautiful but useless. Today it's the mathematical founda...
A line is only one dimensional. A plane is two dimensional. Points are zero-dimensional. How a bunch of zero dimensional points make a line is a bit o...
You mean the decimal representation of a real number? Yes, they're infinitely long. For example 1/3 = .333... and sqrt(2) = 1.4142... and so forth. Ev...
No intrusion at all, I love to talk about the standard real numbers! I'm not sure which part of your question I didn't clarify, I'd be glad to try aga...
In the standard set-theoretic account of the real numbers, the real line is made of points. That is, the line is the union of all the sets that each c...
Yes yes this is the part I understand. Coq is a tool for helping to avoid errors in published math. That was Voevodsky's idea. It's the mystical mathe...
Right. The real numbers are a continuum. The rational numbers aren't because they're not Cauchy complete. The computable reals are not because they ar...
Ok. I will stipulate to being thoroughly confused on this point. But that's ok. I'll stipulate you are correct on this point. I just don't understand ...
Ok that said. This is different from what I understood from the Italian paper, which is that a real number is characterized by (or identified with) a ...
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