fishfry

Is it possible that you're not always as clear in your meaning as you think you are? Can you see that it's possible that this is not my perception? I ...

We're quite in agreement. We tend to talk past each other and I'm content to leave it at that. I'll concede that point. But if you adopt as an axiom c...

Abortion should be legal to age 21 or so. Would solve a lot of parenting problems. Now for a serious answer, or at least a response if not an answer, ...

You haven't convinced me of your point in the least. Perhaps we can mutually agree on at least this. I'm always for achieving agreement.

Contradicts axiom of infinity. What's a particle? What's mass? These are axioms, remember? Everything's defined in terms of a single primitive, \in. Y...

I embarrass myself all the time around here. Thanks for the kind words.

So that I can understand what you mean, can you give an example? What kind of axiom would we add to set theory that would be an axiom for physics?

It doesn't work that way. It's true that physics "uses" the real numbers. And it's true that the real numbers are formalized using infinite sets. It d...

I'm with you on this. It's fine to have a button to like a post, but when you gamify discussion sites, they go downhill.

Much appreciated.

Right. Just like mathematicians can't fly by flapping their arms. The rules of chess are arbitrary and constrained by physical law, as are the axioms ...

Of course that is vacuously true, since there is no axiomatic formulation of physics. The axiom of infinity is inconsistent with known physics since t...

nite set of particles or that physical space extends infinitely outward or whatever. If an inductive set that's not physical "exists," what does that ...

I don't know anything about physics. Nothing I've said here pertains to the physical universe. 2. If infinite energy is applied on an object, that obj...

You would not have begrudged me then, but you will begrudge the living bejeebus out of me now? LOL. Does the phrase, "Give it a rest," have any resona...

I am on record as holding that the axioms of set theory are neither true nor false, as they are syntactic entities whose truth or falsity can only be ...

I used a figure of speech called hyperbole. You pointed out repeatedly that what I said was not literally correct. I conceded that "plenty" of mathema...

I have conceded the word "plenty." I can't continue to argue with you about what (a few, some, many, a strong plurality, a majority, an overwhelming f...

Well then I don't feel bound to justify them. I'll let you have the last word on almost all of this. The one thing I'd like you to explain to me is th...

The axioms aren't false, either, any more than the way the knight moves in chess may be said to be true or false. It's just a rule that's been found b...

Which requires the existence of an inaccessible cardinal, the existence of which is not even provable in ZFC. We're arguing over what other people thi...

My sense of the matter is as follows. The overwhelming majority of working mathematicians are not set theorists or involved in foundations. They pay n...

Ok, so the conversation is shifting now to arguing about what we've been arguing about. Slow day at Chez fishfry, so I'll play. But full disclosure, m...

That's pretty cool!

Glad you found some of this helpful. You talked about a lot of things here I'm not qualified to comment on, but I wanted to go to the end and respond ...

I appreciate your corrections, some of which were on point and some, in my opinion, perhaps not. If I was too sensitive when I read your criticisms, I...

I responded to all of your points but then thought better of it. My challenge was to write something that would give a high-level overview of a diffic...

To put it into context, it takes a long time to get one's mind around even the basics of the ordinals. If you think of my article as kind of a high-le...

Large cardinals require additional set-theoretic axioms, correct. That's the definition of large cardinals. No. Everything we've discussed is provable...

That's the point. I aspire to clear understanding myself. It's an ongoing process.

I emphatically disagree. I wrote my post so as to not need much background at all; pretty much the basics of infinite cardinalities as vaguely underst...

Yes but the same order-type, which is how we define an ordinal. Every possible permutation of a three-element set has the order type of the ordinal 3....

“Infinity” is fully synonymous to “unlimitedness”. One hears this a lot since it's a dictionary definition. But it's not the mathematical definition. ...

I'm not sure what you mean by in-order. Do you mean in its usual order? No. A well-order is an order in which every nonempty subset has a smallest ele...

Are you referring to Cantor's absolute infinite? The point is that the class of all ordinals is not a set. Well that's not my point, it's just a fact ...

Not sure I understand the question. The ordering is given, we don't have to find it. Like the usual ordering on the natural numbers: 0, 1, 2, 3, ... W...

Such a great question. Thank you for the inspiration. I didn't want to hijack this thread with my lengthy exposition, so I posted it in the Math secti...

Just passing by late at night, not following the convo lately. The theory of eternal inflation is a speculative physical theory that posits a a multiv...

You just need to stretch your imagination. Think of each of 0, 1, 2, 3, 4, ... where you can always "add 1." Then think of all of these together in on...

Terrific question. I'm working on a response. I can make it simple but I can't make it short. Anything I write is going to be grossly off-topic to thi...

I describe this as "knowing" versus "knowing about." To know brain surgery takes a lifetime. To know "about" brain surgery takes about thirty seconds ...

Maybe God put all these ideas in your head. I can never understand the mindset of people who use logic to talk about the existence of God. God exists ...

I disrespect constructive math all the time. Actually over the past couple of years a handful of constructivists showed up here and I had interesting ...

Didn't read any more of the thread than this, only jumping in with a mathematical correction. In math there are quantities that are larger than any fi...

I do not believe you have correctly stated Diaconescu's theorem. (Didn't think I knew that one, did you!) I quote from Wiki: So AT BEST, AC implies LE...

Ok ... We can know for certain that a pseudorandom sequence that we generated from an algorithm is not actually random. But given an apparently random...

I'll join you for a hot dog and a beer.

I was just reading about the Frege-Hilbert dispute. As I understand it, Hilbert was saying that axioms are formal things and it doesn't matter what th...

I foresee big trouble with this definition or my name's not Gottlob Frege. Well my name's not Gottlob Frege, but Frege proposed the same definition. T...

That, I believe. It's a small point. But you initially made an absolute statement, and you then qualified it as a relative statement after I pointed o...