fishfry

Whatever, man. "suit your (undisclosed) purpose" -- what does that mean? I'm using specification as in the axiom schema of specification. We are talki...

Nice to have an actual mathematician around here!

Only if you change what a specification is. In set theory, a specification is a predicate, a statement that can be true or false of a given item. The ...

Excellent point. In the abstract, no difference. In practice, huge difference. Water is liquid (no pun intended); housing isn't. In a water shortage, ...

Not entirely, but I'm not disagreeing either. Infinitary set theory has been used in the 20th century as the foundation of math, and math is the langu...

They seem to be using multiverse in a more general way, so in that sense you're right. My understanding of multiverse is as in eternal inflation, whic...

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Falsified by Galileo, who asked questions about things he didn't know, and did experiments to find out. For example he rolled balls down an inclined p...

Way above my pay grade. If Sean Carroll didn't make a video about it, I have no idea :-)

MWI is as you explain it, branching due to QM, as an alternative to wave function collapse. The multiverse theory says that the universe consists of "...

Could well be. But for purposes of this discussion, please note that multiverse theory and the many-worlds interpretation are two entirely different s...

The real numbers include some numbers that are in V and many that aren't. In what way does that specify V? That's like saying I can specify the people...

Awfully good catch, thank you. Especially since the footnotes don't appear on the article page and must be clicked on to see them at all. I commend yo...

Ah, the good old daze. That didn't last long. It's the distinction between two linear orders: ... < a4 < a3 < a2 < a1 < a0. There's no first element b...

I'm already in way over my head and know nothing of this other than a couple of Sean Carroll videos on Youtube. My understanding is that MWI avoids wa...

Sean Carroll explains this by saying that the energy splits too. Each world takes with it half the energy of the parent world, so that conservation of...

Two separate cases. If people have more money for rent but rents are capped then there's no incentive to provide more housing. If water is scarce and ...

Look at it this way. If you give every renter in your town an extra $1000 a month, with no corresponding increase in the number of available rental un...

For sake of conversation, would you have made the same argument in the days of the horse and buggy? Do you object to the "Surrey with a fringe on top?...

As do cats. That's a cat joke. But in fact every sentient creature does the same. Cats, dogs, the more intelligent insects. I lived in a rural area on...

You seemed to be reverting back to the Frege-Hilbert paradigm, which is a pointless discussion because there is no right or wrong, just a different wo...

I wish you'd stop holding back and tell us how you REALLY feel about cars.

I'm perfectly happy to stipulate so for purposes of discussion. After all, there are no infinite sets in physics, at least at the present time. So, wh...

I always get into trouble with these philosophically loaded terms. Any number can be broken up into parts. 2 = 1 + 1, 1 = 1/2 + 1/2. So nothing in mat...

Thanks for that link.

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Pay no attention to those million Uyghurs behind the curtain. Would you have said the same in 1935 about u-no-hoo? Asking for six million friends.

But we're not talking "fact," if by that you mean the real world. The subject was set theory, which is an artificial formal theory. Set theory is not ...

Programmers know that distinction as interface versus implementation. It's not a particularly deep idea. If you swapped out a coal-fired power plant f...

If you don't like the way I drive, stay off of the sidewalk!

Like COBOL, "Common business-oriented language," hyped in the 1960's as a way to let business people write their own programs without the need for pro...

If you could give a specific example, your post would be more clear. As it is, I can't figure out what you're saying.

You looked it up rather than tried to figure it out? You ARE a tired thinker! But thanks for the reference, I did not realize the remark originated wi...

Don't gourmets eat a lot of great food, and thereby hone their palates? Don't lovers of great music attend many concerts, and thereby increase their a...

If you had to guess, what would you say?

You know what they say about second marriages. "The triumph of hope over experience."

Is that like a square circle?

There is no criterion. In fact there are provably more sets than criteria. If by "criterion" you mean a finite-length string of symbols, there are onl...

Thank you. I'll get to your second post later, I'm falling behind. Yes. Everything is a set. Or what they call a "pure set," meaning a set whose eleme...

You're very welcome, glad that helped.

Sets can contain other sets. In fact a set is "something" in addition to its constituent elements. It's a "something" that allows us to treat the elem...

Nonexistence is a lot different than being asleep. If you've ever had general anesthesia, that's the closest you can get to "experiencing" nonexistenc...

Of course the reals consist of rationals and irrationals. That's provable from the axioms. Every model of the reals satisfies the axioms of the reals....

I found the SEP article interesting. It breaks down all the various sub-genres of mathematical structuralism and talks a lot about whether category th...

I don't think there are any set theorists here. You're the only mathematician in the house. The rest of us, speaking for myself, are groupies and hang...

Sure. Euclid didn't have set theory but he talked about points. As far as the modern definition of numbers, there's Russell's type theory and its mode...

Thanks, I made the correction.

Ok good. Yes. But that should be no surprise. In set theory everything is a set. There are no urelements in standard set theory. In math every single ...

It's perhaps a little cleaner in terms of exposition. Not a big deal either way.

I answered this in my most recent post to you. Given two ordinals, it's always the case that one is an element of the other or vice versa. So for ordi...