fishfry

You retract or stand by your claim that there is no empty set?

If it's not a set, which do you disagree with: The axiom schema of specification? Or that the natural numbers are a set? Does the smiley mean that you...

Are you keeping it secret?

Don't worry, nobody noticed or cares. You only ruffled a feather or two of mine, and I'm easily ruffled. Very few working mathematicians care about fo...

Do you know how to implement 2 and 5? Yes or no?

Someone using your handle wrote: I ask again: How do you implement 2 and 5?

You said you offered suggestions on how to implement 2 and 5. I didn't see them. Changing the subject doesn't answer my question. How do you implement...

Ok. How do you implement 2 and 5?

Because nobody knows how to implement 2 and 5, or even if it's possible to do so.

So what do you make of the set \{x \in \mathbb N : x \neq x \}? You reject the axiom schema of specification? You don't think \mathbb N is a set? I re...

I found this but I don't know anything about it beyond Googling around.

\pi is no longer defined geometrically. Here is the modern analytic definition. First you establish the theory of convergent power series in one compl...

I'm not personally in accord with this point of view. The relationships among category theory, set theory, various flavors of type theory, and other c...

From what I've seen, constructivists typically allow weak forms of choice, for the reason that otherwise you can't get satisfactory math. So it wouldn...

Now that's something I've never run across. Both too big and too small at the same time. But it takes a weak form of the axiom of choice to have a non...

You were already clear. I reviewed the wiki article on subcountability and nothing you said caused me to change anything I wrote. https://en.wikipedia...

Let us know when you've figured out how to implement 2 and 5.

You reject all formal systems not based strictly on physical reality? Do you drive on the correct side of the road appropriate to your jurisdiction? T...

The computable numbers are countable. That's because the set of Turing machines is countable. Over a countable alphabet there are countably many TMs o...

Happy to put this into perspective. First, this is a philosophical message board and not a mathematical or a general purpose on. It's natural that whe...

Were you like this when you learned to play chess? "This is the knight." "But no it's not REALLY a knight. Real knights don't make moves like that, th...

I'm not sure exactly what you're looking for. To my knowledge, and I'm no specialist in these matters, the second-order theory of the real numbers is ...

Didn't Plato point out that what we experience is but shadow on a cave? And that the true reality lies outside, unseen and unseeable by us? But is wha...

Too few, clearly. There are only countably many of them. I do apprehend the point that the computable reals are computably uncountable, since there is...

Whatever you do, don't tell @"Metaphysician Undercover". This information upsets him terribly.

Ok. But isn't he conflating human experience with reality? He's right that for humans, the present is an experience of flow. But we have no idea what ...

To add to the Wiki quote, something I mentioned earlier: The hyperreals are not Cauchy-complete. No non-Archimedean field can be. Which leads to one o...

That seems unduly restrictive. By that criterion you would have rejected Riemann's non-Euclidean geometry in the 1840's because it was so obviously un...

Wait, what? That's two things. The thing that exists and the number one. If a thing exists and there's no conscious entity around to comprehend it, th...

You invoked the extended real numbers and claimed it has something to do with L-S, which of course it does not. Unless I misunderstood your point.

Thanks. That would make sense. Physics would get more difficult I imagine.

It means essentially that CH is equivalent to the fact that all models of the hyperreals are isomorphic. The idea is that the particular model of hype...

Makes sense. I've never met any besides here. Must not hang out among the right philosophers. I can certainly see Peirce's objection that a true conti...

I've previously called your philosophy mathematical nihilism, and once again you confirm it. You start by saying you don't believe in the empty set; b...

Ok you're right. Closets and empty grocery bags aren't really on point, even though they can be helpful visualizations, such as a grocery bag containi...

That witless twit Prince Charles flew 16,000 miles in private jets in eleven days before posing for a photo with Greta. That's what turns people again...

A closet is an enclosed space in which I hang my clothing. One day I remove all the clothing from my closet. Do I still have a closet? Do I not in fac...

I only get these feelings when @"Mephist" is trying to explain something to me.

LOL. @"Mephist" was making the point that one can do "set theory without elements" as in Lawvere's elementary theory of the category of sets, which un...

Who argues that, exactly, besides the Peirceans on this forum? I've actually never run across this point of view except for here. And how does that sq...

Ah. Thank you. That was very interesting and helpful.

So THAT's how it happened.

If you have a set that includes itself as an element, you're no longer in the realm of standard set theory, in which self-membership is forbidden by t...

Oh I see. Good point. Funny but it never occurred to me to be confused by that. The tangent planes are conceptual thingies attached to each point but ...

That's the intuition I'm working with at the moment, special case that it may be. Yes I just checked that out. I'll keep searching around for an insig...

I stand by my remark. The tangent bundle of a sphere is most definitely a fiber bundle. https://en.wikipedia.org/wiki/Tangent_bundle Can you give me t...

Have you seen any of the movies Minority Report, Blade Runner, Total Recall, The Adjustment Bureau, or A Scanner Darkly?

Ok I will have a look. Many links have been posted recently. Can you repost the one you want me to look at please?

Not clear to me. I literally and honestly did not understand what you said in this post. Perhaps it's a lost cause. A fiber bundle is like the collect...

There's one decimal place for each natural number. A decimal expression .abcdef... means a/10 + b/100 + c/1000 + ... There's one place for each negati...