fishfry

Newton either. LOL. This was an old thread!

Neural nets run on conventional computers. They're a clever way of organizing data mining, but they are not a new paradigm of computation. They are ph...

An algorithm can never be creative. In particular, there is no hope whatsoever that the current big data and machine learning approach to AI can ever ...

Masochist: Beat me. Sadist: No!

Never helps. Agree. I'm reminded of the blitz, when Hitler's Luftwaffe bombed London every night for eight months from 1940-41. If it happened today, ...

Yes. Here's one striking example. There's no proof that serotonin insufficiency causes depression and mental illness, yet millions are on SSRIs. These...

:up: :up: :up: :up: :up:

Reminds me of Calvinball.

Yes but your (3) is under the heading that says: "Gödel apparently characterises the syntactic view as consisting of three requirements:" So he is cha...

@"TheMadFool" This is also a good link if you're interested.

Wrong article. The Wiki page on "constructible sets" has something to do with topology. Different usage. This is the relevant page. https://en.wikiped...

Above mine too actually. My point was that Gödel apparently believed in an expansive view of the set-theoretic universe, and that his Platonism was pr...

My sense is that these mundane physical considerations were not on Gödel's mind. He believed in the Platonic existence of abstract sets including larg...

Ok, I think we're all clear and in agreement then. We can start with the inference rules of ND, and, one-by-one, introduce as assumptions the standard...

I found an answer on math.SE which you may or may not find satisfactory. See the checked answer by Asaf Karagila. I'm repeating it verbatim here: http...

Yes but there are no axioms in any deduction system. First you have the rules of deduction, then you add in some rules of set theory, say, and you cra...

Indeed. It was Hilbert who said, "Wir müssen wissen – wir werden wissen ("We must know — we will know."). And as I recall. it was either a few days be...

Ok I waited a bit. I did not understand ND from its Wiki page. But I did completely understand it from the Google description: To prove P implies Q, I...

Ok. I Googled "natural deduction as basis for math" and the following popped up right at the top: Now this is just what I call perfectly normal mathem...

I don't know, I'm asking you. I don't know anything about it other than that it comes up when students are discussing logic. I glanced at the Wiki art...

I no longer have any idea where you are going with this. I am sure the fault is all on my side. I can't respond intelligibly because I just don't know...

Math uses axiomatic systems, period. I didn't study much formal logic. Yes but the subject of the OP is axiomatic systems in math. Not that threads do...

I thought we were talking about math, not logic. At least the OP was about math FWIW. Is ND offering an alternative foundation of math? Is it somehow ...

Now you really have me confused. What does that mean? Can you give me an example? You honestly have me at a loss. The entire conversation is about axi...

Yes but no nontrivial collection of axioms (strong enough to found the usual arithmetic of the natural numbers) can be complete. The claim that all ma...

Yes that's my interpretation of all this. I'm basing it on my prior knowledge that Gödel was a Platonist and held that the continuum hypothesis has a ...

This is exactly the view that Gödel opposed. He believed that mathematics is objective; that mathematical truth is something that we study, not someth...

How do you suppose that looked in 1945 and into the 1950s? Perhaps you don't remember the "duck and cover" drills that schoolkids did in anticipation ...

I did start reading a bit, and found this nugget: I shall definitely remember this the next time I cross swords with yet another neo-intuitiionist or ...

I'm entirely in agreement, except that this is the exact discussion that disappeared overnight. I don't want to repost it and upset whoever got upset ...

I would like to re-post the part of the discussion that I was interested in: Namely, does the expansion of space take place everywhere, including betw...

Perhaps I misunderstood. You said: But in fact that's an accurate account of a position Gödel is refuting, not thinking. Are we more or less in agreem...

The article describes Gödel's account of the "syntactic view," as it clearly states. From the article you linked: "The argument uses the Second Incomp...

I'm reminded of Richard Feynman's great essay, Los Alamos from Below (pdf link). It's about his time working as a low-level scientist at the Los Alamo...

LOL. Me too.

I'm going to let you have the last word. I'm out. But for the record, can you please name the specific individuals involved in this deception? We need...

But enough about women's beach volleyball! Or is that, butt enough?

A philosophy crank is more like it. You have zero familiarity with the 20th century literature on the philosophy of set theory. You haven't read Maddy...

As opposed to the rest of us ignorant cattle. It's striking how often these kinds of lofty sentiments eventually come down to raw elitism. That's why ...

Do you like James Howard Kunstler? He's a proponent of downsized living. His novel is called, "A World Made By Hand." Good essayist. His main thesis i...

Yup. That's how it works. The wealthy can buy politicians and lawyers. The poor have no money. That leaves the working stiffs to pay for it all.

Which math gets prioritized is of course a matter of historical contingency. Set theory in the 20th century, maybe category theory / type theory / top...

Rather than try to understand set theory on its own terms, you just want to fight with it. Why? I'm taking the trouble to explain it to you, on its ow...

This has murky and unclear relevance to what went before in the same post. I can't tell if you are trying to explain something to me or promoting an a...

As I understand it, cities in the late 1800's had streets covered in horse manure and didn't smell very good in the summer. It's easy to romanticize t...

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?...

I've already agreed numerous times that if you insist on your own definition, you're right. You can't convince me that your way of looking at it isn't...

What's trivial is saying that the Vitali set is "specified" because all its elements are real numbers. That's like saying the guests at a particular h...

Yes ok I meant assuming the negation. But if you don't specify one or the other, you're right.

Is Z supposed to be Zermelo set theory? In Wiki they call it Z^-, is that the same thing? https://en.wikipedia.org/wiki/Zermelo_set_theory Why do you ...