@PeteJ, I've glanced at your site and clearly you have written a number of articles and you're thoughtful and serious. But at least based on your comments here and in my brief scan of your continuum paper, I detect a maddening vagueness and lack of specificity. You make generality after generality and never anchor your claims in specifics. I get the feeling you are lacking in peer review or any kind of feedback. I have respect for your work, and I'm especially impressed that you read through Weyl's Das Kontinuum. I do not want my remarks to sound like cheap message board sniping. But you have simply not convinced me of your point of view. In fact you've convinced me that you have not done your homework. I hope you'll take my remarks as pointed but constructive criticism.
[ps] -- Writing this after my post is complete. I know I have a particular style ... I can come off as critical past the line of civility sometimes. I want you to know that if I didn't find your ideas interesting, and if I didn't
desperately want to understand you, I wouldn't have bothered at all. I would like to better understand the meaning of Das Kontinuum, which I confess I've always wanted to read but never have.
So please, just accept my word that my criticism is my
struggle to understand you. I want to understand the Weyl viewpoint. I know he and Brouwer were having very deep thoughts back then, and that these thoughts are now
re-ascendant in the world by way of neo-intuitionism, constructive math, computer science, Curry-Howard, Homotopy type theory, computerized proof assistants, and all the rest of the startling modern developments in foundations. So believe me, I know there's something there. And I'd love to understand what it is you're talking about. You're relating intuitionism to deeper ideas in philosophy. I'd like to understand that.
You know, if you think of me as decently knowledgable in math but a total philosophical ignoramus, that's not too far from the truth. When you say that set theory has to be an extension from from deep formulation and without such a thing the world can't exist, I think you are really far out there, man. This stuff means a lot to you but it's way over my head; and the parts I do understand, seem false. Like needing a metaphysics in order for there to be existence. Surely the world is prior. Unless I misunderstand you.
I'm just trying to understand. That's where my response is coming from. Now I'll just let 'er rip.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
There are many. Zeno has a go at proving this. Are you really not aware of these paradoxes? If not I'll find a couple of references.
Zeno?
Zeno?? All this is about Zeno? Ok, I'll play. Please pick any one of Zeno's several paradoxes -- pick a specific one. State your thesis ("Reifying the real numbers is bad metaphysics" or whatever -- please state a clear thesis so I do know what you are saying), and show how any one of Zeno's paradoxes supports your thesis. I must say that I find this remark of yours trivial in the extreme. I was expecting something a lot more subtle. But I'm willing to hear you state your case and clarify your thinking.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Russell didn't manage to do it so it can't be easy. What is the fundamental set?
I said that set theory is fundamental to math and math is fundamental to physics; and you ask "what is the fundamental set?" That's a disingenuous remark, playing some kind of word game instead of engaging with what I wrote. But since you ask, every set used in mathematics can be built up starting with the empty set and taking successive powersets. This procedure is the
von Neumann universe of sets. It contains every set that can possibly be used in standard mathematics.
But let me restate my point so you can either grapple with it or not. Set theory is the foundation of math; and math is essential modern physics. And Russell is not a very convincing example here.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Western thinkers tend to make sets (categories) fundamental and as a result cannot make sense of metaphysics. I have no opinion on mathematicians unless they are also philosophers. Afaik I agree with Weyl in all respects.
WHICH WESTERN THINKERS? This is an example of your lack of specificity and your lack of doing your homework. Which Western thinkers said what about what? Convince me you're not just waving your hands about things you haven't really challenged yourself to verify.
Which Western thinkers can't make sense of metaphysics? Are you taking on all of modern philosophy? Maybe you're right, I don't know enough philosophy to disagree. But at least state exactly who and what you are talking about. Else you're saying nothing and convincing no one.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Surely you are aware of the paradoxes caused by realistic views of space-time.
Pretend I'm not. Tell me about some of them. Identify them by name. Tell me how they destroy Western metaphysics.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
They are numerous.
Then you should have no problem (1) naming some of them; and (2) explaining how they falsify or create problems for Western metaphysics.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Having an inside but no outside would be one.
Like a Mobius strip or a Klein bottle? Non-orientable manifolds are upsetting you? What on earth are you talking about? Give specific examples and show how they support your point.
I am not just giving you a hard time. I'm giving your work a hard review, as a teacher would. You are woefully lacking in specifics and your reader has no idea what you're talking about.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Being finite or infinite would be another since both idea don't work.
Explain what you mean. There is nothing that is both finite and infinite at the same time since those terms mean the opposite of each other. It is true that there are sets that are infinite in one definition and finite in another. For example if you don't assume the axiom of choice, there is an infinite set that's Dedekind-finite. That means it's not bijective to any finite natural number; but it's also not bijective with any of its proper subsets. Is that what you're talking about?
What are you talking about?
Both don't work? You mean there are no finite sets AND no infinite sets? I'm afraid you are simply talking out of your hat.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
This is an extyensively explored area of philosophy.
By whom? You have not given me a single clue as to what you are talking about.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Lots of people make the mistake of 'reifying the reals', some of whom are mathematicians.
Name one.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
I have no general complaints against mathematicians. They are usually well aware their discipline is formal and not existential.
You haven't stopped complaining about mathematicians since you started your posts in this thread. Without managing to name a single one.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Bertrand Russell.
Laughable example. Russell did no math outside of his foundational attempts, which were totally blown up by Gödel. Surely you can get past the primitive foundational stumblings of 1900. Is that where you're stuck?
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
If we assume the extended continuum of space-time is fundamental paradoxes immediately arise.
What is the extended continuum of spacetime? In view of modern quantum physics, such a thing is questionable on the one hand; and inaccessible to our current theories even if such a thing did exist. What are you talking about?
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
I'm not sure it;s fair to ask me to list them when this is so well known.
List them or retract your remark. What paradoxes? Zeno? Are we in high school?
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
All good then, since I agree. Unfortunately philosophers regularly do just this.
Which philosophers?
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Lol. I fear it would takes more than a Wiki page to cover the ground, The Perennial philosophy proposes that all categories of thought are reducible, and must be reduced for a fundamental theory. Thus mathematics must be reduced.
Reduced to what? You're using jargon that has meaning to you but not to your readers.
Tell me, does chess need to be reduced? Isn't chess just a formal system? Isn't math just a formal system? Why does math need to be reduced, and to what must it be reduced, and why, and who says so, and to what effect?
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Number and form would be created phenomena and not really real.
Created by whom? Numbers aren't real? I'll certainly agree that numbers are
abstract objects. That doesn't make them any less real. The law that says you go on green and stop on red is an abstract thing. A martian physicist can distinguish red from green by their wavelengths, but she can't tell you which means go and which means stop because that is a social convention. Yet if you don't treat it as real you can die. So it's real. See Searle,
The Construction of Social Reality.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Nothing would really exist or ever really happen.
Without someone writing down some philosophy? That's nonsense, utter nonsense.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Extension would be unreal.
No idea what you are talking about.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
Set theory would have to be transcended if it is to be axiomatised, as explained by Weyl and by Spencer Brown in
Laws of Form. If you want to follow any of this up I'll post references.
I don't want references. I want you to explain yourself to me, a reasonably intelligent person who is reasonably well informed about math and set theory. Wiki calls the Laws of Form a "cult classic." It certainly was when I first heard about it fifty years ago.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
My view also. I'm not fighting the mathematicians. Not sure why you think I am.
You haven't stopped saying "mathematicians do this and mathematicians do that" since this thread started and when challenged, all you can come up with is Bertrand Russell. You have convinced me that you have not challenged yourself to to your homework and support your ideas with specifics.
PeteJ wrote: ↑Fri Aug 28, 2020 1:47 pm
I don't think were disagreeing on any mathematical issue.
You haven't stated any mathematical issues. You don't seem to know any mathematics beyond some vague notions from the foundational wars of the Frege/Russell era.
If you went through your own work and every time you say, "Mathematicians believe ..." or "Western philosophers believe ..." and did your homework and replaced that with, "Fred Bloggs believed ..." you would have a solid piece of argumentative writing. As it is, I am unmoved. And frustrated, because you clearly have things to say. I just can't find anything solid to grab on to. You don't like finite sets, you don't like infinite sets, you don't like non-orientable manifolds, you think Zeno's paradoxes invalidate 2000 years of Western philosophy, you take Bertrand Russell as an example of a mathematician with wrong ideas.
I want you to challenge your own vagueness and write something compelling. Take a red pencil to your own work and replace every generality with a specific supporting example.