You clearly do not understand, if you think that I accept the Fourier transform. I accept it as an example of an unresolved problem. — Metaphysician Undercover
And when that unresolved problem is united with the bad metaphysics of special relativity, the result is the uncertainty principle of quantum mechanics. — Metaphysician Undercover
Relativist seemed to be arguing that a metaphysician is better trained to do metaphysics than a physicist, yet there is some metaphysics, such as the metaphysics of time, which a physicist is better trained to do. — Metaphysician Undercover
However, the uncertainty principle is clear evidence that physicists should leave the metaphysics of time in the hands of metaphysicians. — Metaphysician Undercover
Thanks for offering your take on this. I think this is exactly where the unresolved problem lies. It appears like the size of a chosen base unit might be completely arbitrarily decided upon. — Metaphysician Undercover
Yet the possible divisions are not arbitrary because divisibility is dependent on the size of the proposed base unit. Take 440 HZ as the baseline, for example. From this baseline, one octave (as a unit) upward brings us to 880HZ, and one octave downward brings us to 220HZ. So the higher octave consists of 440 HZ, and has different divisibility properties from the lower octave which consists of 220 HZ. This results in a complexity of problems in music. — Metaphysician Undercover
My understanding is that, for example, the Planck length is the length at which our current theories of physics break down and may no longer be applied. So that we can't sensibly speak of what might be happening below that scale. We can't say that reality is continuous or discrete; only that our current theories only allow us to measure to a discrete limit. — fishfry
But I am still confused about your conclusion. You're saying that a situation is ontological if there's no knowledge I could have that would settle the matter. Whereas I seem to mean something different. There's what we can know, and there's what really is. Two different things. — fishfry
I am surprised you've heard of it. Yet you don't agree that 2 + 2 and 4 refer to the same thing. In my prior conversations with you, you've convinced me that you utterly reject symbolic mathematical formalisms. And without those, there certainly aren't any convergent infinite trigonometric series. Those are very abstract gadgets. There's a mismatch in your level of discourse. — fishfry
We keep coming back to the same point. Nobody is making metaphysical claims except you. I agree that SOME scientists think their theories are True with a capital T, but I don't. You're fighting against someone's opinion that isn't mine. — fishfry
Ok, fine. I stipulate that. Science isn't metaphysics, science is not ontology. What of it? I've been conceding you this point for days. You won't even acknowledge that I've said that, you just keep coming back with arguments as if I haven't said it. — fishfry
Do you understand that I make no ontological or metaphysical claims for science? — fishfry
I do not believe that "two plus two" and "four" refer to the same thing. — Metaphysician Undercover
Do you recognize that scientists, in their scientific endeavours, regularly employ metaphysical principles? — Metaphysician Undercover
saying that "2+2" and "4" refer to the very same thing, you make a metaphysical (ontological) claim. — Metaphysician Undercover
I'm the rhetorical foil of last resort? I'm not sure how to take that — fishfry
If Descartes's vortices are coming back that would be great news. Have you a specific link please? — fishfry
No, that's a psychological claim — Gregory
Mathematics is ultimately guided by utility, and even those who might seem to be engaged in pure math are doing what they are doing (choosing whichever problems they choose to be working on instead of working on other problems) for a reason, so utility cannot be removed from mathematics. — Metaphysician Undercover
This is true only if "utility" includes fascination with exploring a subject, finding what's behind the next intellectual door, where an investigation might lead, etc. That's been my motivation for many years. — jgill
No way! I just tagged you because you were "openminded and pluralistic about math" in the past with me — Gregory
I only read it in the Stanford Encyclopedia of Philosophy on Descartes Physics. It said people are having renewed interest in it. I watched a video once that showed how his definitions of forces and reactions couldn't work on a billiard table. The guy said he had another video on Descartes "flawed" optics, but I couldn't find it and even the first video isn't around anymore. Sad — Gregory
at least after a few decades when the new ideas start to sink in! — fishfry
Lol, true. It actually says in the first paragraph of the Stanford article "It is this unique amalgam of both old and new concepts of the physical world that may account for the current revival of scholarly interest in Descartes’ physics." — Gregory
Sean Carroll explicitly says this. He says the world is a brute fact of quantum fluctuation, using Russell's old phrase btw — Gregory
Physicists seem to be on a roll these days. Unfortunately, I’m not talking about a string of new discoveries about the fundamental nature of reality, but of a panoply of speculative notions ranging from the plausible but empirically untestable (and therefore non-scientific), such as Sean Carroll’s marketing of the many-worlds interpretation of quantum mechanics, to sheer nonsense on stilts, like the idea that is the subject of this essay.
Thought that was interesting in the context of our conversation.
https://medium.com/science-and-philosophy/the-universe-simulates-itself-into-existence-and-other-nonsense-from-modern-physics-32e958b690b
There's no mismatch in my discourse, you simply refuse to try and understand what I'm saying. — Metaphysician Undercover
I believe that two plus two equals four. I do not believe that "two plus two" and "four" refer to the same thing. — Metaphysician Undercover
Since you think that they refer to the same thing, you and I give "2+2=4" different meaning. We simply interpret this phrase differently. — Metaphysician Undercover
It is an ontological difference. So I reject some conclusions of mathematical formalism as unsound, based in unsound premises. — Metaphysician Undercover
This does not exclude me from taking a look at some of these unsound conclusions. Comparing unsound conclusions with what is really the case helps in the effort to produce better premises. — Metaphysician Undercover
The premises, axioms, theories, are metaphysical claims. whether you recognize this or not. I know we disagree on this, and you think that such premises might be based in something called "pure mathematics". but I explained to you in the other thread why this is an unsound principle itself. There is no such thing as "pure mathematics" in an absolute sense. Mathematics is ultimately guided by utility, and even those who might seem to be engaged in pure math are doing what they are doing (choosing whichever problems they choose to be working on instead of working on other problems) for a reason, so utility cannot be removed from mathematics. — Metaphysician Undercover
Do you recognize that scientists, in their scientific endeavours, regularly employ metaphysical principles? — Metaphysician Undercover
In saying that "2+2" and "4" refer to the very same thing, you make a metaphysical (ontological) claim. — Metaphysician Undercover
No, I'm making a claim of Peano arithmetic, a purely syntactic system. — fishfry
You pointedly ignored my argument and wouldn't even engage with my having presented it. — fishfry
This is exactly my point, such axioms are based in ontological principles, they are not "pure mathematics. You can insist that there is no ontology to them all that you want, refusing to consider the evidence, in denial, that's a matter of your own free choice. — Metaphysician Undercover
Actually I demonstrated your faulty interpretation of the premise of extensionality. That two symbols refer to something of "equal" value is not sufficient for the conclusion that they refer to "the same" thing. Being the same implies being equal, but being equal does not imply being the same. You commit a fallacy of conversion. — Metaphysician Undercover
You are the one in denial, insisting that mathematical axioms are exempt from judgements of true and false, being "pure mathematics", and absolutely abstract, refusing to accept the truth in this matter. — Metaphysician Undercover
It isn't an epistemological limit. — fdrake
Being the same implies being equal, but being equal does not imply being the same. — Metaphysician Undercover
PA is a formal symbolic system no different in principle than the game of chess. — fishfry
Note that as usual I ask you direct, probing questions and you'll respond by changing the subject. — fishfry
There is no middle 'e' in judgment. Jus' sayin' but nevermind . Axioms are formal statements, strings of symbols that are well-formed according to specific syntactic rules. — fishfry
Therefore there can be no "truth" in axioms; only logical consistency and interestingness. — fishfry
Depends on the contexts of usage. — jgill
It's not that bad! — fdrake
How can they represent the same Platonic ideal when "+" represents an ideal in itself, which is part of "2+2", but not part of "4"? — Metaphysician Undercover
I can concede that "2+2" and "4" are equal but not the same. — jgill
↪jgill
How can they represent the same Platonic ideal when "+" represents an ideal in itself, which is part of "2+2", but not part of "4"? — Metaphysician Undercover
If you have some mathematical framework in which 2 + 2 and 4 do not represent the exact same abstract mathematical object, I would appreciate your filling in the details. — fishfry
Did you see my reply here? Link. — fdrake
I remember a physics prof in university spending maybe 15 minutes scolding me when I said something like "the uncertainty principle says we can't know...", they responded "The uncertainty principle has nothing to do with how much we know about particles, it's not about our knowledge of the particles, it's about the particles" - not that exactly since it was a lot of years ago now, but that was definitely the gist. They were pretty mad at the suggestion it was epistemic, and their research was quantum theory, so I trust 'em. — fdrake
Edit: I have another story like that which is pretty funny. We had an analysis lecturer that was extremely eccentric, and one of the masters theses they were willing to supervise was on space filling curves. They handily included a "picture of a space filling curve in a subset of the plane", which was just a completely black square. I asked another prof if the eccentric prof actually wrote out code to draw the space filling curve, since it was the kind of thing he'd do if he could. The other prof got pretty angry and said "Computers can't do that, it's noncomputable, the construction relies upon the axiom of choice!". — fdrake
Irrelevant. 4-ness is the ideal in discussion. — jgill
Well maybe. I think that point's a stretch. Plato could be wrong. But more to the point, 4 already includes within itself the possibility of being partitioned into 2 + 2. or 1 + 1 + 2, or 1 + 1 + 1 + 1. This is in fact the mathematical subject of partitions. It's what Ramanujan was working on inThe Man Who Knew Infinity. IMO doing a good job of explaining the partition function to a general Hollywood audience is one of the greatest math feats in cinematic history.
Point being that if 4 is an "ideal" or whatever you call it by itself, it ALREADY CONTAINS the possibility of all its positive integer partitions.
Truly, 2 + 2 and 4 are the same Platonic object. I don't find your argument convincing for this reason:
Sure, 2 + 2 expresses the fact that 2 and + can be combined to make 4. But 4 already expresses the fact that 4 can be represented as 2 + 2. Partitions are a natural and built-in aspect of a number.
Am I at least representing your position correctly? — fishfry
When it comes to metaphysics. physicists are the last people I'd listen to; and celebrity physicists the least of all :-) — fishfry
Most physicists, or at least many, actually think their theories are True in some absolute sense. — fishfry
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