On Thursday, March 7, 2019 at 11:47:41 AM UTC-6, Bruno Marchal wrote: > > > On 6 Mar 2019, at 22:10, Philip Thrift <[email protected] <javascript:>> > wrote: > > > > On Wednesday, March 6, 2019 at 12:20:13 PM UTC-6, Bruno Marchal wrote: >> >> >> >> We cannot predict in advance if a machine will stop. The extensional >> equality of machines, or combinators, is unsolvable. >> >> > > There is some conceptual and practical division between mathematics and > applied mathematics > > > Yes. But note that the division we can made there are dependent of the > metaphysics. > > Then Gödel has shown that we can apply mathematics to metamathematics, and > that a large part of metamathematics is in mathematics, so mathematics have > application in mathematics. But that is obvious through the representation > theorems, and my factors. We can say that the theory of complex analysis > has found extraordinary application in the pure number theory, like Riemann > discovered. > > Category theory is born from the discovery of abstract pattern relying > many application of some branch of math to another branch of math. It helps > mathematician to not reinvent the wheel all the time. > > > > (and there are institutionally separate Mathematics (PM, P for "Pure") and > Applied Mathematics (AM) Departments or Divisions at *some* universities. > > > Yes. That has been the root of my problem with some local academician. I > naively stated that I decide to study mathematics because I saw application > of mathematical logic (the second recursion theorem) to biology (like I > have shown in my paper “Amoeba, Planaria and Dreaming machine”. But I was > told that mathematical logic was taught in the section of Pure Mathematics, > where it was very badly seen to apply mathematics to anything but > mathematics. This illustrates it makes no sense to decide that some part of > math are pure or not. > > And this is even more true with mechanism. There is no more an > ontological physical reality, or any gods of that sort (which have never > been tested, actually, except with my work, of course, where the test was > negative for “Matter”). So the fundamental reality becomes mathematical. > And we are pure mathematical object living in a mathematical reality. That > is not entirely correct, because the internal phenomenology, for technical > reason, escapes even the whole of mathematics. So, eventually, the reality > is theological, to be correct. But the theology of the machines is a > theory, which today, is classified in pure mathematics (the logic of > provability). > > > > > > > There is a PM and an AM way of approaching what "computing" is. > > > > Yes, even in arithmetic. The universal machine discover that there is a > big difference between being implemented by a nameable “in principle” > universal number, and being implemented by something emerging from an > infinity of computations from the first person points of view. The first > leads to the theory G* (the “scientific theology of the ideally sound > machine”), and the others leads to quantum logic and physics, and the right > one, if mechanism is correct. > > > > > > > In an AM way of thinking, no computer can run forever, assuming what > scientists theorize about the future of the universe (big freeze, crunch, > etc.). > > > And assuming some physical reality. If you do serious metaphysics, it is > better to invoke an ontological commitment only in last ressort. Invoking > an ontological or primary physical universe is like saying “and god made > it”. That does not work. It is wishful thinking, provably if Mechanism is > assumed. > > > > > > AM would see computing as being nothing more than what can be done on > material computers, natural or manmade. > > > Computation have been discovered in arithmetic, before physics. > > Of course, the fact that we have cells and brains suggest, once we > understand that a computation is an arithmetical notion, that the physical > reality too is Turing complete. But with mechanism, to solve the mind-body > problem, you have to derive the physical reality (and its Turing > completeness) from arithmetic. It is nota question of choice. > > Of course you can say that in your religion, machine cannot have souls, > that you are not a machine, and so you can believe in the fantasy you want. > That is what we do since we have put theology out of science (just to make > it possible for some tyran to exploit people). > > Or you can try to build a precise non computationalist theory of mind, and > how to test it, in which case the computationalist theory will gives many > hint. Indeed, if some logics the universal machine gives for matter is > contradicted by nature, we do have a precise hint how to transform the > machine theory to get a correct non mechanist theory. > Today, such theory does not exist, Nature follows perfectly well > Mechanism,and the theory of apparent matter given by all classical > universal machine, thanks to QM. > > There is no evidence for your metaphysical ontological commitment. Given > that it makes the mind-body problem unsolvable since a long time, and that > mechanism explains consciousness and matter already, up to the infinite > confirmation we must test, like any theory about any reality. We never know > any publicly communicable truth. > > Bruno > > > > I was a Brown University student 1971-1979 (all 3 degrees: bachelors, masters, Ph.D. in Applied Mathematics).
There is: Division of Applied Mathematics Department of Mathematics Department of Philosophy Why the word "Division" instead of "Department" came in front I'm not sure (it divided from the Mathematics department?), but it began at the end of WWII to be a link to US federal government interest in applying mathematics to science. The Division divided :) in 1979, spinning off Department of Computer Science. The subject of Mathematic Logic (all the incompleteness theorems, etc.) is taught in Department of Philosophy. Still is in 2019 I think. That Department is where the mathematical logicians are. The general mindset (at the time): Mathematics is the fun stuff, Applied Mathematics is the real stuff. But there is crossover. - pt -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
