> On 25 Aug 2019, at 14:01, Bruce Kellett <[email protected]> wrote: > > On Sun, Aug 25, 2019 at 9:39 PM Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > On 25 Aug 2019, at 10:10, Bruce Kellett <[email protected] > <mailto:[email protected]>> wrote: >> The mathematical structure might describe these things, but descriptions are >> not the things they describe. > > I think you confuse the mathematical structure, and the theory describing > that mathematical structure. Those are very different things. > > I think that is exactly the mistake that you make all the time.
Where? I don’t remind you ever show this. Contrarily, when you say that a mathematical structure describe things, that is like saying that the physical universe describes the content of a book on physics. A reality, be it physical or mathematical, is not a description, but the thing being described by some theory. PA describes a portion of the Arithmetical Reality, which can be shown never completely described by *any* (effective) theory. I take this as a strong evidence that the arithmetical reality is independent of me, and actually, quite above me (and that is provable when we assume mechanism). You might have a conventionalist philosophy of mathematics, but if that philosophy was true, why would we give a million of dollars for a solution to Riemann hypothesis? Or how to explain why the formula of the partition of numbers is so much more difficult than the formula for the composition of numbers, as I showed once. The composition of n is the number of way you can describe n as a sum of numbers, taking the order into account. The partition of n is the same, except the order of the sum is not taking into account. The number of composition is simply 2^(n-1), but the number of partitions is given by the most complex (in the two sense of the word) formula in mathematics. If the arithmetical reality was conventional, I would have simplified all this already :) You don’t need to accept full realism. You need to accept that phi_x(y) converges or not. You need to believe that the program i stops on x or does not stop on x. Whatever number x is. Nothing more. If you do metaphysics/theology with the scientific attitude, you cannot invoke words like “truth”, “real”, “god”, “universe” in your theory, but you might use them in some meta-theory, to give sense to your theory, temporarily. Bruno > > Bruce > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/CAFxXSLRP%3DvVVFd_H4wyuhao6smXyQ-vp%3DXfW3pzezmEcZF13-Q%40mail.gmail.com > > <https://groups.google.com/d/msgid/everything-list/CAFxXSLRP%3DvVVFd_H4wyuhao6smXyQ-vp%3DXfW3pzezmEcZF13-Q%40mail.gmail.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/831F468F-5609-455B-8070-14D851B9992B%40ulb.ac.be.
