On Sun, Aug 25, 2019 at 11:03 PM Bruno Marchal <marc...@ulb.ac.be> wrote:
> On 25 Aug 2019, at 14:01, Bruce Kellett <bhkellet...@gmail.com> wrote: > > On Sun, Aug 25, 2019 at 9:39 PM Bruno Marchal <marc...@ulb.ac.be> wrote: > >> On 25 Aug 2019, at 10:10, Bruce Kellett <bhkellet...@gmail.com> 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. > I have said it many times. A mathematical structure is an abstract human construct. Such a structure might go some way towards describing physical reality, but the map is not the territory. > 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. > You beg the question. You are assuming that the mathematical structure is the reality, and that the physical universe is the description of that structure. Wrong way round, yet again. A reality, be it physical or mathematical, is not a description, but the > thing being described by some theory. > You are using your own mathematician's understanding of the relationship between a theory and a reality. You claim that a model that instantiates the theory is a reality for that theory. That is just a matter of particular linguistic usage, and it has nothing to do with the relationship between physical reality and the mathematical theories used to (partially) describe it. > 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 really do get hung up on what you think Godel proved when he showed that some true statements in arithmetic are not theorems. That simply uses a notion of "truth" that is outside theorems of the system. It has nothing to do with existence or an ontology. 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 :) > Arithmetic is defined by certain axioms. Systems of axioms can have consequences that were not dreamed of when the axioms were formulated. There is nothing more to it than that -- it is not some super revealed "truth". > 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. > Some computations halt and some do not. And you can't always tell in advance which is which ... this is not the source of all wisdom. Bruce 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 > -- 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 everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLTaDDLvetZRqQCLQ2fneRg_i%3DHuDsQde3mnMBZ6FQ1H4A%40mail.gmail.com.
