> On 28 Jun 2018, at 21:30, John Clark <[email protected]> wrote: > > On Thu, Jun 28, 2018 at 11:26 AM, Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > >You can store a sequence of numbers in one number. For example you can > store the sequence 7, 7, 7, 9, 8, 7, 9, 7, 6, 6 in the number x with (unique) > prime decomposition > How can pure numbers do a unique prime decomposition? I don't want to know > how you do it, I don't want to know how a computer does it, I want to know > how a pure number does it. > >
That is well known by logicians since 1931. The computational reality is embeddable in the arithmetical reality. If you are a digital machine, you have no means to distinguish if you are run by a physical thing or an arithmetical thing. But you seem to confuse arithmetical theories, which can be identified with digital machine or numbers, and the arithmetical reality or truth, which cannot be identify with any number. > > > Then you can define, following Gödel [...] > > Definitions can't conjure things into existence. Sure. That is why we assume 0 and its successor. Then we can explain how dreams appears, and how the physical laws appears, in a testable way. This works, at least. Physicalism does not work. It stumbles on the mind-body problem. > > > You can define divides, =<, prime, etc. > > Definitions can't conjure things into existence. > > >you would still need to define the exponentiation > > Definitions can't conjure things into existence. > > >Matter is also unchanging and unchangeable in the Block-Universe picture. > > Screw the Block-Universe picture, subjectively matter changes and > subjectively pure numbers do not. But the subjectivity is not a number. It changes also all the time. The S4Grz logic of the knowledge of the digital machine/number is a temporal logic. > > > >>How can the integer "7" be in a different state? > > >By adding one to it, > > The technical term for that is "8". The integer 8 has no memory , you can't > say yesterday it was 7 so somebody must have added a 1 to it because > yesterday 8 existed just as it does today and and tomorrow there will still > be no change. I can store information in 7 magnetic spots on a computers > hard drive but I can's store information in 7. You cannot store anything in 7 with the Gödel encoding that I have described. But you can store a number in any number multiple of two, as its decomposition will be 2^n * 3 ^…, so that will store n in the first place in the register. > > > >Arithmetic indeed implements also the buggy computations, but that is a > relative notion. At the bare level of the sigma_1 truth, all computations are > correct, like a physical computer getting an incorrect answer due to some > bugs, does not violate the physical laws, nor the laws of arithmetic. > > If correct calculations exist in Plato's mystical heaven It exists like prime number exists. Mystical is wrong here, but correct for the []p & p type of modes. Using it here is a confusion. There is nothing mystical in arithmetic, or you could qualify as mystical all theories in natural sciences. > then incorrect ones must too, and for every correct calculation there are an > infinite number of incorrect ones with no way of telling one from the other > because in heaven nothing can actually DO anything. Physicalist argument per authority. > > >The physical reality and the arithmetical reality can contain buggy > computations, and correct one as well. > > Arithmetical errors can happen in modern computers largely caused by cosmic > rays but they are rare, but if you picked at computation at random from > Plato's heaven the probability it is wrong is 100%. For who? What do you mean exactly by an incorrect computation? I would say that by definition all computations are correct. They might be buggy from the point of view of someone wanting to do something with the computation. Obviously a program computing Fibonacci is incorrect if your goal is to compute the factorial function, but the UD makes all computations, and as such they are all “correct”, simply because there is no notion of being incorrect for a computation. They might depart from a goal or a specification, but that is not part of what is a computation. Only a theoretical statement can be incorrect with respect to some interpretation. A computation just is, like a prime number, etc. > > > >>And by "thing" I mean an object with the ability to exist in more than > one state and yet still be recognizable. > > >Yes, but such object does not need to be physical. > > Then if I add 1 to seven the number 7 no longer exists and neither does the > number 1, and until I did that just now the number 8 did not exist. You loss me here. Bruno > > John K Clark > > > > > > > > > > >> > > > -- > 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 post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- 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.
