RE: Numbers, Machine and Father Ted

2006-10-23 Thread Stathis Papaioannou
Bruno Marchal writes: > >> Church thesis just assert that a universal turing machine can compute > >> all computable functions from N to N. > >> It relate a mathematical object with a human cognitive notion. It does > >> not invoke physical machine at all. > > > > In a sense that is true, but a

RE: Numbers, Machine and Father Ted

2006-10-23 Thread Stathis Papaioannou
In an excellent and clear post Peter Jones writes: > Matter is a bare substrate with no properties of its own. The question > may well be asked at this point: what roles does it perform ? Why not > dispense with matter and just have bundles of properties -- what does > matter add to a merely abs

RE: To observe is to......EC

2006-10-23 Thread Colin Hales
> Colin Hales wrote: > > > 3) The current state of the proof is 'now' the thin slice of the > present. > > Just a couple of questions for the moment Colin, until I've a little > more time. Actually, that's precisely what it's about - 'time'. Just > how thin is this slice of yours?

RE: Numbers, Machine and Father Ted

2006-10-23 Thread Stathis Papaioannou
Peter Jones writes: > > > Bruno's versions of COMP must embed Platonism (passim) > > > > > > You keep saying that, and I keep telling you that I need only > > Arithmetical Realism, which is defined by the belief that classical > > logic is sound for arithmetic. > > You need a UD -- a UD which e

Re: Numbers, Machine and Father Ted

2006-10-23 Thread David Nyman
Bruno Marchal wrote: > I answer you, but it is at the same time a test, because most of my > yesterday (sunday 22 october) posts seems not having been send > successfully. > (Some arrived at the archive, but not in my mail box, others nowhere, I > will wait a whole and resend them: it was message

Re: To observe is to......EC

2006-10-23 Thread David Nyman
Colin Geoffrey Hales wrote: > 3) The current state of the proof is 'now' the thin slice of the present. Just a couple of questions for the moment Colin, until I've a little more time. Actually, that's precisely what it's about - 'time'. Just how thin is this slice of yours? And is it important w

Re: Numbers, Machine and Father Ted

2006-10-23 Thread Bruno Marchal
Hi Stathis, I answer you, but it is at the same time a test, because most of my yesterday (sunday 22 october) posts seems not having been send successfully. (Some arrived at the archive, but not in my mail box, others nowhere, I will wait a whole and resend them: it was message for Peter and D

Re: Numbers, Machine and Father Ted

2006-10-23 Thread 1Z
David Nyman wrote: > Bruno Marchal wrote: > > > > As usual, the truth of a mathematical existence-claim does not > > > prove Platonism. > > > > By Platonism, or better "arithmetical realism" I just mean the belief > > by many mathematician in the non constructive proof of "OR" statements. > > >

Re: Numbers, Machine and Father Ted

2006-10-23 Thread David Nyman
Bruno Marchal wrote: > > As usual, the truth of a mathematical existence-claim does not > > prove Platonism. > > By Platonism, or better "arithmetical realism" I just mean the belief > by many mathematician in the non constructive proof of "OR" statements. > Lest we go yet another round in the '

Re: Numbers, Machine and Father Ted

2006-10-23 Thread David Nyman
Bruno Marchal wrote: > Here I disagree, or if you want make that distinction (introduced by > Peter), you can sum up the conclusion of the UD Argument by: > > Computationalism entails COMP. Bruno, could you distinguish between your remarks vis-a-vis comp, that on the one hand: a belief in 'prima

Re: Numbers, Machine and Father Ted

2006-10-23 Thread 1Z
Bruno Marchal wrote: > Le 22-oct.-06, 1Z ([EMAIL PROTECTED]) wrote: > > > > Bruno's versions of COMP must embed Platonism (passim) > > > You keep saying that, and I keep telling you that I need only > Arithmetical Realism, which is defined by the belief that classical > logic is sound for arithm

Re: Numbers, Machine and Father Ted

2006-10-23 Thread 1Z
Stathis Papaioannou wrote: > Bruno Marchal writes: > > > > Le 21-oct.-06, à 06:02, Stathis Papaioannou a écrit : > > > > > > > > > > > Bruno Marchal writes: > > > > > The UD is both massively parallel > > and massively sequential. Recall the UD generates all programs and > > execut

Re: Numbers, Machine and Father Ted

2006-10-23 Thread 1Z
Bruno Marchal wrote: > Le 20-oct.-06, à 17:04, 1Z a écrit : > > > As usual, the truth of a mathematical existence-claim does not > > prove Platonism. > > By Platonism, or better "arithmetical realism" I just mean the belief > by many mathematician in the non constructive proof of "OR" statements.

Re: Numbers, Machine and Father Ted

2006-10-23 Thread Bruno Marchal
Le 22-oct.-06, 1Z ([EMAIL PROTECTED]) wrote: > Bruno's versions of COMP must embed Platonism (passim) You keep saying that, and I keep telling you that I need only Arithmetical Realism, which is defined by the belief that classical logic is sound for arithmetic. I use often the expression "

Re: Numbers, Machine and Father Ted

2006-10-23 Thread Bruno Marchal
Le 20-oct.-06, à 17:04, 1Z a écrit : > As usual, the truth of a mathematical existence-claim does not > prove Platonism. By Platonism, or better "arithmetical realism" I just mean the belief by many mathematician in the non constructive proof of "OR" statements. Do you recall the proof I have