Re: Numbers in Leibniz
On 10/29/2012 1:15 AM, Roger Clough wrote: Hi Bruno Still waiting for the storm to shut things down. Numbers are not discussed specifically as far as I can find yet, in my books on Leibniz. Which probably means that they are simply numbers, with no ontological status. Sort of like space or time. Inextended and everywhere. Numbers are definitely not monads, because no corporeal body is attached. Although they can whenever thought of appear in the minds of particular men in the intellects of their monads. Hi Roger, Physical bodies and, by extension, physical worlds follow from mutually consistent aspects of the individual 1p of monads; they are not attached. Leibniz, IMHO, bungled this badly in his discussions of the Monadology. Given that monads have no windows, it logically follows that /they do not have any external aspect/. Monads do not see the outsides of each other in any direct way. All that monads have as percepts of that which is other than themselves are those aspects of their own 1p that cannot be reconsidered as belonging to their identity in the moment of the observation/appearance. Leibniz does refer to a proposed universal language, which is simply everywhere as well as possibly in each head. Numbers would no doubt be the same, both everywhere and in individual minds at times. Yes, this is the Pre-Established Harmony, but as I have argued before this concept is deeply flawed because it tries to claim that the solution to NP-Hard problem (of choosing the best possible world) is somehow accessible (for the creation of the monads by God) prior to the availability of resources with which to actually perform the computation of the solution. One cannot know the content of a solution before one computes it, even if one is omniscient! So numbers are universal and can be treated mathematically as always. I agree, but the concept of numbers has no meaning prior to the existence of objects that can be counted. To think otherwise is equivalent to claiming that unspecified statements are true or false even in the absence of the possibility of discovering the fact. -- Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Numbers in Leibniz
On 29 Oct 2012, at 06:15, Roger Clough wrote: Hi Bruno Still waiting for the storm to shut things down. Take care. Numbers are not discussed specifically as far as I can find yet, in my books on Leibniz. Which probably means that they are simply numbers, with no ontological status. Sort of like space or time. Inextended and everywhere. I can be OK. I think that numbers are not even 'inextended' as extension does not apply to them. Then, of course variant of extension, like length in base 10, or number of Kb, can of course be defined. Numbers are definitely not monads, because no corporeal body is attached. For me, numbers, body, language, machine, etc. are basically synonymous. There are nuances, be they are not useful before they play a (usually relative) rôle. Although they can whenever thought of appear in the minds of particular men in the intellects of their monads. Leibniz does refer to a proposed universal language, which is simply everywhere as well as possibly in each head. I think Leibniz got the intuition of universal number (machine, language, program, etc.). Numbers would no doubt be the same, both everywhere and in individual minds at times. OK. So numbers are universal and can be treated mathematically as always. They are universal in that sense. But some numbers are universal in the Turing sense, and, as language, might be closer to Leibniz intuition. Such universal numbers can emulate the behavior of all other number. typical incarnation: the brain, the computer, the three bodies problem, the quantum zero body problem, game of life, fortran, lisp, algol, c++, combinators, arithmetic, etc. They all faithfully mirrors each other. They are like the golem. You can instruct them by using words, or numbers, so that they become slave, like your PC or MAC. Like the golem, the math explain it is risky and that you can loose control. With comp, you can make them becoming yourself, and an infinitely of them already are. Bruno Roger Clough, rclo...@verizon.net 10/29/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Roger Clough Receiver: everything-list Time: 2012-10-28, 18:31:25 Subject: Re: Re: A mirror of the universe. Hi Bruno Marchal I still haven't sorted the issue of numbers out. I suppose I ought to do some research in my Leibniz books. Aside from that, monads have to be attached to corporeal bodies, and numbers aren't like that. I find the following unsatisfactory, but since numbers are like ideas, they can be in the minds of individual homunculi in individual monads, but that doesn't sound satisfactoriy to me. Not universakl enough. My best guess for now is that the supreme monad (the One) undoubtedly somehow possesses the numbers. Hurricane coming. Roger Clough, rclo...@verizon.net 10/28/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Bruno Marchal Receiver: everything-list Time: 2012-10-27, 09:31:59 Subject: Re: A mirror of the universe. On 26 Oct 2012, at 14:44, Roger Clough wrote: Dear Bruno and Alberto, I agree some what with both of you. As to the idea of a genetic algorithm can isolate anticipative programs, I think that anticipation is the analogue of inertia for computations, as Mach saw inertia. It is a relation between any one and the class of computations that it belongs to such that any incomplete string has a completion in the collections of others like it. This is like an error correction or compression mechanism. -- Onward! Stephen ROGER: For what it's worth--- like Mach's inertia, each monad mirrors the rest of the universe. In arithmetic, each universal numbers mirrors all other universal numbers. The tiny Turing universal part of arithmetical truth is already a dynamical Indra Net. Your monad really looks like the (universal) intensional numbers. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything- l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything- l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group,
Re: Numbers in Leibniz
On 29 Oct 2012, at 14:36, Stephen P. King wrote: So numbers are universal and can be treated mathematically as always. I agree, but the concept of numbers has no meaning prior to the existence of objects that can be counted. To think otherwise is equivalent to claiming that unspecified statements are true or false even in the absence of the possibility of discovering the fact. I think you confuse numbers, and the concept of numbers. And then your argument is not valid, as with numbers, the miracle is that we can specify the concept of numbers, as this result in defining some arithmetical sigma_1 complete theory in terms of 0, s(0), ... and the laws of addition and multiplication, that everybody understands (unless philosophers?). Bruno PS BTW, from a computer scientist perspective, your use of NP never succeed to make sense. I don't dare to ask you to elaborate, as I am afraid you might aggravate your case. The NP question is fundamental and has many interesting feature, but it concerns a local tractability issue, and is a priori, unless justification, not relevant for the arithmetical body issue, nor number's theology (including physics) issue, etc. When you say: Yes, this is the Pre-Established Harmony, but as I have argued before this concept is deeply flawed because it tries to claim that the solution to NP-Hard problem (of choosing the best possible world) is somehow accessible (for the creation of the monads by God) prior to the availability of resources with which to actually perform the computation of the solution. One cannot know the content of a solution before one computes it, even if one is omniscient! I don't find any sense. I hope you don't mind my frankness. I wouldn't say this if I did not respect some intuition of yours. But math and formalism can't be a pretext for not doing the elementary reasoning in the philosophy of mind. If you use math, you have to be clearer on the link with philosophy or theology. To be understandable by others. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Numbers in Leibniz
Hi Bruno Still waiting for the storm to shut things down. Numbers are not discussed specifically as far as I can find yet, in my books on Leibniz. Which probably means that they are simply numbers, with no ontological status. Sort of like space or time. Inextended and everywhere. Numbers are definitely not monads, because no corporeal body is attached. Although they can whenever thought of appear in the minds of particular men in the intellects of their monads. Leibniz does refer to a proposed universal language, which is simply everywhere as well as possibly in each head. Numbers would no doubt be the same, both everywhere and in individual minds at times. So numbers are universal and can be treated mathematically as always. Roger Clough, rclo...@verizon.net 10/29/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Roger Clough Receiver: everything-list Time: 2012-10-28, 18:31:25 Subject: Re: Re: A mirror of the universe. Hi Bruno Marchal I still haven't sorted the issue of numbers out. I suppose I ought to do some research in my Leibniz books. Aside from that, monads have to be attached to corporeal bodies, and numbers aren't like that. I find the following unsatisfactory, but since numbers are like ideas, they can be in the minds of individual homunculi in individual monads, but that doesn't sound satisfactoriy to me. Not universakl enough. My best guess for now is that the supreme monad (the One) undoubtedly somehow possesses the numbers. Hurricane coming. Roger Clough, rclo...@verizon.net 10/28/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Bruno Marchal Receiver: everything-list Time: 2012-10-27, 09:31:59 Subject: Re: A mirror of the universe. On 26 Oct 2012, at 14:44, Roger Clough wrote: Dear Bruno and Alberto, I agree some what with both of you. As to the idea of a genetic algorithm can isolate anticipative programs, I think that anticipation is the analogue of inertia for computations, as Mach saw inertia. It is a relation between any one and the class of computations that it belongs to such that any incomplete string has a completion in the collections of others like it. This is like an error correction or compression mechanism. -- Onward! Stephen ROGER: For what it's worth--- like Mach's inertia, each monad mirrors the rest of the universe. In arithmetic, each universal numbers mirrors all other universal numbers. The tiny Turing universal part of arithmetical truth is already a dynamical Indra Net. Your monad really looks like the (universal) intensional numbers. Bruno -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
