Bruno, in the line you touched with 'numbers: I was arguing on another list 'pro' D.Bohm's "there are no numbers in nature" position when a listmember asked: "aren't you part of nature? then why are you saying that numbers - existing in your mind - are not 'part of nature'?" Since then I formulate it something like: numbers came into existence as products of 'our' thinking. (Maybe better worded). You wrote: > What I mean is that their arithmetical property are independent of us. ..< That may branch into the question how much of 'societal' knowledge is part of an individual belief - rejectable or intrinsically adherent? (Some may call this a fundamental domain of memes). With the 'invention' of numbers (arithmetical, that is) human mentality turned into a computing animal - as a species-characteristic. I separate this from the assignment of quantities to well chosen units in numbers. Quantities may have their natural role in natural processes - unconted in our units, just mass-wise, and we, later on - in physical laws - applied the arithmetical ordering to the observations in the quantized natural events. Such quantizing (restricted to models of already discovered elements) renders some processes 'chaotic' or even paradoxical, while nature processes them without any problem in her unrestricted (total) interconnectedness (not included - even known ALL in our quantized working models).
Sorry for the "physicistically" unorthodox idea. Best regards John Mikes ----- Original Message ----- From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, January 12, 2004 9:50 AM Subject: Re: Is the universe computable? > At 13:36 09/01/04 +0100, Georges Quenot wrote: > >Bruno Marchal wrote: > > > > > It seems, but it isn't. Well, actually I have known *one* mathematician, > > > (a russian logician) who indeed makes a serious try to develop > > > some mathematics without that infinite act of faith (I don't recall > > > its name for the moment). Such attempt are known as "ultrafinitism". > > > Of course a lot of people (especially during the week-end) *pretend* > > > not doing that infinite act of faith, but do it all the time implicitly. > > > >This is not what I meant. I did not refer to people not willing > >to accept that natural numbers exist at all but to people not > >wlling to accept that natural numbers exist *by themselves*. > >Rather, they want to see them either as only a production of > >human (or human-like) people or only a production of a God. > > > What I mean is that their arithmetical property are independent > of us. Do you think those people believe that the proposition > "17 is prime" is meaningless without a human in the neighborhood? > Giving that I hope getting some understanding of the complex human > from something simpler (number property) the approach of those > people will never work, for me. > Also, I would take (without added explanations) an expression > like "numbers are a production of God" as equivalent to > arithmetical realism. Of course if you add that God is a > mathematical-conventionalist and that God could have chose > that only even numbers exist, then I would disagree. > (Despite my training in believing at least five impossible > proposition each day before breakfast ;-) > > > >And I said "unfortunately" because some not only do not want to > >see natural numbers as existing by themselves but they do not > >want the idea to be simply presented as logically possible and > >even see/designate evil in people working at popularizing it. > > > OK, but then some want you being dead because of the color of the skin, > or the length of your nose, ... I am not sure it is not premature wanting > to enlighten everyone at once ... > I guess you were only talking about those hard-aristotelians who > like to dismiss Plato's questions as childish. Evil ? Perhaps could you be > more precise on those people. I have not met people seeing evil > in arithmetical platonism, have you? > > Bruno >