From: nelson_p@apollo.hp.com (Peter Nelson)
Subject: Re: The Two Faces of Ayn Rand
Date: Fri, 11 Dec 1992 18:28:00 GMT
Distribution: usa
Organization: Hewlett-Packard Corporation, Chelmsford, MA

In article <184592@pyramid.pyramid.com> pcollac@pyrnova.mis.pyramid.com (Paul Collacchi) writes:
>In article <Bz00qG.7r5@apollo.hp.com>, nelson_p@apollo.hp.com (Peter
>Nelson) writes:
>|> In article <Byx2I3.JvB@news.udel.edu> yale@brahms.udel.edu
>(Christopher Rob Robe) writes:
>|> 
>|> >  Science is just as guilty as philosophy in claiming certain facts
>|> >  without one hundred percent proof.  Many scientific mathematical
>|> >  truths have never been proven, even the basic concepts of geometery on
>|> >  which science is grounded has never been proven. No one has ever seen
>|> >  a perfect triangle, nor circle.   ALong the same lines, scientist are
>|> >  readily assuming that perfect ones do exist.
>|> 
>|>   This is idiotic.  A line or point, in geometry is a theoretical
>|>   concept.  It is NOT assumed to "exist" in the physical world.
>|>   I have a globe on my desk.  It has a line circling the world at
>|>   the equator.   Next week I'll be flying to Tahiti (really!). 
>|>   If we have clear weather should I look down as we pass over the 
>|>   equator and expect to see a huge line going across the ocean?!
>|>   
>|
>The point might not be so idiotic, Peter.  It goes to the heart of 
>the weaknesses of formal systems; namely, that they cannot be proved
>to render anything "real."  Mathematics works great on assumed 
>theoretical contructs, but no one can prove that any real thing is
>properly rendered by those contructs.

  I agree, and mathematics would be nothing more than a possibly
  interesting intellectual pastime if it weren't for the fact that
  I can apply mathematical rules to the real world and they still 
  work.   E.g., the distance between two points can be computed
  in the real world using the same techniques as I would to compute
  the distance between two theoretical points in 3-space in the
  formal model, and it produces the same result, within the limits
  of our ability to measure it.    But this doesn't mean dimensionless
  points *exist* in the real world, as the other poster suggested, it
  just means that I can find real-world analogues to which I can 
  apply the same operations, and get the same results.  


>Logic is the same.  All logical arguments *assume* certain premises.  
                                    
  But does this mean that any arbitrary axiom is as good as another?
  Could I create a geometry that says "parallel lines meet at one
  point"?   I imagine I could but it would be a very different 
  one from what we're used to.   What would be its mapping to the
  real world?


>I don't agree that science leads to "progress". 

  But recall that I defined "progress" in a specific way:  I say
  science allows the creation of conceptual, theoretical models that,
  over time, map ever more closely to the real world.   By "map ever
  more closely to the real world" I mean that the error we detect
  between our model and what we can measure in the physical world
  gets smaller and smaller.   I do NOT mean by "progress" that our
  lives get better, happier, or whatever.

  I say this "progress" feature of science is unique, or at least 
  rare.   Religion, for instance, also consists of an abstract model
  of the world and how it works.  Different religions all have different
  models but they all share the problem that there's no way to improve
  the model and tell if it's really improved.   I mean I could pray 
  to some deity for more information, e.g., "tell me if you have hair".
  and get a message back, in my head, saying "yes".   So now we have
  a more precise model, not just God in His Heaven, but God in His Heaven
  with hair!   The trouble is I have no way of knowing if this model is
  more accurate.   And there's no way for anyone else to independently
  verify my "discovery".  So while I have a new model I haven't replaced 
  the old one.   Thus, while religious thinking can generate a multi-
  plicity of models, it can't refine an existing model.  

  Whereas in science you start off with a model (I'm oversimplifying)
  that says there are atoms, and these are the smallest things in the
  universe.  And then you get a model that says, "Nope, atoms are
  subdivisible into protons, neutrons, and electrons".   And then you
  get a model which says that even these are subdivisible.  The result
  of this process is not 3 competing models, as it would be in religion
  or ethical philosophy, but each one replacing the earlier one.   


>And what good is it to establish what the facts are?  Nothing will tell
>us what they mean, and what we should do about them.

  True, although they might tell you more about what your options are
  to do something about them.   


---peter




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