Re: Epistemology 201: The Science of Science

From: Lester Zick (lesterDELzick_at_worldnet.att.net)
Date: 03/25/05 

Date: Fri, 25 Mar 2005 22:52:09 GMT

On Fri, 25 Mar 2005 16:44:15 -0500, "robert j. kolker"
<nowhere@nowhere.net> in comp.ai.philosophy wrote:

>Lester Zick wrote:

>> Infinitessimals are the only way to generalize infinity.
>
>Wrong (as usual). Cauchy elimninated infinitesimals by using limits and
>convergence. Infinitesimals were reintroduced to respectable mathematics
>by the theory of hyperreals invented by Abraham Robinson around 1960.
>Infinitesimals are -a- way to deal with the very large and the very
>small, but not the only way. Infinitesimals have no application
>whatsoever to transfinite cardinals or ordinals.
>
>You have to go to the theory of -fields- (a particular kind of algebraic
>structure) to find infinitesimals. Non-Archimedean fields in particular.
>Google for details. In non-ordered systems infinitesimals have no place.
>After all what does being very (infinitely?) small unless large/small
>have a meaning.

Yeah, Bob, look here the problem is that you can eliminate
infinitessimals by waving a magic wand but that doesn't explain
the magic wand. You're just saying infinitessimals don't exist. Yet
the calculus used them. Are you saying differentiation and integration
don't exist or don't work? You need to be a lot more specific about
the nature of your magic wand. Just saying Cauchy did it or Joe Blow
did it doesn't explain what they did such that we still use
infinitessimals in differentials and integrals that you claim don't
exist.

Regards - Lester

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... Infinitesimals were reintroduced to respectable mathematics ... infinitessimals by waving a magic wand but that doesn't explain ... You're just saying infinitessimals don't exist. ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... Infinitesimals were reintroduced to respectable mathematics ... infinitessimals by waving a magic wand but that doesn't explain ... You're just saying infinitessimals don't exist. ...
    (sci.cognitive)
  • Re: Distinct linear orderings on Z
    ... >> Infinitessimals are the only way to generalize infinity. ... Infinitesimals were reintroduced to respectable mathematics ... > Bob Kolker ...
    (sci.math)
  • Re: Distinct linear orderings on Z
    ... Cauchy elimninated infinitesimals by using limits and ... convergence. ... Infinitesimals were reintroduced to respectable mathematics ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... > infinitessimals by waving a magic wand but that doesn't explain ... differential equations) WITHOUT infinitesimals. ... Bob Kolker ...
    (sci.cognitive)