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| | #22 (permalink) | |
| Commentator Join Date: May 2007
Posts: 59
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| | #23 (permalink) | ||
| Super Moderator Join Date: May 2007 Location: Indiana, USA
Posts: 998
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It's true that in the 1800's, Calculus was placed on a more rigourous foundation that used limits, and epsilon-delta definitions. But this didn't really answer the questions Berkely raised as much as it avoided talking about the problems that lead to the questions. IMO it was just an evasive technique to silence the critics. Even later (1960's?), Abraham Robinson's work on infinitesimals and non-standard analysis showed that Newton's approach was generally workable, in that we can define infinitely small quanities and we use them consistently. In other words, there was nothing terribly wrong with Newton's basic approach aside from some vagueness ... IMO the primary problem was just that most people (esp Berkeley) did not understand Newton's overall thought process. Newton didn't help matters, as he seemed to hate publishing his ideas or dealing with questions about them. Quote:
![]() Last edited by yaaarrrgg : 05-29-2007 at 11:18 AM. | ||
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| | #24 (permalink) | ||||
| pragmatic idealist Join Date: May 2007
Posts: 190
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Also, the precise definition of limit doesn't really stray all that far from Newton either. I think the world was not yet ready for a formal idea of infinitesimals when Newton was around. Somehow it requires a greater suspension of disbelief. That's my opinion only. Quote:
Second, Berkeley wrote from an even worse perspective than not understanding...he wrote from a "gotcha!" perspective, to "prove" that math wasn't on any sounder a foundation than religion. As such, "understanding" the math was beside the point. He would have made his (self-serving) argument either way. But it doesn't make his criticisms invalid, IMO. | ||||
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| | #27 (permalink) | |
| Commentator Join Date: May 2007
Posts: 59
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| | #28 (permalink) | |
| Super Moderator Join Date: May 2007 Location: Indiana, USA
Posts: 998
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After thinking more about it... it does makes sense that he would have a problem with "fluxions." The existence of anything that is by definition un-perceivable pretty much sinks his entire theory. ![]() | |
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