Quote:
Originally Posted by yaaarrrgg  I don't see what basis Berkeley would have in arguing the point any further. |
That's an ad hominem argument.
Quote:
|
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.
|
I disagree. The method defined
exactly what was meant by "limit," which is what Berkeley and others were asking. It was not evasive. It was a sound, precise definition that settled the issue.
Quote:
|
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
|
I think everyone knew that already. Newton is widely hailed as one of the most important minds in history.
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:
|
IMO the primary problem was just that most people (esp Berkeley) did not understand Newton's overall thought process.
|
Two things: first, mathematicians themselves (who certainly understood Newton's ideas) became increasingly uncomfortable with the lack of precision. Newton himself was squirmy on the topic.
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.