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Old 05-28-2007   #21 (permalink)
bns
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Default Re: Favorite Philosophers

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Originally Posted by SigmaX View Post
...I may be on the path to nihilism myself...
SigmaX
Be careful, there are no living nihilists.
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Old 05-29-2007   #22 (permalink)
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Easy there, Godwin.
In other words it is not popular to tell the truth.I don´t think it is possible to make dictinction between somebody´s work and life.If you are not humanist in your life you can not be that in your work.
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Old 05-29-2007   #23 (permalink)
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Default Re: Favorite Philosophers

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Berkeley's criticism of Calculus was very fair and very well-done.

Mathematicians of the time knew two things very well:

(a) that Calculus worked; and
(b) that Calculus was on shaky theoretical footing.

They knew what they meant, but they didn't know how to explain it or prove it formally. Oh, the verbal hoops they jumped through.

In the 1800's they fixed it, vindicating (to some extent) Berkeley's complaints.

[Aside: I have no idea what Berkeley wrote on philosophy, I'm only familiar with his famous rant against "ghosts of departed quantities" ]
Berkeley believed that things don't exist unless they are perceived. For example, Berkeley would say: a tree will vanish if no one's looking at it. Which is why I think overall, I don't see how Newton was required to give a better defense of the ideas than to merely say that we all stopped looking at the quantities, and they simply vanished. I don't see what basis Berkeley would have in arguing the point any further.

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.

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He's western. The ancient Greeks, as well as the Romans are considered to be part of western culture.

Easy there, Godwin.
But Heidegger really was a nazi ... this isn't an analogy.

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Old 05-29-2007   #24 (permalink)
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I don't see what basis Berkeley would have in arguing the point any further.
That's an ad hominem argument.

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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.
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.

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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.

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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.
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Old 05-29-2007   #25 (permalink)
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Default Re: Favorite Philosophers

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But Heidegger really was a nazi ... this isn't an analogy.
I know, it was intended as a joke. I laughed, even if no one else did.
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Old 05-31-2007   #26 (permalink)
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My favorite is Socrates.

It's because of how he realize how stupid people are.
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Old 05-31-2007   #27 (permalink)
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Berkeley would say: a tree will vanish if no one's looking at it.
You probably know that is just begining of his philosophy and it is not fair to stop here.Berkeley is not my favorite philosopher but we have to be fair when we analize his work.He was aware of problems wich his philosophy leed to and he made wayout."A tree will vanish if no one's looking at it."this means that existence of world depends of as,and he knew it is not good position.World exist even if it is no humans alive.So,how world exist?Because God is waching to the world.We can disagree with Berkeley but this is (in my opinion) fantastic wayout.
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Old 05-31-2007   #28 (permalink)
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Default Re: Favorite Philosophers

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You probably know that is just begining of his philosophy and it is not fair to stop here.Berkeley is not my favorite philosopher but we have to be fair when we analize his work.He was aware of problems wich his philosophy leed to and he made wayout."A tree will vanish if no one's looking at it."this means that existence of world depends of as,and he knew it is not good position.World exist even if it is no humans alive.So,how world exist?Because God is waching to the world.We can disagree with Berkeley but this is (in my opinion) fantastic wayout.
That's a good point ... I admit I'm being a bit harsh towards Berkeley. Berkeley had a clever solution in that he asserted we all exist in the mind of God.

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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Old 05-31-2007   #29 (permalink)
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Theory shows that nothing can exsist without God so your argument is not in place.We can go like this forever,but only thing I tryed to point is that Berkeley was not naive philosopher.
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