Guest guest Posted March 9, 2006 Report Share Posted March 9, 2006 In a message dated 3/8/2006 8:10:10 PM Pacific Standard Time, Nisargadatta writes: Thu, 09 Mar 2006 01:26:19 -0000 " toombaru2006 " <lastrain [NonDualPhil] Re: Math, Path Nisargadatta , ADHHUB wrote: > > > In a message dated 3/8/2006 7:43:33 AM Pacific Standard Time, > Nisargadatta writes: > > Wed, 8 Mar 2006 07:36:02 -0800 > Pete S <pedsie5 > Re: [NonDualPhil] Re: Math, Path & Analogies > > > On Mar 7, 2006, at 1:25 PM, billrishel wrote: > > > > >> P: Ok! I know that in arguing about math with you, > >> I'm getting way over my head. But axioms I can argue > >> because they just required intuition. Axioms are > >> math facts that we take as self-evident. All theories > > > > B: Axioms are *assumptions*. > > It is actually a very interesting point that *does* have > > bearing on nondual philosophy. Careful study of the > > philosophy of science and mathematics reveals that there > > are *no* known absolutes. The average person has no idea > > of this. > > > > In mathematics we say: IF a, b, b THEN w, x, y, z, etc. > > That's a big IF. > > P: Yes, Axioms are assumptions, I have not > disputed that, but some assumptions are correct > in the sense that they produce useful results, and others > are not. Yes, again, certain modern scientific theories seem > to coincide with certain Hindu, and Buddhist's ideas, and > some try to use such coincidences as proof of all sort > of mystical nonsense. The rush to certainty and the > proliferation of fantasy is a powerful temptation for the > incautious spiritualist. > > > > > > B: There is never any verification of any axioms in mathematics. > > > > In the history of mathematics this was not fully realized > > until the time of the non-Euclidean geometries. Prior to > > that people generally thought that the axioms (in geometry > > they use the term " postulates " , but is the same thing) were > > *true* and defined the inherent nature of space. But then > > along came some guys that proved there could be a consistent > > geometry without the " parallel postulate " . Then along came > > Riemann who came up with a different non-Euclidean geometry > > from the other guys, and which later became fundamental for > > Einstein's theory of relativity. > > P: Well, since I'm not a mathematician maybe > we are understanding verification differently. > > When I say the results verify the axiom, I'm not referring > to results as proof of the universal truth of a > given assumption. I simply mean that such axiom was > the right one to use for that solution. Like in your paragraph > above, if you want to land a rocket on the Moon, you should > start by assuming space is curved and you should calculate > your trajectory accordingly. If I assume I have an orange seed > in my hand, and what I want is oranges, then getting an > orange tree after planting it, is my verification that my > assumption was right. That doesn't say lemon seeds are > false and orange seeds are right. Walking to the store, > a straight line is, still, the shortest distance between two > points. And for such purpose that is still the right axiom. > > I'll let the issue rest. > > > > Do you really think such a dry, analytical response is worthy of the > insightful mind you've been given? > > Phil > > Do you really believe that there exists a 'you' that has been given a mind? toombaru In one context, yes. Quote Link to comment Share on other sites More sharing options...
Guest guest Posted March 9, 2006 Report Share Posted March 9, 2006 Nisargadatta , ADHHUB wrote: > > > In a message dated 3/8/2006 7:43:33 AM Pacific Standard Time, > Nisargadatta writes: > > Wed, 8 Mar 2006 07:36:02 -0800 > Pete S <pedsie5 > Re: [NonDualPhil] Re: Math, Path & Analogies > > > On Mar 7, 2006, at 1:25 PM, billrishel wrote: > > > > >> P: Ok! I know that in arguing about math with you, > >> I'm getting way over my head. But axioms I can argue > >> because they just required intuition. Axioms are > >> math facts that we take as self-evident. All theories > > > > B: Axioms are *assumptions*. > > It is actually a very interesting point that *does* have > > bearing on nondual philosophy. Careful study of the > > philosophy of science and mathematics reveals that there > > are *no* known absolutes. The average person has no idea > > of this. > > > > In mathematics we say: IF a, b, b THEN w, x, y, z, etc. > > That's a big IF. > > P: Yes, Axioms are assumptions, I have not > disputed that, but some assumptions are correct > in the sense that they produce useful results, and others > are not. Yes, again, certain modern scientific theories seem > to coincide with certain Hindu, and Buddhist's ideas, and > some try to use such coincidences as proof of all sort > of mystical nonsense. The rush to certainty and the > proliferation of fantasy is a powerful temptation for the > incautious spiritualist. > > > > > > B: There is never any verification of any axioms in mathematics. > > > > In the history of mathematics this was not fully realized > > until the time of the non-Euclidean geometries. Prior to > > that people generally thought that the axioms (in geometry > > they use the term " postulates " , but is the same thing) were > > *true* and defined the inherent nature of space. But then > > along came some guys that proved there could be a consistent > > geometry without the " parallel postulate " . Then along came > > Riemann who came up with a different non-Euclidean geometry > > from the other guys, and which later became fundamental for > > Einstein's theory of relativity. > > P: Well, since I'm not a mathematician maybe > we are understanding verification differently. > > When I say the results verify the axiom, I'm not referring > to results as proof of the universal truth of a > given assumption. I simply mean that such axiom was > the right one to use for that solution. Like in your paragraph > above, if you want to land a rocket on the Moon, you should > start by assuming space is curved and you should calculate > your trajectory accordingly. If I assume I have an orange seed > in my hand, and what I want is oranges, then getting an > orange tree after planting it, is my verification that my > assumption was right. That doesn't say lemon seeds are > false and orange seeds are right. Walking to the store, > a straight line is, still, the shortest distance between two > points. And for such purpose that is still the right axiom. > > I'll let the issue rest. > > > > Do you really think such a dry, analytical response is worthy of the > insightful mind you've been given? > > Phil > > Do you really believe that there exists a 'you' that has been given a mind? toombaru Quote Link to comment Share on other sites More sharing options...
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