[NonDualPhil] Math, Path

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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