Anirvacaniya and Godel's incompleteness theorems

[wundermonk]

Greetings all,

One interesting result in the foundation of mathematics is Godel's incompleteness theorem.

The theorem states that in a "sufficiently strong" (technical definition of what constitutes this is beyond the scope of this thread) axiomatic system the following are true:

(1)There are true statements which cannot be proven to be true.
(2)There are statements that can not be proven to be either true or false.

Focussing on (2) above, I find a lot of similarity between that and the Advaitin conception of "anirvacaniya" or indeterminacy of the nature of the world.

The Advaitin argument is roughly the following:

(a)It is impossible to prove that the external world exists independent of cognition - this is the Advaitin's anti-realist (anti-Nyaya) position.

(b)However, cognition and the objects of cognition do follow some causal law. This is meant to imply that the world of cognition is not a mere cognitive construct but does have some causal factors outside of cognition - this is the anti-idealist (anti Madhyamika Buddhist) position. The classical example to drive home this point is the rope-snake analogy. Why does cognition misfire when a rope is perceived as a snake? Clearly, there is a rope out there. Yet, when it is wrongly cognized as a snake, where exactly is the snake that caused this cognition? In his introduction to the Brahmasutras, Shankara explains miscognitions as due to superposition of the not-self on the self.

So, the Advaitin argues that the status of the world is anirvacaniya - indeterminable to be either existent (as the Nyaya would claim) or non-existent (as the Madhyamika Buddhist would claim). That is, the world can not be assigned any determinate ontological status.

Yet, provisionally granting/assuming the existence of the external world, we can go about discussing/debating/arguing/disagreeing about it. This is the vyavaharika level. At the paramarthika (absolute) level, only Brahman exists.

Any thoughts/comments?

[JaiMaaDurga]

Namaste wundermonk,

I have mentioned the theorems in other threads in passing; though
some philosophers and mathematicians have been critical of any
consideration of them as having broader implications outside of
mathematics, they have indeed sparked considerable thought and
discussion among non-mathematicians

What you have raised also brings to mind how most Western thought has
only recently begun to venture into such territory, as carried by the vehicle
of scientific advancement in the vast (cosmology and the anthropic principle) and the minute (quantum mechanics)..
I shall say more later..

JAI MATA DI

[wundermonk]

Hi JMD,

I did not intend to imply that Godel's theorems somehow vindicate the Advaitin position or some such thing. That would be uncharitable to both the Advaitin as well as Godel/logicians.

I just found the parallels noteworthy.

In any case, are you aware of any unprovable true statements or statements that can neither be proven true/false in some field of math that are relatively easy to understand? I know that Godel does indeed construct such statements but his construction seems a bit too involved - talking of meta-math, self-referential statements, etc.