Church's thesis & Sankara's argument re: Cause of liberation
Jaldhar H. Vyas
jaldhar at BRAINCELLS.COM
Thu Mar 28 12:58:48 CST 2002
A forwarded message from Bhadraiah Mallampalli <vaidix at hotmail.com> which
I think you might find interesting.
---------- Forwarded message ----------
Alonzo Church's thesis & Sankara's argument re: cause of liberation
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While the Church keeps saying there is only one way for salvation, another
Church was knowingly or unknowingly to himself proving something opposite!
The computer scientist & mathematician Alonzo Church, in 1930s, had proposed
what is called unsolvability of the halting problem. It is stated as:
"There is no algorithm that, given a program of language L and an input to
that program, can determine whether or not the given program will eventually
halt on the given input."
This thesis can be proven mathematically for a specific known computer
language, but a generic statement like the one above is unprovable. So
Church's original thesis was never proved. In the words of Davis, Sigal,
Weyuker' in their book "Computability, Complexity and Languages" this is
explained : "But, since the word algorithm has no general definition
separated from a particular language, Church's thesis cannot be proved as a
mathematical theorem". One example of such a program not known if it halts
is: "Every even number >= 4 is the sum of two primes" This is the 250 year
old Goldbach's conjecture which is never known to halt for its search on
its way to infinity.
But in all these 70 YEARS since Church published his thesis little did
Church or any one realize that a similar line of thought was adopted by
Sankara about 1200 years ago when he declared after elaborate argumentation:
"There is no material cause for liberation".
I refuse to tolerate a cynical "Oh, one more thing found in the Veda!"
Now, discussion regarding this: First, let us formulate Sankara's assertion
using terms of computer science:
"It is not a case that there is a logical argument A in a human language L
and an input instruction I that, a human being H who thinks the language L
on receiving the input I, would eventually attain liberation and stop
thinking." I hope it is close enough.
The first objection to a relation to the above modified Sankara's statement
may be that, Sankara only proved it logically using human language, and not
using a mathematical method, so Church and Sankara are on the same line.
This objection is not valid because in the first place nobody has proved
that mathematics is equal to logic. And the present way of representing
mathematical logic is not necessarily the right one.
A lot of work needs to be done figuring out where we are with Sankara's
argument. Relation between logic and mathematics apart, other items like:
whether Sanskrit is a human language or a formal system, did we really
understand Sankara's argument in the right spirit, and how we translate it
into a formal language so on.
And this is not to say that Sankara's conclusion is limited to Church's
thesis re: halting problem! All I am trying to say is, that one of Sankara's
statements is isomorphic to one of the topics (if not propositions or
theorems) of computer science.
Best regards
Bhadraiah Mallampalli
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