pramANa (was Re: [Advaita-l] Re: Women and Vedas)
S Jayanarayanan
sjayana at yahoo.com
Mon Apr 10 14:34:01 CDT 2006
--- Vidyasankar Sundaresan <svidyasankar at hotmail.com> wrote:
>
> >
> >In mathematics, A Pramana could be equated to a Theory(or a
> corollary) and
> >it defenitely needs proof, comprehensible by the human
> mind-intellect.
> >
>
> The Sanskrit word pramANa is not to be translated as theory or
> corollary.
> There are other terms for these concepts, e.g. paksha
> (theory/position),
> siddhAnta (conclusion, that which has been proved), rAddhAnta (same
> as
> siddhAnta, related to the word Rddhi, just as siddhAnta is related
> to
> siddhi), upagamana/abhyupagamana (in most contexts, this word
> refers to that
> which is assumed as true at the start of a reductio ad absurdum
> argument),
> abhyupagantavya (corollary, as it follows from a previously
> established
> siddhAnta) etc.
>
> In vedAnta, a pramANa is pure and simple, a means of knowledge.
IMO, pramANa can be translated as "Right Means to Cognition".
PramA is that which arises when the conditions for knowledge are
present, so pramA may be translated as "Cognition". The right means
of acquiring pramA are the pramANas.
PrAmANyam may be proof or evidence.
> Perhaps the
> best English word to capture the spirit of the word pramANa in this
> context
> is "axiom," not theory nor corollary.
PramANa is actually different from axiom, as I will explain below:
> By definition, an axiom is
> not in need
> of proof, because otherwise, you will land in an infinite chain of
> unproved
> statements. If you say that a statement A is a pramANa, and also
> that that A
> needs proof by something else, then that something else, B, will
> need proof
> from a third statement, C, and so on, ad infinitum. At the root,
> you need to
> accept some axiom as not requiring proof. That is your pramANa. An
> axiom
> need not even be comprehensible by evey human mind, e.g. some
> axioms in
> certain non-Euclidean geometries that cannot grasped by our minds,
> which are
> conditioned by the Euclidean world that we perceive, or some axioms
> of
> quantum physics, which are incomprehensible to most of us,
> conditioned as we
> are by the classical world that we perceive.
Mathematics as it exists in the 21st century has gone beyond ideas
like perception or comprehensibility.
As an example, consider this axiomatic system:
Axiom 1: ABB.
Axiom 2: Rule - If string contains 'A' then replace with 'AB'.
Theorem (from above two axioms): ABBB.
Can a string like "ABB" be taken as a pramANa? I don't think so. But
it can be taken as an axiom. The "formalists" argue that one can in
principle consider ANY string as an axiom, so long as the axioms so
chosen are internally consistent (i.e. no two axioms contradict each
other), and then develop the axiomatic system by proving theorems.
Today, most (all?) branches of mathematics have been reduced to such
axiomatic systems.
One may ask the question: "What if the axiomatic system is
meaningless, how do we know that it is true?"
The mathematician's reply would be, "We deal with axioms and
theorems, not 'meaning' and 'truth'."
It has now been recognized that no axiomatic system can incorporate
"meaning" or "truth" into itself. John Searle has argued that such
symbol-manipulation misses the ultimate human cognition - MEANING,
but most physicalists dismiss his ideas as "meaningless" :-)
The book "Goedel, Escher, Bach" by Hofstadter contains many such
examples of axiomatic systems all of which are symbol-manipulation.
This leads to the fundamental hypothesis of artificial intelligence:
"All human intelligence is in essence symbol-manipulation."
Since computers can perform symbol-manipulation, it is possible to
construct a computer that mimics the human brain.
So much for mathematics. Science is a bit different.
-------------------------------------------------------------------
Science considers a means of knowledge that is not accepted by
mathematicians: experience. All scientific hypotheses (or "scientific
axioms") can be tested by experimentation.
For example, consider the two hypotheses:
Hypothesis A: Horses exist.
Hypothesis B: Unicorns exist.
We know hypothesis A is true and B is false - through experience. It
may be possible to consider both as axioms in mathematics, but not so
in science, for science bows down to experiment.
-------------------------------------------------------------------
Now comparing the above with MImAmsA-VedAnta epistemology, it is
clear that the "axioms" of mathematics are not necessarily pramANas,
for MImAmsA definitely accepts MEANING of a statement as a cognition.
Also, the "axioms" of MImAmsA cannot be arbitrarily chosen, but
depend upon experience, inference, and the Vedas. Moreover,
MImAmsA-VedAnta seems to accept the idea of "truth" rather than
merely "theorem", so it would be difficult to say that these are
synonymous terms.
the pratyaksha-anumAna in MImAmsA-VedAnta can be taken as a
scientific epistemology without the idea of hypothesis testing, but
the most crucial difference between MImAmsA-VedAnta and
mathematical-scientific theories is in VERBAL COGNITION. As we are
viewing this computer, all we actually see are black pixels embedded
in white pixels. But the mind sees something quite different - WORDS
AND MEANINGS. This verbal cognition belongs neither in science (which
would say that there is nothing outside of black and white pixels),
nor mathematics (which doesn't have to do with meaning at all), but
in linguistics. Without this crucial verbal cognition,
MImAmsA-VedAnta would not be able to uphold shruti as a means of
cognition at all.
> Yet, there is no doubt
> in most
> educated people's minds that quantum physics accurately describes
> some
> aspects of the universe that we live in. The point is, what we
> perceive may
> have to be set aside, if we are to gain a superior understanding.
> Asking for
> "classical" proof of an axiom in a system that goes beyond the
> "classical"
> world is to miss a vital opportunity for better learning.
>
> Regards,
> Vidyasankar
>
Regards,
Kartik
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