**Invited talk at the International Conference
on
"Methodology and Science"
Viswa Bharati, Santiniketan, 28-30 Dec 2004
**=========================================================

Why deduction is MORE fallible than induction: Ending the tyranny of

Western metaphysics in mathematics and science

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Centre for Computer Science, MCRP University, Bhopal

&

Centre for Studies in Civilizations, New Delhi

Western thought is premised on the belief that deduction is
infallible whereas induction is fallible. As such the ideal of truth that is
held up is that of formal mathematical truth, as in proofs in the kind of
mathematics that is socially dominant today. It is hence believed that
mathematical manipulations, needed to deduce refutable conclusions from physical
hypothesis, do not themselves add to the hypothesis underlying a physical
theory, so that refuting the conclusions of the theory refutes the physical
hypothesis, and not the mathematics.

Contrary to the way deduction has been seen in the West, I see the key issue
here as concerning the illegitimate elevation of metaphysics over physics and
the consequent arbitrariness that creeps into the notion of scientific and
mathematical truth: which has hence come to depend upon the authority of Western
metaphysics.

Thus, it is evident that the validity of a deduction varies with the logic used.
For example, any B can be validly deduced from A and not-A, in two-valued logic,
but such a deduction would be invalid with Buddhist logic, Jaina logic, or
quantum logic, or with any one of infinitely many different systems of logic
that one can conceive of.

Among the infinitely many different systems of logic that are conceivable why
should we particularly choose 2-valued logic or even those logics in which the
above deduction is valid? Historically speaking it is easy enough to understand
how, under the influence of Christian rational theology (via Islamic rational
theology, and its precursors in African "Greeks"), the West made the mistake of
regarding logic as universal. Understanding the historical origin of this
deep-seated but mistaken Western belief, of course, does not oblige us to
continue with it.

Therefore, while 2-valued logic may have seemed perfect and unchanging to those
who were ignorant (like Kant) of other cultures, there is no need to continue
with this mistake, unless one regards Western customs as infallible! The alleged
infallibility of deduction is merely a myth sponsored by theology: if deduction
is infallible, it leads infallibly merely to cultural truths not universal
truths. (This also means that a variety of Western philosophical claims need to
be either thought out afresh or else abandoned as unsound or of limited validity
within a cultural context.)

Two valued logic has also been used, of course, in Indian tradition, but the
point is that in India there has been a diversity of beliefs regarding logic,
from the earliest recorded history. Given the variety of customs, which logic
should one choose? Clearly, if the choice of logic is regarded as a cultural
matter, there can be no universal logic (unless, of course, all alternative
cultures are physically eliminated, as certain religions have attempted to do).
Therefore, the only acceptable alternative is to decide the nature of logic
empirically, depending upon the nature of time, for example.

Deciding the nature of logic empirically, is quite compatible with Indian
tradition, in which pratyaksa or the empirically manifest is the first
pramana.But isn't the empirical fallible? This is quite true. One might well
mistake a snake for a rope. In case of doubt, the right thing to do would be to
prod the snake/rope with a stick--that is, we repeat the observation with
greater accuracy. If the doubt persists, we prod harder.... One can of course
persist with the philosophical doubt long after there is no practical doubt, and
even after the snake is dead with prodding. That is, the fallibility of the
empirical means that, even the empirical refutation of a physical theory is
necessarily an inductive matter. (Popper actually maintained that refutation
related to deduction, and validation to induction. To this end he argued that a
series of favourable observations did not amplify the probability of occurrence
of an event. Technically speaking, while Popper was right in maintaining that
probabilities are not ampliative, he was wrong in supposing that one can obtain
probabilities from empirical data, which lead only to estimates of
probabilities, which estimates may well be ampliative.)

Thus (1) logic can only be decided empirically, and (2) since the empirical is
fallible, empirical decisions are necessarily inductive. That is, (3) the nature
of the logic to be used for deduction can only be decided inductively from
experience: hence deduction is necessarily _more_ fallible than induction.