Indian Syllogism

[Shyam Ranganathan]

Dear list, and Prof. Hayes

Prof. Hayes wrote:

> When I first started writing about Buddhist logic, I was using such
> terms as "valid" and "sound" to refer to arguments that the Buddhists
> called "good" or "correct" (samyak). At the time I was taking a graduate
> course in philosophy of logics, and my professor, Hans Herzberger,
> warned me off using the terminology of deductive logic when writing of
> Dignāga. He demonstrated that an argument considered "correct" by
> Dignāga could still yield a false conclusion. The failures all stemmed
> from making new empirical discoveries. For example, if a North American
> has repeatedly observed that all mammals give live birth to their young,
> it would be considered a "correct" argument to conclude when one sees a
> mammal, that the animal gives live birth to its offspring. If one were
> then to visit Australia and see one of the mammals there than lays eggs,
> one's previously "correct" argument would yield a false conclusion. This
> is something no deductive argument can do. (Do Australian human beings
> give live birth or lay eggs? Never having been south of the equator, I
> remain agnostic on this matter.)

 Could the problem here be merely the conflation of "validity" with "soundness"
with the idea of samyak? Certainly, sound arguments cannot yeild false
conclusions, for a sound argument is simply a valid argument with true premises
and thus a true conclusion. But a valid argument can certainly yeild a false
conclusion, provided that some or all of the premises are false. Thus, in the
example you provide, the false premiss is that mamals give live birth to their
young.

While I know even less about Buddhist logic than I do about Nyaya, it seems to
me suspicious that 'samyak' could be both 'validity' and 'soundness', as these
are distinct concepts.


>The deductive argument, on the other
> hand, is rather barren and uninteresting. It works only when the major
> premise is analytic. How often are we called upon in real life to make
> inferences about the marital status of bachelors?

Ah. I'm quite sure this is not true.

As a proof that this must not be so, consider an argument with a necessarily
false premise, such as "p and not p", where "p" is any proposition that one
cares (for instance, "I ate breakfast today"). According to the standard
definition of deductive validity --- a valid argument is an argument with no
distribution of truth values across its atomic propositions such that all the
premises turn out to be true while the conclusion is false ---*any* argument
that employs this claim as a premise will be valid, for there will be no
distribution of truth values across the atomic propositions such that all the
premises will be true while the conclusion is false. Self contradictory
premises are certainly not analytically true. And moreover, none of the other
premises in such an argument need to be analytic either.

Thus, if we continue with "p" means "I ate breakfast this morning" and say "q"
is "I love seitan" and "r" is "Frege was a proto-Nazi", the argument

p and not p (I ate breakfast this morning, and I didn’t eat breakfast this
morning)
q (I love seitan)
therefore r (therefore Frege was a proto-Nazi)

is deductively valid.

None of these premises are analytic. Or, if one likes, consider a Humean example
where "p" is "the sun rises every day" and "q" is "the sun rises on tuesdays."
Modus ponens with these propositions is perfectly deductive and valid:

p->q (if the sun rises every day, then the sun will rise on tuesday)
p (the sun rises every day)
.'. q (the sun will rise on tuesday)

Nothing analytic here, but this is the very archetype of a valid deductive
inference we teach in our symbolic logic classes.


> For a long time I have tried to discuss Indian inferential schemata in
> their own terms. One imposes unrealistic expectations on them when they
> are called deductive. They just end up looking like failed deductive
> arguments. A hundred years ago or so this "failure" was seen by some as
> evidence that the philosophers of classical India were substandard
> logicians. If one sees Nyāya as trying to present an Aristotelian
> syllogism, then the Nyāya inferential scheme ends up looking like a
> rather poor, at at least clumsy, attempt at a syllogism. If, on the
> other hand, one looks at what the Indians were actually trying to do in
> anumāna theory, it turns out they were doing an excellent job at
> practical reasoning.
>
> I see it, therefore, as a practice in charity of interpretation to see
> the classical Indians as offering something more like Peirce's abductive
> logic (or inference to the best explanation) than something like
> mathematical deduction or Boolean algebra. Perhaps this is caving in to
> political correctness of some kind, but I do think there is rather more
> at stake here than politesse. (I hope so; I'm a complete failure at
> being polite.)
>

I certainly agree that if it turned out that all of our efforts to use the
concepts of deductive logic to discuss Nyaya or Buddhist logic turned out that
we were painting their efforts as failed, we would be well advised to revise
our conceptualization of their efforts. But so far, it seems that the trouble
we've been having is in distinguishing between the *scheme* and the
propositions that are substituted into the scheme. It is the scheme that
determines validity, not the propositions. And we thus need some way of
conceptualizing the scheme apart from the employments of the schemes that so
many of the Indian philosophers gave in their writings. And here, it is their
intentions that make a big difference: how did they regard their schemes? One
way to test this would be to see if Nyaya or Buddhist logicians regarded facts
that contradicted the conclusions of their argument schemes as having
implications for the truth of the premises in the argument. If something like
modus tollens could be observed in their thinking, we have a straight forward
deductive system at play.

Best

Shyam

Shyam Ranganathan
Department of Philosophy
York University (Toronto)