Indian Syllogism

[Richard P. Hayes]

On Thu, 2006-03-09 at 22:24 +0100, Plamen Gradinarov wrote:

> > If something like modus tollens could be observed in their thinking, we have a straight forward
> > deductive system at play.
> 
> Anvaya-vyatireki is a clear case of modus tollens.
> 
> If there is smoke on the hill, then there is fire on the hill.
> There is no fire on the hill. 
> Therefore, there is no smoke on the hill.

Perhaps there is no real point in being careful, but I tend to do so
anyway. The inferential schema used in India can be translated into
modus tollens, as it can also be translated into set theoretical
language. Like any translation, there may be some distortions. The
classical Indian schemata as they were used in India were neither framed
as something that can be handled by our propositional calculus, as modus
tollens is, nor was they framed in terms of the relations among sets.
They were framed in terms of examples of two particular things co-
existing in a particular locus (anvaya) and in terms of two particular
things being absent in a locus (vyatireka). From those particular
observations, both of which are necessary, one derives a vyāpti. I would
suggest that the statement of the vyāpti, given the limitations on
observation, can only be a reasonable proposition, but never a certainty
(niścaya). For that reason I would take care to avoid using the language
of deduction, because, as I said earlier, such language may raise
expectations that cannot be fulfilled.

There is nothing more I have to say on this. I have stated my reasons
for exercising terminological caution, and nothing anyone has said yet
has shown me that such caution is seriously misleading anyone or
misrepresenting classical Indian inferential schemata. This whole issue
is of such little consequence that there is no obvious point in wasting
further time and bandwidth on it.

-- 
Richard Hayes
Department of Philosophy
University of New Mexico