[Buddha-l] Non-arising

[Dan Lusthaus]

Hi David,

I didn't say it is not "amenable" -- what I said is when one converts an 
Indian syllogism into a mathematical logical language something is lost in 
the translation, and that is because "Formal logic" has come to mean "Form" 
(eidos) devoid of "content" -- which, the mathematicians believe, is 
therefore more "pure", i.e., form purified of content. The Indian version 
remains deeply wedded to content.

Two structurally identical statements will not guarantee that they are 
equally true (or false, or indeterminate). Their content, and more 
importantly, the way in which they share or refuse to share content 
determines their truth value.

In addition, the Indians were not above using almost poetic evocations as 
part of their syllogism.

For example:

(slightly modified for simplicity)

THESIS: There is fire on the mountain
REASON: because there is smoke there.
EXAMPLE:
Where there is smoke there is fire,
INCLUSIVE EX.: Like a kitchen stove
EXCLUSIONARY EX.: Unlike a lake.

(NB: Everything that comes after "Example" is considered one part of the 
argument, so Dignaga's three-part syllogism consists of Thesis, Reason, and 
Example, but notice that the example is multipart, though in practice one 
can abbreviate this last part -- though must be able to give the full 
version on demand)

Modern logicians would insist that once the principle ("where there is smoke 
there is fire") is given in the example, the logical work is done, and the 
conclusion (which is a reiteration of the thesis) is proven. So why did 
Dignaga not only insist on retaining the inclusive and exclusionary 
examples, but also insist that they were integral to the validity of the 
argument?

That's complex, but here's a simple version, which also illustrates the 
poetic function of the examples. In this case let's look at the Exclusionary 
example (vipak.sa).

"Unlike a lake", on first blush looks like a simple statement that there is 
no fire in water, which is part of the answer (indicating that there are 
indeed places devoid of fire, so determining which places, like the 
mountain, have fire, has parameters). But that example is doing more, though 
by connotation (i.e., the reader, hearer has to supply some of the 
implications), not simple denotation (Another difference from the Western 
approach to logic since Aristotle, which strove for univocality).

One of the objections to the argument about fire on the mountain being 
proven by the principle "Where there is smoke there is fire" that a modern 
person might raise is that we have (today) all sorts of smokes that are not 
accompanied by fire, like smoke machines used on stage and in films. The 
univocalist might respond "Technically, that is not 'smoke', since I define 
smoke as exclusively that which is produced by fire," but that only begs a 
tautological question. Nagarjuna would be salivating to have at such a 
narrow-minded opponent.

The Indian vipaksa is a more elegant solution. Lakes can have fog. Fog looks 
like smoke. Yet, when one looks at a lake covered with fog, one does not 
think "FIRE!". One thinks "fog," and doesn't confuse them. Why? Because fire 
doesn't usually burn in water (given Indian-style funerals on the Ganges, 
etc., they are aware of the exceptions; but they still know the difference 
between smoke and fog).

Now it's not that one can't find a way to express all that in Western logic 
notations, but not as elegantly and simply, and probably not in a way that 
would be structurally identical regardless of the content of the argument.

As for Dharmakirti's impact, I draw a line there because determining what he 
and those subsequent to him did with Dignaga's system is still a matter of 
great debate (infinitely more complicated by centuries of Tibetan tweaking, 
which they think were discoveries of things already intrinsic to Dharmakirti 
and Dignaga). So I am bracketing that -- I have no idea at what point Indian 
and or Buddhist logic became more "formal" in the Western sense, if at all. 
Perhaps with Navya-Nyaya, but I have my doubts...

Dan