[Buddha-l] Non-arising

[David Andrews]

Hello Dan,

Thank you very much for taking the time to answer my questions.

I think it only fair to point out that few working mathematicians are 
likely to believe that mathematical arguments become in any sense better 
by being 'purified' of content. (I'm not even sure if they would mean 
anything at all so purified. Granted that I haven't looked into 
literature on the subject written after the nineties.) Gödel would, I 
think, have objected quite strenuously, since his incompleteness 
theorems rely on commonly accepted intuitions that apply to the standard 
model of integers, whose existence he would have accepted as a proponent 
of mathematical Platonism.

I do agree, however, that at least part of the thrust of the more 
canonical forms of logic (e.g., first order predicate calculus) is to 
throw light on (if not to fully capture) the idea of mathematical proof, 
not to capture the kinds of syllogisms that you discuss.

The example you gave would seem to covered, at least in part, by the 
traditional distinction between inductive rather than deductive 
processes, touching as it does on drawing conclusions about the real 
world based on limited observations of it. I'm no expert on the 
philosophy of science, but I don't think one can go very far down that 
road without running into the problems that seem to me to have derailed 
the Logical Positivist program. But I suppose that road would also 
diverge rather quickly from any historical Buddhist analysis.

I do agree, however, with your point that defining smoke as being that 
which is produced by fire is certainly a pointless distraction from the 
inductive force of Dignaga's argument. I'm not sure, however, that the 
objection on purely tautological grounds is justified given the 
historical importance of definitions in mathematics. (I am thinking, for 
example, of the critical importance of the definition of a notions like 
'function', 'ordinal' and 'open set' to the development of set theory 
and to the history of mathematics.)

Well, I know that all my questions can't be answered through an email 
discussion.

It would helpful if you could provide me some references to the 
literature. My specific interest would be the comparative analysis of 
historical treatments of so-called Buddhist logic and modern treatments 
of logic in a more general sense of the term.

Thanks,

David.

On 28/02/2010 3:23 PM, Dan Lusthaus wrote:
> 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.
>