There are several questions here. Let us distinguish between the formulations of Modus Tollens and Reduction ad Absurdum within symbolic logic, on the one hand, and the use of these words in informal logic, as found in Aristotle.

From the point of view of symbolic logic, the two rules of inference are distinct:

Modus Tollens, defined in modern logic, is this inference form:

 not q, if p then q |-  not p


Reductio ad absurdum, on one formulation, is this rule.

Gamma, p |- q and not q, then Gamma |- not p (where Gamma is a set of premisses)

Rules can be distinct, but turn out to be equivalent.

From Reduction ad absurdum, one can derive Modus Tollens, since Modus Tollens is just a special case of Reductio ad absurdum. It is not obvious to me off that one can derive RA from MT.

The question of whether or not the rules are distinct in informal formulations, such as the kinds of formulations found in Aristotle, is an exegetical question.

I have never seen a formulation of the rule of RA in the Indian tradition, though it is used all the time and there is a name for it.

The tradition is clearly aware of the equivalence between a statement and its contrapositive, which, as Alistair pointed out, it related to MT.

The rule of contraposition:

 if p then q |-  if not q then not p 

is equivalent to the rule of MT.

Best wishes,
Brendan





On 7/1/21 8:21 AM, Franco wrote:
Dear Alex,
Thank you, but I’m not sure that this formulation counts as modus tollens. It is usually stated in the form: if a, then b. Not b, therefore not a.
Thus:
If there would have been smoke on the mountain, there would have been fire there. But there is no smoke, therefore ...
Best wishes,
Eli


Sent from my iPad

On 01.07.2021, at 13:49, Alex Watson <alex.watson@ashoka.edu.in> wrote:

Dear Eli

Let's take as an example of modus tollens:

Major premise: wherever there is smoke there is fire
Minor premise: there is no fire on the mountain
Conclusion: there is no smoke on the mountain

I don't think Indian logicians would see this as a prasaṅga, 
nor western philosophers as a case of reductio ad absurdum,
as it doesn't conclude something absurd or undesirable, 
therefore we are not compelled to reject one of the premises.

Yours Alex

--
Alex Watson
Professor of Indian Philosophy
Ashoka University

> Dear friends,
I have been wondering about something that is perhaps only tangent to 
the discussion. Can one distinguish between reductio ad absurdum 
(prasanga) and modus tollens (also prasanga?) in the Indian tradition? 
I am not sure that the distinction between the two is clear in the 
Western tradition either.
With best wishes,
Eli

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Brendan S. Gillon                       email: brendan.gillon@mcgill.ca
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