Indian Syllogism

[Shyam Ranganathan]

Dear list members

This debate reminds me of the controversy in the philosophy of science in the
twentieth century as to whether the hypothetico-inductive model put forward by
people such as Carl Hempel was genuinely deductive, or whether it was
inductive. According to this model of science, scientists formulate hypotheses,
which then constitute a universally quantified premise (much like the first
premise of the standard syllogism) in an argument with standard deductive
properties, and the goal then is to find instances in reality that contradict
the deductive implications of the argument, thus falsifying the hypothesis.
Thus, consider the hypothesis "the sun rises every day." According to the
hypothetico-deductive model, we'd sub this into modus ponens,

p -> q (if p then q)
p
.'. q (therefore q)

where p is something like "the sun rises every day" and q would be some
observational consequence, like "the sun rises on Tuesday". Find an instance of
the sun not rising on Tuesday, and one would be licensed to make the following
modus tollens:

p -> q
~q (not q)
.'. ~p (therefore not p)

Every one could agree that modus ponens and modus tollens is deductive, but the
question was whether the hypothetico-deductive model, which supplies premises
with hypotheses is deductive. Few doubted that it was. But the critics always
pointed out that hypotheses rarely come to people in a flash (though Hemple
liked to think this) and they were usually the result of some type of inductive
generalization.

So, which is it? Could the argument over whether it is deductive or inductive be
merely a word game, where each measures the argument in a different way (some
counting the process of hypothesis formation as part of the inference, while
others include it outside)? Doesn't this mirror the argument over whether the
vyapti is part of the Nyaya inference or not?

I don't think it's a word game, but rather has to do with how we define
deductive arguments. Of course, the canonical criterion of a deductive argument
is that it has an argument form whose premises cannot all be true while the
conclusion is false. However, invalid deductive arguments are, on the normal
understanding, deductive arguments that fail this criterion. To complicate
things, inductive arguments seem to fail the criterion of deductivety, but seem
ok altogether. In other words, both inductive arguments and invalid deductive
arguments fail to preserve the truth of a conclusion along all true premises in
some distribution of truth values across atomic propositions. So, then, the
question is, how can we tell the difference between an invalid deductive
argument and an inductive argument?

This question always comes up in a critical thinking class, for it is not
obvious how in real life we are to treat arguments that fail the test for
deductivety. If they are invalid deductive arguments, they're bad arguments. If
they're invalid arguments, then they may be good arguments of a different kind.
And the answer to the question is: it depends upon how the authors of the
argument regard their argument.

Thus, I suggest to determine whether the Nyaya scheme is deductive or inductive,
we need to not evaluate it from the perspective of our ideal of deductivity, but
from how they regarded their arguments. Did they see it as yeilding apodictic
necessity? Or did they regard it in some other fashion. My suspicion is the
former, but I'm no expert in Nyaya logic.

Best,
Shyam (Ranganathan)
Department of Philosophy
York University, Toronto