Indian Syllogism -- correction

[Shyam Ranganathan]

Dear list members

Forgive me. My email program sent my message before I finished checking it.

I've corrected the errors bellow.

The most important corrections are:

(a) the criterion of a *valid* deductive argument is that the conclusion cannot
be false while the premises are all true

(b)if an argument fails the criterion of valid deductivity, it may either be an
invalid deductive argument (which is a bad argument) or a inductive argument
(which may be a good argument)


Sincere apologies

Shyam


Quoting Shyam Ranganathan <srangan at YORKU.CA>:

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?

[Correction here:]
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 [*valid*]
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 with
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?


[Correction here:]

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 [*inductive*] 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.


[Correction:]

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 [the Nyaya philosophers ] 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