Indian Logic Forum

Plamen

I would like to re-open this metalogical discussion because of its paramount improtance for defining the nature of Indian inferential mechanism, its scope, volume, and sphere of application.

My thesis would be that Indian inference is a clear-cut deductive procedure by all criteria we may apply to it.

The inferential knowledge (anumiti) is a result of deductive reasoning known as tritiya paramarsa (third intuition) of the inferential mark. To be effectuated, this third intuition requires a general rule (prathama paramarsa) and an individual instance (dvitiya paramarsa) by means of which the conclusion is safely deduced from the universal intuition. We have a reasoning from the universal through instantiation to the particular, which is the regular course of any deduction.

All claims that Indian inferential schema does not offer any quarantees that the conclusion reached is quite apodictic do not meet the criteria of historical representation and logical correctness.

First of all, it is not true that flaws in the deduction turn the inferential procedures into inductive. Neither it is true that infallibility does not coexist with inductivity. Full induction is a good example of infallible reasoning. Due to the same reason, probabilistic is not co-extensive with inductive.

Arguments that udaharana and nigamana are introduced because of the certainty insuficiency of the intuitions proper to anumana are not valid because contradicting the motivation logic behind dividing inference into svartha and parartha. Notwithstanding its reduced number of members, svarthanumana is quite a valid means of cognition based on apodictic certainty (niscaya). And this is an established tenet for old Naiyayikas, Buddhist logicians, and Nyaya-Vaisesikas. All the three paramarsas of the syncretic NV are apodictic (based on certainty), niscaya is a regular category of Pracina Nyaya, niscaya is also a basic characteristic of inferential mark as elucidated by Dharmakirti and Dharmottara. In NB, Dharmakirti says quite definitely that certainty is the immanent characteristic of the mark in the context of its trairUpya - there is no anumAna without the linga being with all certainty established in the anumeya (lingasyAnumeye sattvam eva). To this Dharmottara comments:

yadyApi cAtra niZcita-grahaNaM na kRtaM tathApyante kRtaM prakrAntayor dvayor api rUpayor apekSaNIyam | (kAzI saMskRta granthamAlA 22, pr. 31)

Which means that certainty is the mode in which not only the first, but all the three forms of the inferential mark subsist. Inference is not intended to produce certainty, anumAna is rather based on certainty provided by means other than indirect knowledge, i.e., by pratyaksa.

Second, let's try a formal approach and reformulate atra dhumah tatra vahnih as all S that have P1 have also P2, where S is the paksa (locus), P1 is the dhumavattva (the state of being possessed of smoke) and P2 is the vahnimattva (the state of being possessed by fire). Then we can easily see that the classical Barbara could be also reformulated in the selfsame locus-based terms as all S (beings) that possess the P1 property of human-ness do also possess the P2 property of mortality.

A further step in transforming the classical Indian syllogism is to turn it from its locality (paksatva) form into a subject-predicate (paksadharmata) form

All S are P
X is S
.:. X is P

where S is the class of all smoking hills, P is fiery, and X is a particular individual of the S class, this particular smoking hill.

A perfect case of deductive reasoning with not a hint at probabilistic consclusions.

I would agree with Shyam Ranganathan that "Nyaya logic isn't propositional logic (i.e, the logic of propositions) but something more like the Aristotelian logic of classes."

Paksadharmata is the driving svarupa-sambadha of any Indian type of inference, hence we have a classical and very much refined at that paradigm of a predicate logic.

All postmodern and as a matter of fact "postcolonial" (in the sense of more literature than logic) talk about the probabilistic, inductive, or nonmonotonic nature of "Indian logcal schemas" flows from the inability to see that the way we reach the universal rule of invariable concomitance has nothing to do with the character of the inferential process per se. We establish the universal vyapti by means of ordinary pratyaksa (from everyday experience), extraordinary pratyaksa (samanya-laksana), or even arthapatti - bearing in mind the universality of language as anadi-samketa (beginningless convention).

Plamen

What follows is a summary of the Indology List discussion on Indian Syllogism

Peter Scharf

As I believe Plamen attempted to point out 25.2.06

Given the premises:in A
1. Wherever there is smoke there is fire
2. There's smoke on the mountain

It is a deduction, not induction, to conclude

3. There is fire on the mountain.

This is no less a deduction than in B
1. All men are mortal
2 Socrates is a man
Therefore
3 Socrates is mortal

To establish the major premise in B or the vyApti in A is another
matter. Induction is involved in establishing a vyApti and is
objected to on these grounds by, for example, the Carvaka, as being
only probable, not universal. The same charge could be laid against
B1. If it is argued that B1 is universal because it is an analytic
statement rather than inductive, a similar argument could be put
forward with regard to 1 by defining smoke as that which is produced
by fire. If it is admitted that B1 requires verification just as A1
is admitted in the Indian arena, the same sort of reasoning from
anvaya and vyatireka would be used. One could for instancce put
forward the counterexample to B1, of Yuddhisthira, who obtained
heaven with his body.

**************************************************
Peter M. Scharf (401) 863-2720 office
Department of Classics (401) 863-2123 dept
Brown University
PO Box 1856 (401) 863-7484 fax
Providence, RI 02912 Scharf@brown.edu
http://www.brown.edu/Departments/Classics/Scharf/
http://sanskritlibrary.org/

*********************

Richard Hayes

What Peter M. Scharf wrote on the Indian inference schema (which I
resist calling a syllogism) is exactly right (or at least is in exact
agreement with what I believe---we could both be wrong). If the
classical Indian schema is taken as a whole, that is, if how one arrives
at vyāpti is taken into account, then the schema as a whole cannot yield
the certainty of a deductive argument. It can yield only a probable (but
perhaps highly reasonable) conclusion.

That it is fallible is its greatest strength, I would dare to opine. But
that is perhaps a matter of taste. I thrive on uncertainty and get
overcome with nausea when people start having fits of certainty about
things. The only cure I have found for imagined certainty is a healthy
dose of mockery.

--
Richard Hayes
Department of Philosophy
University of New Mexico

********************

Plamen Gradinarov

I believe the way we arrive at the universal (and apodictic) character of the invariable concomitance (vyapti) has nothing to do with the Indian inferential mechanism, in the same way as the way we arrive at the universality of "All men are mortal" is not part of the Aristotelian syllogism. Our certitude that the major premise is true is arrived at by means of practice, experience (both ordinary and extraordinary), or authority. There is no whatsoever difference between

Universal affirmative:

All men are mortal
Socrates is a man
.:. Socrates is mortal

and

All dhumavan paksas are vahniman
Parvato dhumavan
.:. Parvato vahniman

Both are perfect examples of deductive reasoning.

Particular affirmative:

Some mortals are men (the condition being zoon politikon)
Socrates is a mortal (zoon politikon)
.:. Socrates is a man

and

Some vahniman paksas are dhumavan (the upadhi being wet indhanam)
Parvato vahniman (where the fuel is wet)
.:. Parvato dhumavan

Best regards,
Plamen

***************

Richard

> I believe the way we arrive at the universal (and apodictic) character
> of the invariable concomitance (vyapti) has nothing to do with the
> Indian inferential mechanism

It could be argued that the use of positive and negative examples is to
give a precedent for seeing an instance of the pakб№Јa with an instance of
the hetu, and to give a precedence for seeing both absent at the same
time and the same place. The presence of the examples, if it has any
purpose at all, seems to be to give a basis for believing that there is
a vyāpti. The proposition that there is a vyāpti is synthetic, not
analytic.

When unpacks the full implications of anvaya and vyatireka, it amounts
to saying "In every instance observed so far, the hetu has been present
only when the pakб№Јa has not been absent." This leaves open the
possibility, as Peter observed, that future observations may well
deviate from the past. It is not part of the very definition of smoke
that it is accompanied by fire; it has simply been observed so far that
smoky loci and also fiery. This makes the inferential schema one that
yields high probability but not certainty. So the inference schema is
much like Hume's famous example of the sun rising tomorrow; it is by no
means certain that the sun will rise tomorrow, but that the sun will
probably rise tomorrow is how the smart money bets.

There are, of courses, cases cited in Indian philosophy of lines of
reasoning that involve analytic claims. We have the famous example of
the barren woman's son. By definition a barren woman has no children.
Somewhat more interesting is the example of the horned hare. I have
heard animated arguments among Tibetans over whether it is an analytic
truth or a synthetic truth that hares have no horns. If anyone settles
that dispute definitively, I'll let you know.

As an aside, here in New Mexico a favorite joke to pull on visitors is
to tell them that somewhere out in the arid foothills there is a huge
jack rabbit that has antlers. It's called a jackalope. Tourists are
advised to keep their eyes open for them. Once when a Tibetan geshe was
visiting New Mexico, his friend bought a statue of a jackalope in a
tourist shop and said "See, Geshe-la, this proves that it's not
impossible for a rabbit to have horns. One can imagine such a thing. If
one can imagine something, it's not a logical impossibility. So it can't
be true by definition that rabbits do not have horns. It's a synthetic
truth." The geshe was unimpressed. He said "That's not a rabbit. If it
were, it would not have horns. It's a jackalope."

******************

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

* * *
Corrections

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)

Shyam

********************

Richard

On Wed, 2006-03-08 at 12:48 -0500, Shyam Ranganathan wrote:

> 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?

Yes, you have captured the debate precisely. Like you, I don't think
this is a word game at all. Over the years, however, I have noticed a
slight shift in the definition of inductive argument. When I was a young
pup, I was taught that an inductive argument is one in which a
generalization is formed from particular observations. Now, as an old
dog, I teach the young pups in my classes that an inductive argument is
one that is not deductive in nature, but one that nevertheless offers a
good reason to believe a conclusion on the basis of evidence. Deductive
arguments are valid or invalid; and valid arguments are sound or
unsound. Inductive arguments, on the other hand are strong or weak.

When I first started writing about Buddhist logic, I was using such
terms as "valid" and "sound" to refer to arguments that the Buddhists
called "good" or "correct" (samyak). At the time I was taking a graduate
course in philosophy of logics, and my professor, Hans Herzberger,
warned me off using the terminology of deductive logic when writing of
Dignāga. He demonstrated that an argument considered "correct" by
Dignāga could still yield a false conclusion. The failures all stemmed
from making new empirical discoveries. For example, if a North American
has repeatedly observed that all mammals give live birth to their young,
it would be considered a "correct" argument to conclude when one sees a
mammal, that the animal gives live birth to its offspring. If one were
then to visit Australia and see one of the mammals there than lays eggs,
one's previously "correct" argument would yield a false conclusion. This
is something no deductive argument can do. (Do Australian human beings
give live birth or lay eggs? Never having been south of the equator, I
remain agnostic on this matter.)

> To complicate things, inductive arguments seem to fail the criterion
> of deductivety, but seem ok altogether.

Right. Almost all the arguments that we make in daily life are, in fact,
pretty much like the canonical arguments used in classical India. The
classical Indian inferential schema works beautifully in practical life.
Like life itself, it has risks, but one learns to minimize them by
careful empirical observation. The deductive argument, on the other
hand, is rather barren and uninteresting. It works only when the major
premise is analytic. How often are we called upon in real life to make
inferences about the marital status of bachelors?

> 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.

For a long time I have tried to discuss Indian inferential schemata in
their own terms. One imposes unrealistic expectations on them when they
are called deductive. They just end up looking like failed deductive
arguments. A hundred years ago or so this "failure" was seen by some as
evidence that the philosophers of classical India were substandard
logicians. If one sees Nyāya as trying to present an Aristotelian
syllogism, then the Nyāya inferential scheme ends up looking like a
rather poor, at at least clumsy, attempt at a syllogism. If, on the
other hand, one looks at what the Indians were actually trying to do in
anumāna theory, it turns out they were doing an excellent job at
practical reasoning.

I see it, therefore, as a practice in charity of interpretation to see
the classical Indians as offering something more like Peirce's abductive
logic (or inference to the best explanation) than something like
mathematical deduction or Boolean algebra. Perhaps this is caving in to
political correctness of some kind, but I do think there is rather more
at stake here than politesse. (I hope so; I'm a complete failure at
being polite.)

Richard Hayes
Department of Philosophy
University of New Mexico
http://www.unm.edu/~rhayes

********************

Shyam

Prof. Hayes wrote:

> When I first started writing about Buddhist logic, I was using such
> terms as "valid" and "sound" to refer to arguments that the Buddhists
> called "good" or "correct" (samyak). At the time I was taking a graduate
> course in philosophy of logics, and my professor, Hans Herzberger,
> warned me off using the terminology of deductive logic when writing of
> DignГ„ВЃga. He demonstrated that an argument considered "correct" by
> DignГ„ВЃga could still yield a false conclusion. The failures all stemmed
> from making new empirical discoveries. For example, if a North American
> has repeatedly observed that all mammals give live birth to their young,
> it would be considered a "correct" argument to conclude when one sees a
> mammal, that the animal gives live birth to its offspring. If one were
> then to visit Australia and see one of the mammals there than lays eggs,
> one's previously "correct" argument would yield a false conclusion. This
> is something no deductive argument can do. (Do Australian human beings
> give live birth or lay eggs? Never having been south of the equator, I
> remain agnostic on this matter.)

Could the problem here be merely the conflation of "validity" with "soundness"
with the idea of samyak? Certainly, sound arguments cannot yeild false
conclusions, for a sound argument is simply a valid argument with true premises
and thus a true conclusion. But a valid argument can certainly yeild a false
conclusion, provided that some or all of the premises are false. Thus, in the
example you provide, the false premiss is that mamals give live birth to their
young.

While I know even less about Buddhist logic than I do about Nyaya, it seems to
me suspicious that 'samyak' could be both 'validity' and 'soundness', as these
are distinct concepts.

>The deductive argument, on the other
> hand, is rather barren and uninteresting. It works only when the major
> premise is analytic. How often are we called upon in real life to make
> inferences about the marital status of bachelors?

Ah. I'm quite sure this is not true.

As a proof that this must not be so, consider an argument with a necessarily
false premise, such as "p and not p", where "p" is any proposition that one
cares (for instance, "I ate breakfast today"). According to the standard
definition of deductive validity --- a valid argument is an argument with no
distribution of truth values across its atomic propositions such that all the
premises turn out to be true while the conclusion is false ---*any* argument
that employs this claim as a premise will be valid, for there will be no
distribution of truth values across the atomic propositions such that all the
premises will be true while the conclusion is false. Self contradictory
premises are certainly not analytically true. And moreover, none of the other
premises in such an argument need to be analytic either.

Thus, if we continue with "p" means "I ate breakfast this morning" and say "q"
is "I love seitan" and "r" is "Frege was a proto-Nazi", the argument

p and not p (I ate breakfast this morning, and I didn't eat breakfast this
morning)
q (I love seitan)
therefore r (therefore Frege was a proto-Nazi)

is deductively valid.

None of these premises are analytic. Or, if one likes, consider a Humean example
where "p" is "the sun rises every day" and "q" is "the sun rises on tuesdays."
Modus ponens with these propositions is perfectly deductive and valid:

p->q (if the sun rises every day, then the sun will rise on tuesday)
p (the sun rises every day)
.'. q (the sun will rise on tuesday)

Nothing analytic here, but this is the very archetype of a valid deductive
inference we teach in our symbolic logic classes.

> For a long time I have tried to discuss Indian inferential schemata in
> their own terms. One imposes unrealistic expectations on them when they
> are called deductive. They just end up looking like failed deductive
> arguments. A hundred years ago or so this "failure" was seen by some as
> evidence that the philosophers of classical India were substandard
> logicians. If one sees NyГ„ВЃya as trying to present an Aristotelian
> syllogism, then the NyГ„ВЃya inferential scheme ends up looking like a
> rather poor, at at least clumsy, attempt at a syllogism. If, on the
> other hand, one looks at what the Indians were actually trying to do in
> anumГ„ВЃna theory, it turns out they were doing an excellent job at
> practical reasoning.
>
> I see it, therefore, as a practice in charity of interpretation to see
> the classical Indians as offering something more like Peirce's abductive
> logic (or inference to the best explanation) than something like
> mathematical deduction or Boolean algebra. Perhaps this is caving in to
> political correctness of some kind, but I do think there is rather more
> at stake here than politesse. (I hope so; I'm a complete failure at
> being polite.)
>

I certainly agree that if it turned out that all of our efforts to use the
concepts of deductive logic to discuss Nyaya or Buddhist logic turned out that
we were painting their efforts as failed, we would be well advised to revise
our conceptualization of their efforts. But so far, it seems that the trouble
we've been having is in distinguishing between the *scheme* and the
propositions that are substituted into the scheme. It is the scheme that
determines validity, not the propositions. And we thus need some way of
conceptualizing the scheme apart from the employments of the schemes that so
many of the Indian philosophers gave in their writings. And here, it is their
intentions that make a big difference: how did they regard their schemes? One
way to test this would be to see if Nyaya or Buddhist logicians regarded facts
that contradicted the conclusions of their argument schemes as having
implications for the truth of the premises in the argument. If something like
modus tollens could be observed in their thinking, we have a straight forward
deductive system at play.

Best

Shyam Ranganathan
Department of Philosophy
York University (Toronto)

*********************

Plamen

> If something like modus tollens could be observed in their thinking, we have a straight forward
> deductive system at play.

Anvaya-vyatireki is a clear case of modus tollens.

If there is smoke on the hill, then there is fire on the hill.
There is no fire on the hill.
Therefore, there is no smoke on the hill.

The absence of probandum (sAdhyAbhAva) here is contrapositively regarded as the vyApya (pervaded), while the absence of probans (sAdhanAtyaya) is correctly intuited in the third instance of parAmarZa as the vyApaka (pervading).

*********************

Richard

Perhaps there is no real point in being careful, but I tend to do so
anyway. The inferential schema used in India can be translated into
modus tollens, as it can also be translated into set theoretical
language. Like any translation, there may be some distortions. The
classical Indian schemata as they were used in India were neither framed
as something that can be handled by our propositional calculus, as modus
tollens is, nor was they framed in terms of the relations among sets.
They were framed in terms of examples of two particular things co-
existing in a particular locus (anvaya) and in terms of two particular
things being absent in a locus (vyatireka). From those particular
observations, both of which are necessary, one derives a vyāpti. I would
suggest that the statement of the vyāpti, given the limitations on
observation, can only be a reasonable proposition, but never a certainty
(niЕ›caya). For that reason I would take care to avoid using the language
of deduction, because, as I said earlier, such language may raise
expectations that cannot be fulfilled.

There is nothing more I have to say on this. I have stated my reasons
for exercising terminological caution, and nothing anyone has said yet
has shown me that such caution is seriously misleading anyone or
misrepresenting classical Indian inferential schemata. This whole issue
is of such little consequence that there is no obvious point in wasting
further time and bandwidth on it.

Richard Hayes
Department of Philosophy
University of New Mexico

RCS · Posted: Wed Feb 25, 2009 5:19 am Post subject:

1. All men are mortal
2 Socrates is a man
Therefore
3 Socrates is mortal

There is a MAJOR problem here. How has it been determined that all men are mortals?

Plamen · Posted: Sun Mar 08, 2009 12:20 pm Post subject:

In formal logic, this is not a problem. Since no one has proved the opposite, 1 is held to be true. Provided 1 and 2 are true, it follows that 3 is also true.

In Indian logic, 1 is ascertained by means of yogaja-pratyaksa, in European - by means of induction.

tantidharo · Posted: Sun Apr 12, 2009 7:38 am Post subject:

Plamen,

It would be of some interest to me if you could, on the one hand, abduce from the foregone contributions a stageal summing up, and, on the other hand, chart therein any probable paths of predictive agency, including perhaps an accommodating gesture by way of response to Richard Hayes’s dismissal of the value of the inquiry’s continuation.

Troy

RCS

Plamen · Posted: Sun Jul 26, 2009 8:38 pm Post subject:

In modus tollens, it is the absence of fire that proves the absence of smoke - only the upadhi is a little bit different: provided the locus is not water.