Indian Logic Forum

Plamen

Ferenc Ruzsa wrote
The centrality of udaahara.na in old Nyaaya inference
---- Abstract: ----

The five-membered naiyaayika inference seems unnecessarily complex. The following three questions are inherently interrelated:
вЂ“ What is the role of the fourth and fifth members, when they are but repetitions of the second (proof) and the first (proposition/conclusion)?
вЂ“ Why do we have in the third member an example instead of a statement of the general rule?
вЂ“ Why are there two examples, positive and contrary, when the rules illustrated by them are but contrapositives of each other, i.e. they are logically equivalent?

Later Nyaaya practically dropped the last two members, keeping them only for rhetoric reasons in public arguments (paraarthaanumaana). And already Dharmakiirti suggested that the first two members only constitute a valid inference (the general rule being implied by them). But the Suutra is very strict on the five members: omitting or adding an extra member means unconditional defeat in a debate (nigrahasthaana).

Already in the Suutra we find clear awareness of the fact that no example is a valid substitution of the general rule: one kind of false reason, hetvaabhaasa is the savyabhicaara, where there is an exception to the rule. And later Nyaaya develops the theory of the upaadhis, restricting conditions to correct such faulty inferences.

The two kinds of example are generally justified with reference to those rather unusual cases where either of the two is not possible (kevalaanvayin, kevalavyatirekin). This explanation, although ingenious, is not fully convincing as it is extremely difficult to find a plausible example of a kevala-vyatireki lingam.

We get closer to a possible answer once we get rid of the notion that the anumaana is but a contorted version of the very simple Barbara-type syllogism. Then we may recognise that the Nyaaya inference is essentially inductive and intensional, in contrast to the basically extensional and strictly deductive nature of traditional European logic. Here the question is not, вЂ?Given these premisses, what follows?вЂ™ but rather вЂ?How can we get the right premisses?вЂ™ And it is the function of the udaahara.na to establish them.

The premiss being sought is always a necessary relation; purely extensional or accidental universality, like вЂ?all chairs here are brownвЂ™ is not considered. This is already suggested by Prasastapaada and explicitly stated by Dharmakiirti. So this premiss, the general rule, must be a natural or metaphysical law.

The two kinds of example represent two complementary research strategies to find, confirm or reject such laws, e.g. there is no smoke without fire. Focusing our attention on smoky objects, we try to remember a case when there was no fire nearby; and then focusing on essentially non-fiery objects, we try to find a case when there was still some smoke there. The stock example is very suggestive. вЂ?As in the kitchenвЂ™ is clearly not a single case of co-occurrence of fire and smoke, but refers to innumerable observations, and furthermore the causal relation could also be easily observed there. 'Not as on the lakeвЂ™ again suggests many observations, and also helps to clarify the concept of smoke вЂ“ for there may be dhuuma on the lake, in the sense of вЂ?mistвЂ™.

Presenting this double strategy is a convincing way to prove a general law; and in a debate it is a fair offer to the opponent: try in both ways to find a counter-example! And if you canвЂ™t, then accept my rule.

In a real debate this could be a long and complicated process; that is why at the end it was very useful to recall the other premiss (there is smoke on the mountain) and the proposition (there is fire on the mountain) вЂ“ since they were announced hours, perhaps days ago; and in the meantime the meaning of smoke has also become more definite, so we should now check if it was really smoke or only mist we saw.

* * *
The Gaurava of the PaNCAvayava of the Naiyayikas was pointed out by the Advaitins centuries ago.See VedAntaparibhASA of DharmarajAdhvarIndra.

There, it is clearly argued by the author that either of the triads-PratijNA,Hetu,UdAharaNa or UdAharaNa, Upanaya,Nigamana will do.His statement is-Vayam Tryavayave SthitAH=Advaitins rest on three limbs.
Regards
K.Maheswaran Nair

* * *

Professor Nair points out that certain Advaitins held only three of the five elements of the paNCAvayava to be required for the validity of an argument. Many other examples of non-Naiyaayikas who make such a point could be given. These do not weigh in favour of the unoriginality of Professor Ruzca's surprisingly rejected paper. His abstract already mentions that even later Naiyaayikas practically dropped the last two members. That all five are not necessary is of course not a new idea, but he goes on to offer a specific thesis for why they were included (given at the bottom of this message). This differs from the traditional explanation in terms of kevalaanvayin and kevalavyatirekin hetus. As to whether it differs from explanations already put forward in secondary literature, no one has yet pointed to other occurrences.

Alex Watson

* * *

A relatively recent volume on "The role of the example in (dRSTAnta) in classical Indian logic", which has come out in Vienna (editors Katsura/Steinkellner, Wiener Studien zur Tibetologie und Buddhismuskunde 58, Vienna 2004), contains several papers on the topic especially of the example in Buddhist and other forms of Indian logic, and also (though less directly) on the role of the fourth and fifth of the paГ±cāvayavāбёҐ.

The idea that examples are associated with metatheoretical reflections, which Ferenc Rusza also seems to drive at in his abstract, is in this volume quite poignantly put forward in Claus Oetke's paper "The Role of the Example in Ancient Indian Logic" (pp.175-195). Oetke outlines several ways in which examples can be considered as relevant for establishing/controlling the regularity of general hypotheses, some of which are similar to what Ferenc seems to have in mind. Oetke's paper is framed in an approach to Indian logic as sharing significant character traits with what is nowadays called "nonmonotonic reasoning" or "default reasoning", i.e. reasoning which operates on the assumption of normality conditions; this assessment has recently been called into question by John Taber [cf. his lengthy article "Is Indian Logic Nonmonotonic?", Philosophy East and West 4/2 (2004), 143-170; based on Oetke's "Ancient Indian Logic as a theory of non-monotonic reasoning." Journal of Indian Philosophy 24 (1996), 447-539. Cf. then again Oetke, "In which sense are Indian theories of inference non-monotonic?", Horin 11 (2005), 23-38]. The entire discussion contains many valuable ideas for a more sophisticated methodological approach to the issue of examples (in my opinion, a much more sophisticated approach than the distinction between deductive/inductive or extensional/intensional), and it sets the standard of reasoning quite high for future work in this area.

There is much more on examples in the abovementioned volume (including, among others, an article by Ernst Prets on example and exemplification in early Nyāya and VaiЕ›eб№Јika that summarily presents the relevant textual materials). As far as I know, it represents the current stage of scholarship in this area. If Ferenc Rusza has difficulties gaining access to any of the materials I have referred to, I'd gladly supply some photocopies.

Best regards,
Birgit Kellner

Plamen · Posted: Sat Feb 25, 2006 5:21 pm Post subject:

To my knowledge, the idea of Nyaya inference being intensional and inductive rather than extensional and deductive is as new as wrong. Udaharana doesn't prove the vyapti as expressed previously in the hetu, it only shows an example of invariable concomitance that can help the opponent (or the disciple) grasp the local nature of the general rule (its paksadharmata) rather than its universality. As for the real metalogical question at issue here, how do the Naiyayikas establish the universality of vyapti, the answer is: from practice (purvavat and sesavat) and Yogic perception, samanyatodrsta being one of the forms of it. In any case, correct inference is based on the relation between sadhana and sadhya universally established in the general rule by means other than anumana.

Plamen · Posted: Sun Feb 26, 2006 10:58 am Post subject:

> To my knowledge, the idea of Nyaya inference being intensional and
> inductive rather than extensional and deductive is as new as wrong.

I'm not sure how old something has to be not be considered new, but this
debate has been around for the last fifty years or so. What puzzles me
is how people can still be debating this. By no stretch of the
imagination can an Indian inferential schema qualify as deductive. It
can at best offer evidence that a conclusion is probable, which is what
makes it conform perfectly to the standard definition of inductive
argumentation. Oetke and Taber and others have established this so well
that the question will now be pretty much closed, at least until people
forget their work.

--
Richard Hayes
Department of Philosophy
University of New Mexico

Plamen · Posted: Sun Feb 26, 2006 10:58 am Post subject:

Dear Richard,

I have honestly tried to harness all my Einbildungskraft to imagine how a logical reasoning from a general premiss (atra dhumah tatra vahnih) to an individual conclusion (parvato vahniman) can be called inductive, and - frankly - failed. So I would prefer to be a retrograde and safely consider Indian anumana a perfect example of deductive reasoning.

As for the way we reach the first intuition (of the invariable concomitance of smoke and fire), it is from the repeated observation of their local coexistence as seen in the kitchen, etc. This first intuition (prathama paramarsa), although inductive, is not the inference itself. Inferental knowledge (anumiti) is rather defined as the third intuition (tritiya paramarsa) of the inferential mark; the second intuition being our seeing the smoke over the hill. Of these three intuitions, the first and the second are clearly examples of pratyaksa. It is only the third intuition that qualifies for the name of anumana.

More about this, in my 1991 English translation of Tarka-kaumudi, The Moon-Light of Logic.

Best regards,

Mukund Dhaygude

The inference process is related to object theories. The world comprises of objects (live/conscious/animate objects and non-conscious/inanimate objects). e.g. animal and human species and hills ( animate objects), mountains, rivers etc. (inanimate objects). Nyaya talks of logic as a generic discipline applicable to various knowledge disciplines. So we have logic for mathematics, logic for chemistry, logic for physics, logic for material science, logic for microelectronics, logic for nano-electronics. Nyaya as science implies that there is logico deductive / inductive processes. Panchavayava Nyaya then has to be looked from syllogistic and aphoristic procedures points of views. Such elements are found in Nyaya , Nav Nyaya, Navya Nyaya. B K Matilal is a good reading for this work. A mathematician will represent his logical knowledge/world as sets, as numbers, as relations, as functions, as characters, as tables, as matrices, as series, as sequences. A logician will look at it from proof theoretic point of view. Given datum, are there logical links that drive one to the conclusion?

Please read Sibjiban Bhattachrya's work published by Indian Council of Philosophical Research(ICPR).

The same object then links us to computer geeks that capture the logically proven world through programs. These programs are written in programming languages. The data is the logical datum.

Read Programming Logic / Logic Programming or use Turbo-Prolog a compiler software from Borland.

Thus we can see a continuous link between Prachin Nyaya to Navya Nyaya to Object Theories to Logic Programming to Prolog Software to Artificial Intelligence to Computer Sciences.

In between we fill it up with George Boole's work on Boolean Logic.
We look at temporal logic.
We look at relevance logic.
Boole's work is then converted into analog logic.
Digital logic was a secondary derivative.
Revolution in microelectronics, electronic chip industry could program such logics onto a micro chip since 1965 and we then got into present day micro processor based systems now commonly called as personal computers (PCs).

Look at Cornelius Goekoop's work on The invariable concommitance in Gangesha's Tatvachintamani funded by IBM in late 1960's (1967 published by Dorchet Holland Reidel Publishers since Goekoop is Dutch (Holland) fellow).

Coming back to mainstream we look at an instance of an object and see if the processes of instantiation can lead to process of generalization. These are cognitive processes of human mind that compare, filter , match data with data stored in a black box called mind.

Read Conceptual Structures in Human Mind by Sowa (IBM).

On other side Chomsky went ahead to represent linguistic knowledge mathematically and now we are able to translate from one language to another language automatically using computer as machines.