Monday, June 20, 2011

Zero in Indian philosophy

Grammarians and linguists are familiar with the idea of a function of the ‘absence’ of morphemes which is currently called “zero”. Western linguists beginning with de Saussure's work of 1879 have often postulated the existence of the so-called zero-morphemes where the actual perceptible linguistic form does not match its relevant semantic and syntactic content (see T. Pontillo 2002, p.559ff.). They resorted to this device on the basis of a significant opposition pointed out between comparable morphological structures.
As focused by Al-George (Al-George 1967, p.121), on the other hand, the Indian linguistic zero is not a mere device, adopted for a descriptive purpose. It rather seems to represent “the consequence of a definite philosophy of form”, namely “the category which exists though not embodied in a concrete form, suspended as a pure virtuality at the border between existence and non-existence”.

A more general problem is: How can an absent element perform a function notwithstanding its absence? How comes that an effect can be grasped in absence of its cause?

On the latter problem, see here (on tantra and prasaṅga as a possible answer).


Dominik Wujastyk said...

adarśanam lopaḥ (Pāṇini's definition of lopa, one of his four forms of linguistic zero) means that the morpheme disappears, is invisible. It's not gone, I suppose (who knows what Pāṇini thought philosophically? We can only guess). Therefore, it continues to affect it's environment.

Al-George's article was ahead of its time in 1967, but he allowed his poetic fancy to run away with his brain, I think. And the concept of linguistic zero has been discussed quite a bit by Cardona and others since then.

In his book Rules and Representations, Chomsky said that some of his students had invented a new and exciting concept, that he named "trace elements." His idea was identical with Pāṇini's lopa, and he and his students were 2000 years out of date.


elisa freschi said...

Dear Dominik,

thanks for this insights. Well, the general problem I was trying to highlight is: how can something which does not exist continue to act? In the case of lopa, I agree that the concept of zero seems closely connected with that of substitution. I substitute X with zero, but zero, being just its substitute, will act like X (sthānivat, if I remember the rule correctly). In other cases, other devices are used. Tantra continues to act through a centralised instance, prasaṅga through a "by default" continuance.
Thanks for the remarks concerning Al-George. Of Cardona, I read his two "Panini" books and several articles (Śivasūtras 1969, Paraphrase 1975, Śākalya and Vedic dialects 1991). Would you have something else to suggest on this topic?

windwheel said...

I think the question you are asking is fundamental. Interestingly, a prominent Indian Game theorist, Kaushik Basu raises it in a play 'Crossings at Benares Junction'- his protagonist says the following-
Siddharth: ... see, if everything stops, the earth, you, the protons and atoms inside you and inside me… everything. It does seem obvious, right? That things cannot re-start again?
One way to reason is that whatever happens at any time is caused by the state of the world just before that. Now, if the world is motionless for some time, no matter how brief, there is a time when the world is motionless and just before that the world was motionless. Hence, motionlessness causes motionlessness. Hence, once there is no motion, there cannot be any motion.
This has lots of interesting implications. It means that we can never invent a TV set that can switch itself on. If it does, it is because we have programmed that in and there are small actions occurring inside it all the time. (Pause) What I wonder is, are we reaching this conclusion purely by deduction, or is this just a fact of life — that motion cannot come out of motionlessness.

Basu is wrong for 2 different reasons- one is that the World may be a cellular automaton with a rule which says if x appears in cell y after time t = some function of neighboring cells.
The second is the World may be the intersection of logically incompossible virtual Universes.
One argument for null morphemes is that the surrounding morphemes are behaving as though they were part of a cellular automaton of the sort described above. The second is that it is necessary for the hiatus between incompossible elements in otherwise effable propositions.
My feeling is that modulo arithmetic and board game style primitive cellular autamotons were used a lot before algebraic geometry was well formulated in India and so not 'Grammar' but Mathematical heuristics of a primitive cellular automaton sort were fundamental to ancient Indian thought.

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