In Nyaya-Vaisesika atomic theory atoms are both considered to be both without magnitude and round. How is this possible? For anything to be round, it must have at least a non-zero radius which contradicts its extensionless.

Is my conflation of extensionless with without magnitude the problem?

  • It is interesting to note that one can perform calculus with infinitesimals instead of limits, and my understanding is that they have the property that infinitesimal intervals have measure zero yet can in 2D be described to have different shapes (round, square, etc.). – Rex Kerr May 9 '12 at 15:52
  • I think that may be a solution in mathematical terms. I'd like to know how the buddhists themselves resolved this paradox. – Mozibur Ullah May 9 '12 at 20:00
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    Where did you get the idea that this is a physics Q&A site? We already have one of those. – Cody Gray May 9 '12 at 20:07
  • @CodyGray It seems that the Nyaya-Vaisesika atomic theory is related to modern physics as much as Democritus' atomism is (i.e. not much). Definitely a (history of) philosophy question. – DBK May 9 '12 at 20:28
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    Because we're not using the ancient definition of philosophy here. We're using a modern definition. We can afford to do that, since we're utilizing modern things like the Internet. Yes, this question does appear to be borderline. The other one is not. I'm just trying to figure out if it is a good candidate for migration the Physics site, rather than closing it outright. – Cody Gray May 9 '12 at 20:41

Is my conflation of extensionless with without magnitude the problem?

No, I don't think so-- I think you've put your finger on a genuine conundrum regarding Nyāya atomism.

I'm by no means an expert on Nyāya or Vaiśeṣika philosophies-- my knowledge of them comes largely from Buddhist polemics and debates with them-- but the problem that you raise is one that is in turn raised by various Indian Buddhists, so it is not a new criticism. I'm afraid I don't know the Nyāya-Vaiśeṣika response to this charge; I'd be most interested if someone more knowledgeable can provide it.

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  • This is entrely conjectural, but in your discussions has the issue been raised of differing use of logic? After all, Nyaya is an Indian school of logic, and one should pause before thinking logic is going to be used in the same manner in both cultures, and as Kerr pointed out above synthetic infinitesimals can be used to resolve the paradox, and this uses a non-classical logic. – Mozibur Ullah May 10 '12 at 0:47
  • The use of logic is definitely key; indeed, the works of Dignāga and Dharmakīrti are largely an attempt to use Nyāya logical forms to prove Buddhist doctrine (in pan-Indian debates.) – Michael Dorfman May 10 '12 at 6:30

Define your terms. If round means "every point on the edge is the same distance from the middle" then something extensionless can be round: every point on the edge is a distance of zero from the middle.

But arguably you'd want your definition of round to allow ellipses to be round. So what does roundness mean? I'm sure there could be a definition of what it means to be round that doesn't entail having an extension.

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  • Thats a matter of debate. One can stipulate that the radius must be non-zero for it to be considered actually round. But the radius actually comes a posteria when one begins to understand what roundness means. Most people would consider a ball to be round and not a point. A point becomes round only when using a mathematical description, and even then its the degenerate case. – Mozibur Ullah Sep 16 '12 at 11:21
  • Of course it's a matter of debate. It's philosophy. But my point stands. You can define your terms so as to make it true or false. As long as we agree on the definitions of "round" and so on then we can answer the question. – Seamus Sep 17 '12 at 9:33
  • redefining terms to make an arbitrary statement true or false seems to trivialise the idea of truth... – Mozibur Ullah Sep 17 '12 at 16:49
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    No it doesn't. Surely the truth of "Snow is white" depends on what "snow" and "white" mean. For various terms like "round" there are several legitimate ways one might want to make precise the vague concept. The truth of "extensionless points are round" depends on the definition of those terms. There's nothing trivial about the truth involved here. It's just a fact about how language matches up with reality that sometimes the truth of a sentences depends on how the terms are interpreted. – Seamus Sep 17 '12 at 16:52
  • for most of time for most people vagueness works, mainly because what is discoursed is plain to their senses. However extensionless points are not, so it behoves us to be more careful. Of course it does depend on what those terms mean, but surely one should aim for a truthful meaning: Arguments are marshalled for each definition, and one examines those arguments in the light of experience, theory and intuition. After all, one could argue that an extensionless point by not occupying any space has no existence whatsoever, and thus atoms in this sense are vacuous and sought in vain. – Mozibur Ullah Sep 18 '12 at 2:47

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