As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school. But there are five other Astika or orthodox schools of Hindu philosophy: Purva Mimamsa, Samkhya, Yoga, Vaisheshika, and Nyaya. My question is about the Vaisheshika school, according to which atoms are the cause of the Universe. As I discuss here, the second oldest work of the Vaisheshika school is Prashastapada's Padartha Dharma Sangraha. Now in this excerpt of the Padartha Dharma Sangraha, Prashastapada discusses the nature of numbers:

Number forms the basis of such usages as "one" and the rest. It inheres in one and in many substances. The number inhering in one substance has its eternal and transient manifestations as those of the color etc. of the atom of water and the rest. The number inhering in many substances begins with "Two" and ends with "Parardha" (100,000,000,000,000,000).

I'm interested in the part in bold. The fact that a Parardha equals 100,000,000,000,000,000, i.e. 100 quadrillion, is a parenthetical note given by the translator, but it's confirmed in this chapter of the Vishnu Purana:

A Parárddha, Maitreya, is that number which occurs in the eighteenth place of figures, enumerated according to the rule of decimal notation.

But my question is, why did the Vaisheshika school believe that 100 quadrillion is the largest number? The fact that they believed this seems fairly clear. Here's what this excerpt from Sridhara's Nyaya Kandali, a commentary on Prashastapada's work, says:

The number inherent in more than one substance includes all numbers from two to the highest conceivable number. "Parardha" is that at which all limitations of number ceases.

But what is the reason for this belief? Now as I said, the Vaisheshika school believed in atomism, so is it possible that they thought that 100 quadrillion was the number of atoms in the Universe, and thus the biggest number? Do any Vaisheshika works shed light on this?

  • It could just be that it was the highest named number. There is no point of naming powers of 10 beyond a particular point: a name assigned to 10^(10^100) for example does not add much value to English or Sanskrit. – user1952500 Oct 22 '17 at 3:53
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    @user1952500 But then why would Sridhara's Nyaya Kandali call a Parardha "the highest conceivable number" and "that at which all limitations of number ceases"? That seems like a stronger claim than "it's the highest named number". – Keshav Srinivasan Oct 22 '17 at 4:05

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