From what we have said before it will be easy to see that Mima@msa agrees in the main with Vais'e@sika about the existence of the categories of things such as the five elements, the qualities, rupa, rasa, etc. Kumarila's differences on the points of jati, samavaya, etc. and Prabhakara's peculiarities have also been mentioned before. On some of these points it appears that Kumarila was influenced by Sa@mkhya thought rather than by Nyaya. Sa@mkhya and Vais'e@sika are the only Hindu systems which have tried to construct a physics as a part of their metaphysics; other systems have generally followed them or have differed from them only on minor matters. The physics of Prabhakara and Kumarila have thus but little importance, as they agree in general with the Vais'e@sika view. In fact they were justified in not laying any special stress on this part, because for the performance of sacrifices the common-sense view of Nyaya-Vais'e@sika about the world was most suitable.
The main difference of Mima@msa with Nyaya consists of the theory of knowledge. The former was required to prove that the Veda was self-valid and that it did not derive its validity from God, and also that it was not necessary to test its validity by any other means. To do this it began by trying to establish the self-validity of all knowledge. This would secure for the Veda the advantage that as soon as its orders or injunctions were communicated to us they would appear to us as valid knowledge, and there being nothing to contradict them later on there would be nothing in the world which could render the Vedic injunctions invalid. The other prama@nas such as perception, inference, etc. were described, firstly to indicate that they could not show to us how dharma could be acquired, for dharma was not an existing thing which could be perceived by the other prama@nas, but a thing which could only be produced by acting according to the injunctions of the Vedas. For the knowledge of dharma and adharma therefore the s'abdaprama@na of the Veda was our only source. Secondly it was necessary that we should have a knowledge of the different means of cognition, as without them it would be difficult to discuss and verify the meanings of debatable Vedic sentences. The doctrine of creation and dissolution which is recognized by all other Hindu systems could not be acknowledged by the Mima@msa as it would have endangered the eternality of the Vedas. Even God had to be dispensed with on that account.
The Veda is defined as the collection of Mantras and Brahma@nas (also called the _vidhis_ or injunctive sentences). There are three classes of injunctions (1) apurva-vidhi, (2) niyama-vidhi, and (3) parisa@nkhya-vidhi. Apurva-vidhi is an order which enjoins something not otherwise known, e.g. the grains should be washed (we could not know that this part of the duty was necessary for the sacrifice except by the above injunction). Niyama-vidhi is that where when a thing could have been done in a number of ways, an order is made by the Veda which restricts us to following some definite alternative (e.g. though the chaff from the corn could be separated even by the nails, the order that "corn should be threshed" restricts us to the alternative of threshing as the only course acceptable for the sacrifice). In the niyama-vidhi that which is ordered is already known as possible but only as an alternative, and the vidhi insists upon one of these methods as the only one. In apurva-vidhi the thing to be done would have remained undone and unknown had it not been for the vidhi. In parisa@nkhya-vidhi all that is enjoined is already known but not necessarily as possible alternatives. A certain mantra "I take up the rein" (_imam ag@rbhna@m ras'ana@m_) which could be used in a number of cases should not however be used at the time of holding the reins of an ass.
There are three main principles of interpreting the Vedic sentences. (1) When some sentences are such that connectively they yield a meaning but not individually, then they should be taken together connectively as a whole. (2) If the separate sentences can however yield meanings separately by themselves they should not be connected together. (3) In the case of certain sentences which are incomplete suitable words from the context of immediately preceding sentences are to be supplied.
The vidhis properly interpreted are the main source of dharma. The mantras which are generally hymns in praise of some deities or powers are to be taken as being for the specification of the deity to whom the libation is to be offered. It should be remembered that as dharma can only be acquired by following the injunctions of the Vedas they should all be interpreted as giving us injunctions. Anything therefore found in the Vedas which cannot be connected with the injunctive orders as forming part of them is to be regarded as untrustworthy or at best inexpressive. Thus it is that those sentences in the Vedas which describe existing things merely or praise some deed of injunction (called the _arthavadas_) should be interpreted as forming part of a vidhi-vakya (injunction) or be rejected altogether. Even those expressions which give reasons for the performance of certain actions are to be treated as mere arthavadas and interpreted as praising injunctions. For Vedas have value only as mandates by the performance of which dharma may be acquired.
When a sacrifice is performed according to the injunctions of the Vedas, a capacity which did not exist before and whose existence is proved by the authority of the scriptures is generated either in the action or in the agent. This capacity or positive force called _apurva_ produces in time the beneficent results of the sacrifice (e.g. leads the performer to Heaven). This apurva is like a potency or faculty in the agent which abides in him until the desired results follow [Footnote ref 553].
It is needless to dilate upon these, for the voluminous works of S'abara and Kumarila make an elaborate research into the nature of sacrifices, rituals, and other relevant matters in great detail, which anyhow can have but little interest for a student of philosophy.