Maṇḍana’s Vidhiviveka `Discernment about injunctions’ deals with chiefly two topics at length:

1. What is the nature of a prescription? After many discussions, examining the positions of Prabhākara and Bhartṛhari, the answer is that a Vedic prescription is just the statement that the action prescribed is the instrument to get a desired output.
2. If the above is true, how can one distinguish between fixed and elective rituals?

Let me now elaborate on both topics.

First, a sacrifice is considered by Maṇḍana to be an iṣṭasādhana, i.e., an instrument to something desired. A sacrificial injunction is therefore just the communication that the sacrifice is such (i.e., an instrument to something desired). Thus,

O(x/desire for y)

means

x is an instrument for y

This would work also for negative obligations, e.g.,

O (not eating (x)/desire for y)

means

forming the intention not to eat x is an instrument for y

Please notice that this could also cover cases of negative obligations which apply to everyone (in this case, according to the Viśvajit-metarule, one postulates heaven, i.e., happiness, as result):

O (not doing x/T)

is re-read as:

O (not doing x/desire for heaven)

This, in turn, means:

forming the intention to refrain from doing x is an instrument for heaven

This means that omitting the enjoined action (that is, not forming the intention to refrain from x) only leads to the non-obtainment of heaven. The situation would have been different had the same action x been forbidden, as will be explained immediately below.

What about prohibitions? They communicate one that the action prohibited is an instrument to something undesired, i.e., suffering (duḥkha).
Thus,

F (x/T)

means

x is an instrument for something absolutely undesirable

For instance, the prohibition to perform violence on any living beings (na hiṃsyāt sarvā bhūtāni) has the structure:

F (violence/T)

and not

*O (not violence/T)

because, if respected, it does not lead to any positive result (unlike an obligation), whereas, if transgressed, it leads to a negative output.

This means that prohibitions and prescriptions have a similar structure (both state that a given action is an instrument for something, respectively desirable or undesirable). Prescriptions are, however, in general effective only on people who desire that outcome, whereas prohibitions are effective on everyone, since the forbidden action would lead to outcomes which are absolutely undesirable (pāpa, which will interfere with all of one’s future undertakings).

The main advantage of this structure, as I can see it, is that one avoids the main problems of having a deontic logic, by translating deontic statements into descriptive ones.

What about the śyena, which prescribes one to perform a sacrifice leading to violence? śyena is anartha, i.e., in Maṇḍana’s understanding, it is also an instrument for something undesired, that is suffering (duḥkha). Thus, it should not be performed because it has this structure:

Śyena–»violence

and given:

F(violence/T)

we know that:

violence–»something undesired

Thus,

śyena–»something undesired

Thus, the choice to perform a śyena would be based on a misjudgement of what is at stake, since the positive output (the death of one’s enemy) is anyway less positive than the negative sanction that will follow.
NB: The target reader of Maṇḍana appears to be a rational agent who is completely able to judge the outcomes of their actions (unlike in the case of Prabhākara).

This leads to a problem, however, because if all sacrifices are considered to be just instruments to something desired, how can one account for the difference between elective and fixed results? It would indeed seem that all sacrifices are just recommended if one wants to achieve a given result, no more than that. Why would one perform some every day and some others only on given occasions? If the performance depended on the desire, an opponent suggests, then there would be no fixed sacrifices, since as soon as one gets what one desired, one would stop performing the sacrifice.

Maṇḍana examines various scenarios, including one that says that if one omits the performance of fixed sacrifices, one obtains pāpa (demerit), which will then block any further enterprise. Thus, fixed sacrifice would have as a positive result only the reduction of pāpa, whereas the their omission has a negative result, i.e., accumulation of further pāpa.

But what about the auxiliaries of fixed and elective sacrifices? According to all Mīmāṃsā authors, the former have to be performed as much as one can, the latter exactly as prescribed. Why this difference, if both sacrifices are just the same thing, namely instruments to something desired? Maṇḍana explains that the Vedic prescriptions enjoining fixed sacrifices prescribe them “as long as one lives”. This means that in their case the fixedness does not depend on the nature of the desire (i.e., they are not fixed just because one fixedly desires their output) but rather on the Vedic prescriptions prescribing them.
Thus, due to the metarule that says that the Veda cannot prescribe meaningless things and due to the metarule that only possible things can be prescribed, the “as long as one lives” clause cannot mean to perform auxiliaries exactly as prescribed. Thus, auxiliaries of fixed sacrifices are to be performed only as much as one can.

One might wonder: What about elective sacrifices to be done in order to obtain heaven? Given that heaven is happiness and every one desires happiness all the time, such sacrifices are potentially also to be performed all the time. Should one perform also their auxiliaries as much as possible?

The answer is no, because each elective sacrifice is incumbent on one every day anew and as such one is responsible to perform it (adhikārin) only if one has all relevant sacrificial ingredients. If one lacks them, one is not the adhikārin and therefore does not have to perform the sacrifice. Thus, there is no need to perform a sacrifice as much as one can.

By contrast, in the case of fixed sacrifices, one needs to perform them every day, since they are fixed, one is therefore always the adhikārin of them simply by being alive. Therefore, if one lacks, e.g., a relevant ingredient, one just performs the sacrifice as much as one can.