Are there general rules in Vedic rituals? No, just material entailments

prasaṅga is not frequent in the Śrautasūtras and I failed to find a definition of it. Hence, one has to reconstruct its meaning indirectly, through its usage in the ŚrSū, through its usage in Grammar and Mīmāṃsā and possibly also through its etymological meaning. Every translation is therefore intrinsically tentative.

In its only occurrence in the Aśvalāyana Śrautasūtra (AśvŚrSū 1.1.22) it is opposed to apavāda (certainly meaning "exception"):

prasaṅgād apavādo balīyaḥ

Mylius translates:

Eine Ausnahme (-Regel) ist gewichtiger als eine allgemeine Regel (Mylius 1994: 29a)

That is, "An exceptional [rule] is more forceful than a general rule".

But the meaning seems, more precisely, to be "default occurrence". The prasaṅga is what one expects to happen, what follows by default from the previous discussion. Only secondarily, it defines the "general" rule. Hence,

An exception is stronger than what is automatically entailed.

On prasaṅga, see here. On the problem of reconstructing the meaning of a term, when the technical context is lost, see here.

Tantra and prasaṅga in a Catholic Mass

During a Mass, the hosts are not severally consecrated. Their consecration is valid once for all. Using the terminology of the Indian ritualistics, one could say that it happens once for all, through tantra. Each host is part of the same rite and hence shares all the benefits of any act performed within the rite.

By contrast, imagine the case of two different rituals, like the Sunday Mass and the special Mass celebrated on the day of the Assumption of the Virgin Mary. Both Masses have to be attended compulsory by Catholic believers, but one can attend any of the Masses celebrated on that day or on the evening before. In other words, one is allowed to attend either one of the Sunday Masses celebrated during the whole Sunday or the "Sunday Mass" celebrated on Saturday evening. What happens if the day of the Assumption occurs on a Saturday (as it happens every seven years)? Is one allowed to go to the Saturday evening Mass and fulfil through the same act both duties? If yes, one could say that the function of the Mass celebrated on the Saturday evening as a "Sunday Mass" helps one fulfilling both duties. It fulfills directly the duty to attend the Sunday Mass and indirectly the duty to attend the Mass on the day of the Assumption of the Virgin Mary. This kind of double effect which was not intended could be called prasaṅga.
However, I am inclined to think that a Catholic believer should go to the Mass twice, once on the day of the Assumption of the Virgin Mary (in the present example, on the Saturday) and once on the Sunday (or on the Saturday evening), because the liturgy has a specific prescription about the fact that one has to attend the first and the second one. And, when there is a specific restriction, prasaṅga cannot apply (prasaṅgād apavādo balīyaḥ or prasaṅgo na, niyamaśabdāt).

On tantra, see here. On prasaṅga, see here.

Text, warp and woof

Due to the textile origin of the term tantra (from tan- 'to weave'), one might suggest the idea that it denoted at first the "texture" (note the same metaphor at work in "text") of a ritual, upon which successive rites could have been applied exactly as different kinds of weaving could be woven on the same rough warp.
Jan Gonda analogously emphasises the textile imagery on which this ritual terminology is based, by mentioning «the distinction between the ‘warp’ (tantra) and the ‘woof’ (āvāpa) of a sacrificial rite, that is of the framework, standing model, or those components which has in common with other rites and those that vary from ritual to ritual and are therefore the special characteristic features» (Gonda 1977:510).
Unfortunately, a lexica mention 'woof' as a possible meaning of āvāpa and the etymology supports it, I do not know of any attestation of āvāpa bearing this meaning if not in the context of a contrast to tantra.

How much does this pre-history influence the later history of tantra as "Sacred Text"?

On tantra, see here.

The sentence-meaning? What is added over the word-meaning

One can understand what is the sentence-meaning if one compares it with the meaning of the word-meanings composing the sentence. Is it their sheer sum? Something completely different? Jayanta proposes that it is the additional element over the meanings of the words taken singularly.
Jayanta Bhaṭṭa's Nyāyamañjarī, 5:

Nor is it the case that there is no sentence-meaning separated from word-meanings. That, to begin with, you (the PP) should explain, if you are asked to: "Is there a cognition similar to the word cow, etc., arising from "Bring the white cow!" or are the two cognitions different? In this regard, we should start by saying (tāvat) the sameness of the two runs against direct experience. In the case of a difference of the two cognitions, by contrast, also a difference in their contents is forcibly (balāt) produced (upanata), since if there were no difference in content one would not grasp a difference in the cognitions. And that content which is separated from them (content of the words) is the sentence-meaning. In this way, it should be construed also in case only a word signifying a quality or an action has been pronounced (i.e., even in the case of sentences made of one word only, there is something additional over the sheer meaning of the word).
Therefore it has been said that the sentence-meaning is that in which there is something additional.

(na ca padārthavyatirikto nāsti vākyārthaḥ | idaṃ tāvad bhavān pṛṣṭo vyācaṣṭāṃ | kiṃ gaur iti padādyādṛśī pratipattis tādṛśyeva gauḥ śukla ānīyatām iti vākyād uta bhinne ete pratipattī iti |
tatra tulyatvaṃ tāvat pratipattyor anubhavaviruddham | vailakṣaṇye tu pratītyor viṣayavailoakṣaṇyam api balād upanatam asati viṣayabhede pratītibhedānupapatteḥ | taś ca tad atirikto viṣayḥ sa vākyārthaḥ | evaṃ kevalaguṇakriyāpadoccāraṇe ’pi yojanīyam | tad uktaṃ yatrādhikyaṃ sa vākyārtha iti | )

For further references to posts dedicated to Jayanta and to his linguistic theories, see here.

Post hoc, ergo propter hoc?

A typical fallacy in the doctrine of causality is to confound between what follows (post hoc) and what is caused by something (propter hoc). Extreme examples of this fallacy might be those leading to superstitions:

• I had an accident after having seen a black cat, hence the black cat is the cause of my accident.

But there are many examples and David Hume even claimed that our notion of cause is ultimately grounded in such subtle cases: I see a seed and later a plant, hence I understand that the seed is the cause of a plant. But what I actually saw is only that the plant appeared after the seed.
I am inclined to think that nimitta in Mīmāmṣā is an (indirect) answer to this risk of fallacy. It refers to what must be there before the happening of something, but does not claim to be its cause. In other words, it designates the essential condition for something to occur. A nimitta is necessary for X to occur, but neither is X mechanically linked to it, nor nimitta to X.
In fact, nimitta in Mīmāṃsā primarily denotes the condition for the performance of a naimittika ritual. A typical example of such rituals is the jātakarman, to be performed after the birth of one's son. The birth of one's son is the nimitta for the ritual? Is it also its cause? Not really, since many of us had sons and have not performed any ritual.
Similarly, Mīmāṃsā author speak of nimitta in order to denote what must precede X for X to happen, but is not its cause.
Interestingly, nimitta is, instead, listed in Nyāyavaiśeṣika among the causes (kāraṇa), as the necessary cause in which the result does not inhere, e.g., the potter in the case of the pot.

Did Nyāyavaiśeṣika authors borrow it from its ritual usage?
And, more generally, did Indian authors distinguish between post hoc (after that) and propter hoc (because of that)?

prasaṅga: a term with a long history

Readers of śāstric Sanskrit will know prasaṅga most of all as the "unwanted consequence". Something that follows automatically. Investigating in its past may shed some light also on this meaning.

prasaṅga is not extremely frequent in the Śrautasūtras and I failed to find a definition of it. Hence, one has to reconstruct its meaning indirectly, through its usage in the Śrautasūtras, through its usage in Grammar and Mīmāṃsā and possibly also through its etymological meaning. Every translation is therefore intrinsically tentative.
The following is my (provisional) hypothesis:

In the Śrautasūtras, prasaṅga might denote:

1. 1. temporary and incidental association of two elements or rites
2. 2. chance, i.e., occasion, for an extended application caused by this temporary association

This latter meaning will produce the later, Mīmāṃsaka one, which seems foreshadowed in some Śrautasūtra usages:

1. 3.what happens automatically, through a transport from one rite to another, unless there is an opposite prescription, in similar cases and if need arises

It is worth stressing that the transport does not depend on a centralised instance (as it occurs in the case of tantra). It rather depends on a marginal contact, resulting in a temporary association which is based on a specific need. A tantra-like travel would be that of a whole school sharing the same ship or train, especially booked. A prasaṅga-like one would be the relation between a hitchhiker and the car-driver who gives him a lift. Their association is temporary and based on the former need for an element already in use by the latter.

On tantra and prasaṅga, see here and here. On the methodological problem of reconstructing the meaning of a word, see here.

Academic survival

As readers might have noticed, in the recent times I have been focusing on the problems of Academia. Why? Should not one just focus on one's work? Of course, focusing on one's work is one's biggest contribution. But, globally seen, one can hardly avoid considering the enormous amount of time and energies wasted just because of rivalries and all sorts of purpose-less figthing. In other words, universities and other research centers could achieve much more, if only their team were not busy with internal quarrels. Hence, I think that it makes sense to try to ameliorate the status quo.

I just read in a non-academic blog (the well-known blog by Seth Godin) about an interesting paradox, i.e., people usually do not want to be reminded of what they can do, but chose not to do, although they do not mind day-dreaming about what they could do (if only they could afford it, if only…). They read about cars they will never buy, but are irritated by reading about the TV they could have bought, but chose not to.

This might happen also in the Academia. Colleagues who are too old to travel abroad to conferences, might be positive about more mobility within the department. But colleagues who have chosen not to travel to conferences (e.g., because they are too shy to present their ideas to a wider audience) might be seriously against it. Because the very fact that someone else does it, forces them to reconsider their options. And this is painful.

My proposed solution: belittle yourself. Say that the option you are fighting for is almost insignificant. Make it appear non-appealing, so that the colleagues who have chosen against it, but are afraid to regret their choice are not brought that far.
Do readers have better solutions? And what do they think about the general problem? Did I describe it correctly?

On team work, see here and here. On the risks of criticising the academic establishment (and the need of criticisms), see here.