The prasangika method is to take the philosophical position of an opponent and show that it leads to a contradiction or absurdity. In the case of the vajra slivers argument, presented for example in Chandrakirti’s Madhyamakavatara, the position that things arise in one of four possible ways, each corresponding to certain non-Buddhist philosophical schools, is shown to be impossible.
Being led to a conclusion or consequence (prasanga) is a logical process, as opposed to an empirical or factual one. One is swept along by the unrelenting force of logical compulsion or necessity without recourse to any facts. For example, the idea that things originate from themselves is said to lead to the absurdity that seeds and shoots would be the same, as would food and excrement (Shantideva). Because these outcomes are obviously absurd, the premises are also absurd. This is not a discovery of new knowledge or facts, but a recognition of something that was not fully understood before, when the consequences were not yet worked out. The identity of seeds and shoots, and of food and excrement, are excluded from language as a matter of what Wittgenstein referred to as ‘grammar’, which in his case means something closer to ‘the semantics of English language’ than what we normally mean by ‘grammar’. Because these identities are excluded, self arising from self is also excluded. This is how the philosophical method of prasangika works.
Yet, we do not exclude a ‘self-made man’ from language, so there are cases which, on the face it, in some sense of ‘self-created’ or ‘self arising’, appear to be selves arising from themselves. For the prasangika, these must be different cases of self-arising to the absurd ones. What this shows is that ‘self-arising’ is not clear in meaning; it is related to both legitimate and illegitimate cases. The philosopher then says, “I am only interested in the illegitimate cases: this is the kind of ‘self arising’ which leads to reduction ad absurdum.” But then we can no longer say anything about the general case, ‘arising from itself’. We can only exclude the specific cases–food as excrement, and so on. But these are obvious, and trivial. So the idea of consequence from a general case does not apply.
It is the same with the absurd situations (prasangas) which are presented as consequences of ‘origination from other’. There are obviously illegitimate cases, such as darkness from flames, or water from fire, which are given. There are obviously legitimate cases as well, such as barley shoots and barley seeds, not to mention striking a match, in which light arises from something which was not itself light. These seem to be examples of ‘origination from other’ too. If we cannot specify in general terms which are the illegitimate cases except by listing them, we cannot draw any general conclusions about other-origination at all.
It might be argued–using general terms–that cause ‘necessarily’ ceases before the effect because cause and effect cannot co-exist (necessarily). Here, ‘other-origination’ is stipulated in general terms to be simultaneous cause and effect only: no other kind of other-origination is of concern. But this is not a consequence (prasanga) of anything and nor does it lead to any consequence. It is the stipulation of a rule: nothing counts as simultaneous cause and effect. Now this rule may or may not be accepted as part of the English language; and probably, it is too unclear to be followed as a genuine linguistic rule. But even if it were accepted, we would not have acquired any new knowledge. We would only have ruled out a certain way of talking. And so, that is just what the prasangika does. In insisting that certain claims result in contradiction, he rules out certain ways of talking – specifically, certain philosophical or metaphysical ones.