3. Nagarjuna’s use of dilemma.
As we shall presently see, Nagarjuna often frames his arguments in dilemmatic form. So let me here give you a primer on the formal logic of dilemma. The form he tends to use is what logicians call ‘simple constructive dilemma’, which looks like this:
If X, then Y – and if not X, then Y
(the major premises, or ‘horns’ of the dilemma)
but either X or not X
(the minor premise, left unstated if obvious)
where “X” and “not X” refers to some propositions under consideration and “Y” the (explicit or implicit) intermediate and final conclusion. In Nagarjuna, “Y” usually has the negative content “Z is meaningless or impossible or absurd”, i.e. it asserts that the propositions concerned (“X” or “not X”), or the concepts they involve, are faulty.
The reasoning process involved is thus the following: the major premises (or ‘horns’ or ‘prongs’), are intended to show that the two theses, “X” and “not X”, each leads to some proposition “Y”; the minor premise reminds us that these theses are mutually exclusive and exhaust all available alternatives (it “takes the dilemma by its horns”), and the final conclusion is that only “Y”, their common implication, is left over for us. This form of argument is easily validated, for instance by contraposing the major premises, to obtain “if not Y, then both X and not X”; since “not Y” implies the paradox “both X and “not X”, it follows that its contradictory “Y” is true.
Note that the above dilemma is ‘two-pronged’, i.e. it considers two alternative theses, “X” and “not X”; it is also possible to – and Nagarjuna does so – engage in dilemmatic argument with three (or more) prongs in the major premise and a triple (or larger) disjunction in the minor premise. These have the form (briefly put) “if A or B or C…, then Y; but either A or B or C…; therefore Y” and can be validated in the same way.
Sometimes, Nagarjuna’s argument is not properly dilemmatic in form, but only gives the impression that it is so. This occurs when the content of “Y” is merely “Z cannot be established as meaningful or as possible or as consistent” – i.e. when it signifies a doubt rather than a denial. Dilemma only works (i.e. can only be validated as just shown) if the major premises are proper “if/then” statements, i.e. provided “Y” is some assertoric proposition that logically follows “X” or “not X”. It does not work if “Y” is merely problematic given “X” and/or “not X”. The form “if X, surely Y” should not be confused with “if X, perhaps Y”; the former means “if X, then Y” and the latter means “if X, not-then not Y”; the latter is not logically equivalent to the former, but merely a subaltern of it. Similarly, mutadis mutandis, in the case of “if not X”, of course.
When one or both of the major premises has this less definite form, all we can finally conclude is “maybe Y” (i.e. the content “Z might be meaningless or impossible or absurd”) – which is the same as saying that we reach no final conclusion at all, since “maybe Y” can be said ab initio with regard to anything. At best, we might consider “Y” as inductively slightly more confirmed by the argument, i.e. the “maybe” as having incrementally increased in probability; but that does not deductively prove “Y”. Dilemma, to repeat, can only be validated if the premises are assertoric; it has no validity if either or both of them are merely problematic. Yet Nagarjuna, as we shall see, sometimes considers such pseudo-dilemma as equivalent to dilemma, and the non-conclusion “maybe Y” as equivalent to a negative conclusion “Y”. That is fallacious reasoning on his part.
As we shall see by and by, Nagarjuna indulges in many other logical fallacies in his philosophical discourse. (I have drawn up a list of the nine most striking ones in Appendix 1.)
 Reductio ad absurdum: denying the conclusion while maintaining the minor premise results in denial of the major premise.