# BUDDHIST ILLOGIC

# 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) |

| (the minor premise, left unstated if obvious) |

| (the conclusion) |

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[1].

*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**.)

[1]
*Reductio ad absurdum*: denying the conclusion while maintaining
the minor premise results in denial of the major premise.