## A Buddhist Critique of Boolean Logic

Summary: although Boolean algebra works perfectly well for singular subjects, things in the world are not singular: they have multiple parts.  We argue that the application of a Boolean predicate to a compound subject (i.e. a physical object) should result in a compound truth value. The four compound truth values are {true}. {false}, {true,false}, and {}.  Interestingly, these truth values correspond to a set of logical outcomes used in ancient India called the catuskoti.

Boolean logic is a fantastic symbolic calculus, and we will not challenge its basic tenets.  However, it is not sufficient to adequately describe all of our cognitive operations: the human mind is composed of more than just the rational mind.

In particular, Boolean logic applies to singular (unitary) subjects, and from a Madhyamaka point of view, there are no non-composite subjects in reality.  Although the conceptual mind imputes singularity, all existing objects are composed of a plurality of parts.  Boolean logic, for all of its merit, was not designed to apply to non-singular subjects.

So from the Buddhist point of view, modern logic is not incorrect, but it is a logic which applies only to concepts.  A more general logical system with four outcomes, called the catuskoti (meaning “four corners”) has been used for debate in India before Buddhism began.

The catuskoti offers a plurality of logical outcomes: {true}, {false}, {true,false} and {} (i.e. neither true nor false).  Some things are also said to be beyond this analysis (ineffable), but we will of course not speak of those.  A modern logician would of course balk at the notion of “true and false” and “neither true nor false” as logical outcomes, since they are not logical outcomes with a Boolean algebra: they are contradictory within a logical system in which the premise must resolve to a single truth value.

Boolean algebra is appropriate to synthetic (a priori) statements or deductions.  To use a classical example, if all men are mortal, and Socrates is a man, then we may conclude with certainty that Socrates is mortal.  Statements about the world, however, are less certain.  For example, the way that the name of an object corresponds to its object poses a problem known in philosophical circles as the problem of identity.  To put it simply, if a name is taken to refer to a particular thing, and that thing changes while the name does not, then we have some uncertainty with respect to the correspondence of the name and the object.

Let us take an egg as an our subject of analysis.  Conceptuality, the egg is a single thing, but of course it corresponds to a  region of space filled with egg-matter which is multiple (or at least divisible). We then apply the logical predicate “yellow” to the subject, which corresponds to the question: is the egg yellow? On a classical Boolean analysis, we have the following possible answers:

• True: the inside of the egg (the yolk) is yellow.
• False: the outside of the egg (the egg white or shell) is not yellow.

If we are determined to reduce this answer to a single truth value, we might say that these two answers should be combined with one of the Boolean operators, either AND or OR:

• True: the egg is yellow because some part of it is yellow (true OR false).
• False: the egg is not yellow because some part of it is not yellow (true AND false).

There is a problem with this logic, however.  Suppose we have another predicate, not-yellow, and ask the same question:

• True: the egg is not-yellow because some part of it is not-yellow (true OR false).
• False: the egg is not not-yellow because some part of it is not not-yellow (true AND false).

The problem should be clear: we obtain the same answer asking if the egg is yellow that we do when we ask if it is not-yellow, which entails a contradiction (yellow, because it is a non-compound predicate, is subject to the law of the excluded middle). There is simply no way to simplify the situation (consistently and nonparadoxically) when we start with a subject that is non-uniform with respect to the answer.

A mereological logic (which is better suited to traditional Buddhist analysis) a would answer the question in terms of parts of the object, in which case we have:

• {True, False}: the egg is yellow because a part of it is yellow, and it is not yellow because a part of it is not yellow.

Again, the answer {true,false} is the result of applying a binary (logical) predicate to a compound subject: an object which has the parts {yellow, not-yellow}.  In traditional Buddhist texts, this answer is expressed as the combination of a predicate and its negation, or “yellow and not yellow”.

There is one more outcome to the catuskoti argument, which is “neither yellow nor not-yellow”.  One example of a subject which results in this answer is a word that does not correspond to any actual object.  Take, for example, the horns of a rabbit:

• The horns of a rabbit are not yellow
• The horns of a rabbit are yellow

Both of these statements are equally meaningless: a rabbit does not have horns.  Therefore, there is no basis to say anything about them: since they do not have a color whatsoever, we cannot say that this non-existant color is yellow or not yellow.

When something and it’s nonexistence
Both are absent from before the mind,
No other option does the latter have:
It comes to perfect rest, from concepts free.
~Shantideva

Bibliography:

1. Graham Priest, Beyond True and False
2. Shantideva, Way of the Bodhisattva