Sunday, February 14, 2010

Logic Lecture Feb 17: Jain and Buddhist Skepticism

BCC Logic
Eric Gerlach
2/17/2010


Lecture on Indian Skepticism: Jain and Buddhist Logic

Kanada and Gotama, our last two thinkers, have shown us Indian logic in its positivistic form, much like Aristotle (who we will get to soon) and Russell (who we will get to in the second half of the course when studying modern European logic). Positivist thinking asserts categorical differences between objects and values (ex: “What is good can not be bad, because it is good”). Skepticism, however, tends to attach positivistic categorical judgements with relativity and shades of grey between the black and the white.

Consider the two sides of the Nyaya form of debate, which also happen to be the two sides of a dialectical investigation according to Plato and Aristotle: “X is Y” vs. “X is not Y” (ex: the self is eternal vs. the self is temporary). Notice that the subject is shared, but there is a categorical black vs. white disagreement about it.

IF the world came in such simple forms, then the Nyaya proof by difference obviously follows (as does Aristotle’s syllogisms and Wittgenstein’s truth tables, both of which we will study soon). If we KNOW that things are EITHER Y OR –Y AND NEVER BOTH, then we can discover and understand constant atomic truths about our world.

HERE IS THE PROBLEM: are things ever entirely Y or –Y?

Skeptical thinking says: X can be SOMETIMES Y, SOMETIMES not Y. We can see positivistic and skeptical thinking in India, Greece, China, especially on logical matters. Today, we look at major concepts of the Jains and Buddhists, Indian religions/philosophies that enjoyed logical debate but maintained skeptical positions on the nature of the world and our abilities to make judgments about it.

For both Aristotle and Gotama, we need to get above some/some to know something above merely having an insecure opinion (both are thus positivists). However, a skeptical counter argument always will be: X is only very much Y, never entirely Y. X is very much Y here in space and now in time, generally and to a degree, but never perfectly or fully.

For example, consider that we can all agree that fire is hot but any fire we have seen is cold compared to a star. If we imagine Y and –Y as horizons that have no boundaries (Light vs. Dark) then X can be VERY Y or VERY –Y, but we would not be able to experience a thing as the pole of any opposition in itself (we can imagine something lighter or darker, like adding 1 to any number or subtracting to demonstrate the concept of infinity).

Not only do we try to CLOSE our inferences, judgments and concepts into black vs. white, but we also constantly like questioning black vs. white and revealing it to be shades of grey. No matter our beliefs, we all do both to attack and defend points of view or perspectives.

The Two Principles of Jain Skepticism:
Anekantavada: The multiplicity of Reality, or “non-one-ended-ness”.
Syadvada: The principle of postulation (all views are partial views, as we do not see all).
Jain or proto-Jain teachers and jungle dwelling sages gave these powerful principles to Buddhism and Hinduism, formulating them from the deeper passages of the Upanishads.

Buddhist Qualifications of the Nyaya Debate:

The Buddhists, who enjoyed debate on the nature of reality, took Gautama’s teachings on logic and developed them further. They added that X can be Y ALWAYS or SOMETIMES (and not Y sometimes), and X can be Y EVERYWHERE or SOMEPLACE (and not Y someplace).

Nagarjuna’s Four Things:
Nagarjuna (150-250 CE), the central logician of Buddhism.
His catuskoti (also called the tetralemma) will help with understanding contradiction.
As a Buddhist, he takes the Jain insights to their deepest level as one of the top Logicians of the Buddhist tradition, meaning he was EXPLICITLY following the teachings of Gotama’s Nyaya school and extending it with Buddhist skepticism (like adding the skeptic some/some to the Nyaya form of the two sides of a debate).

To help, use a X as cross (it lends itself here quite nicely) with four points of Y, not Y, (Y and not Y) and not (Y and not Y). Y is positive, not Y is negative, (Y and not Y) is some and some not positively, a contradiction of opposites affirmed, and not (Y and not Y) is some and some not negatively, and strangely can be called the formula of the ‘principle of non-contradiction’.

Nagarjuna’s point is that everything thought in logic or said in grammar must be one of these four things, and not one of them describes reality. Nagarjuna believes that all equally are and are not the All. Notice how this is a beautiful extension of the skeptical position as an extension to the Nyaya sides of debate.