by Denis Wallez

August 22nd, 2012 (August 23rd, 2012)

illustration (attribution, if any possible, is at the end of the article)

why 'emptiness' is, and is not, a middle way between extremes

and why nirvāṇa is primarily 'defined' by negations (of what it is not).

Emptiness is often presented as the middle way between the 'extremes' of essentialism (reification) and of nihilism. Interestingly, Nāgārjuna is seen as the masterful presenter of शून्यता with the help of logic, so let's do some propositional calculus!

Notations (please, don't panic and stick with me!):

letter: true proposition, i.e. "A" means "proposition A is true"

¬: negation, i.e. "¬A" means "proposition A is false"

∨: union, i.e. "A∨B" means "A (is true) or B (is true)"

(both might be true)

&: intersection, i.e. "A&B" means "A (is true) and B (is true)"

(i.e. both must be true) (note: & is usually noted ∧ in maths)

⇒: implication, i.e. "A⇒B" means "if A (is true) then B (is true)"

⇔: equivalence, i.e. "A⇔B" means "B (is true) if and only if A (is true)"

Quick reminder:

Logic statements might themselves be true or false, e.g. stating "A⇒B" is not enough for such a relationship to be true, it is merely an assumption until it is proven true…

So logic can be applied to logical 'propositions' themselves (hence "propositional logic"), e.g. [A⇔B] ⇔ [(A⇒B)&(B⇒A)] which says that the proposed equivalence [A⇔B] itself is true if, and only if, both proposed implications [(A⇒B) and (B⇒A)] are themselves true.

Theorem: [A⇒B] ⇔ [B∨(¬A)]

Verbose proof: A⇒B means that A being true forces B to be true.

If B is false, then A can only be false (otherwise the implication itself would be false! modus tollens), i.e. (¬B) ⇒ (¬B)&(¬A).

However, if B is true, we have no information about A, i.e. we only have the tautology B ⇒ B.

For [A⇒B] to be 'true,' the implication must always be true, i.e. regardless of B being true or(∨) false… hence [A⇒B] ⇔ [(conclusions from B) ∨ (conclusions from ¬B)] which respectively are [(B) ∨ ((¬B)&(¬A))] ⇔ [B ∨ (¬A)]

Let's now apply logic to the extremes of essentialism and nihilism!

Essentialism is the view (or postulate, or assumption) that "what truly exists does so as real, fixed 'entities'"

i.e. existence ⇒ essence

Nihilism is the view that accepting emptiness (i.e. the non-existence of any fixed entity, i.e. ¬essence) means that "nothing at all really exists, everything is an illusion:" (¬essence)⇒(¬existence).

Indeed, the modus ponens from combining [¬essence] and [(¬essence)⇒(¬existence)] is (¬essence)&(¬existence), in other words "absolute nothingness" (lacking both essence and existence).

But, as per the theorem [A⇒B]⇔[B∨(¬A)] above,

nihilism's implication [(¬essence)⇒(¬existence)]

is equivalent to [(¬existence) ∨ (¬(¬essence))] with a double negation,

i.e. [(¬existence) ∨ essence],

i.e. [existence⇒essence],

i.e. essentialism!

Nihilism and essentialism both confuse (in the same way) existence and essence; they differ in their acceptance or refusal of emptiness, a difference which leads either to nothingness or to reified existence. In logical terms, nihilism is only a transposition of essentialism, compounded with an acknowledgement of emptiness.

As such there is nothing between nihilism and essentialism, no 'space,' so there cannot be a middle way between them: a buddhist searching a balance between the classical "two extremes" only finds an empty definition of such a middle ground. Conclusion? The buddhist attempt to avoid the two extremes misleads the practitioner to… emptiness itself. Misleading is a "clever means" here, a teaching method appropriate to auditors still looking 'for' something or somewhere "in the middle"!

Emptiness cannot be between the so-called 'extremes,' but looking for it there will lead to it anyway! Looking between nihilism and essentialism is looking straight into the heart of the confusion.

Nirvāṇa is un-conditioned, nirvāṇa cannot be established (Tarski's undefinability theorem did not let us expect anything else).

Nirvāṇa is out of the conclusions of logic (this is consistent with Gödel's incompleteness theorems: there exists statements that are true but undecidable/unprovable).

A positive/positing view on emptiness (or nirvāṇa) is just as much a delusion as any other 'view,' if not more dangerous; Nāgārjuna told us so much in the Mūlamadhyamakakārikā (§13.8)!

[image from http://en.wikipedia.org/wiki/Propositional_calculus]

#buddhistcircle #Buddhism #Dharma #Nagarjuna #logic #emptiness