Friday, June 21, 2019

Finishing the Fifth Corner of Four

I have now finished reading the Fifth Corner of Four. The final three chapters of the work are particularly interesting because Graham Priest uses the Plurivalent Logical tools he has already adumbrated to provide a formal analysis of the Jinzang Hierarchy, the Net of Indra, and the notion of Enlightenment (especially how it relates to the work of Dogen).

Now these sections of the work started to drift away from my areas of specialization, but it was clear from my reading that Buddhist metaphysical issues can be given a rigorous logical grounding. Take the Jinzang Hierarchy for instance. This concerns the notion of transcending dualities in order to reach Ultimate Reality. Say we have some true description P of Conventional Reality. Since we know that Ultimate Reality is ineffable, we must conclude that ~P is true of Ultimate Reality. But we have already concluded earlier that Ultimate Reality is ineffable, and ~P is just as conceptual as P. Therefore, we must conclude that we are actually also describing conventional reality with the sentence ~P. Thus, the compound proposition P & ~P is true of Conventional Reality.

So to throw off this additional conceptual fetter, it is only natural to conclude that neither conjunct is true of Ultimate Reality, in other words ~(P & ~P) is true of Ultimate Reality. But this is still just another concept, so it too must also describe Conventional Reality. Thus (P & ~P) & ~(P & ~P) is true of Conventional Reality. But then we must negate this new compound proposition in order to reach Ultimate Reality, and so on, ad infinitum.

What Graham Priest concludes from all of this is that the transcendence of all dualities is not a final state that must be reached, but an ever continuing process up the hierarchy. Priest connects this result to the view of enlightenment broached by the Japanese philosopher Dogen. For Dogen, enlightenment is not some ultimate state that must be reached after a long and arduous regime of disciplinary practice, rather, enlightenment is already here, right before our eyes. Indeed, while the notions of samsara and nirvana are useful notions for the practitioner, we can only be enlightened once we see that they are actually one and the same. To borrow a metaphor from Wittgenstein, they are like a ladder which once climbed, must be thrown away.

So to conclude, I would highly recommend this book to anyone interested in Logic or Metaphysics. I would recommend it in particular to 2 classes of people: Firstly, I would recommend it to those who might not be familiar with Buddhist Metaphysics. Secondly, I would recommend it to those who might be curious regarding the applicative capabilities of Non-Classical Logics.

But one thing that especially shines through in my opinion is the perennial usefulness of First Degree Entailment, which Priest makes quite patent throughout the course of the book. Anyone familiar with Non-Classical Logics is certainly aware that FDE can be a base system for a wide variety of other systems of logic. These systems can be reached either by tweaking the truth values (a la K3, LP, Classical Logic, and FDEe) or by adding on a suitable conditional (a la N4 or the Affixing Relevant Logics). This being the case, I think we might be justified in concluding that FDE provides the true 'basement level' consequence relation (to use a term of JC Beall).

I certainly plan on continuing my study of Buddhist Philosophy, and I am now confident that FDE and FDEe are the perfect tools for logical analysis in this endeavor.

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