Reality 101 - Introduction To MAYA!!! Get a grip on reality perception --- move from the black - white duality mindset? The mathematics underlying the East - West dichotomy. ********************** EXCERPTS Let’s start by turning back the clock. It is India in the fifth century BCE, the age of the historical Buddha, and a rather peculiar principle of reasoning appears to be in general use. This principle is called the catuskoti, meaning ‘four corners’. It insists that there are four possibilities regarding any statement: * it might be true (and true only), * false (and false only), * both true and false, * or, neither true nor false. At around the same time, 5,000km to the west in Ancient Athens, Aristotle was laying the foundations of Western logic along very different lines. Among his innovations were two singularly important rules. * One was the Principle of Excluded Middle (PEM), which says that every claim must be either true or false with no other options (the Latin name for this rule, tertium non datur, means literally ‘a third is not given’). * The other rule was the Principle of Non-Contradiction (PNC): nothing can be both true and false at the same time. That is why Western thinkers – even those sympathetic to Buddhist thought – have struggled to grasp how something such as the catuskoti might be possible. Never mind a third not being given, here was a fourth – and that fourth was itself a contradiction. How to make sense of that? Well, contemporary developments in mathematical logic show exactly how to do it. In fact, it’s not hard at all. At the core of the explanation, one has to grasp a very basic mathematical distinction. I speak of the difference between a relation and a function. A relation is something that relates a certain kind of object to some number of others (zero, one, two, etc). A function, on the other hand, is a special kind of relation that links each such object to exactly one thing. Functions give a unique output; relations can give any number of outputs. Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false truth values. In this way, the principles of excluded middle (PEM) and non-contradiction (PNC) are built into the mathematics from the start. But they needn’t be. To get back to something that the Buddha might recognise, all we need to do is make value of into a relation instead of a function. In case this all sounds rather convenient for the purposes of Buddhist apologism, I should mention that the logic I have just described is called First Degree Entailment (FDE). It was originally constructed in the 1960s in an area called relevant logic. Exactly what this is need not concern us, but the US logician Nuel Belnap argued that FDE was a sensible system for databases that might have been fed inconsistent or incomplete information. All of which is to say, it had nothing to do with Buddhism whatsoever. Nagarjuna, probably the most important and influential Buddhist philosopher after the Buddha himself, defined the new version of Buddhism that was emerging at the time: Mahayana. The most important of Nagarjuna’s writings is the Mulamadhyamakakarika, the ‘Fundamental Verses of the Middle Way’. This is a profound and cryptic book, whose principle theme is precisely that everything is empty. Nagarjuna’s reasoning is somewhat opaque, but essentially it seems to go something like this. The language we use frames our conventional reality (our Lebenswelt, as it is called in the German phenomenological tradition). Beneath that there is an ultimate reality, such as the condition of the enlightened dead person. One can experience this directly in certain meditative states, but one cannot describe it. To say anything about it would merely succeed in making it part of our conventional reality; it is, therefore, ineffable. In particular, one cannot describe it by using any of the four possibilities furnished by the catuskoti. Buddhist thought, and Asian thought in general, has often been written off by Western philosophers. How can contradictions be true? What’s all this talk of ineffability? This is all nonsense. The constructions I have described show how to make precise mathematical sense of the Buddhist views. This does not, of course, show that they are true. That’s a different matter. But it does show that these ideas can be made as logically rigorous and coherent as ideas can be. As the Buddha may or may not have said (or both, or neither): ‘There are only two mistakes one can make along the road to truth: not going all the way, and not starting.’ aeon.co/magazine/philosophy/logic-of-buddhist-philosophy/ **********************
Posted on: Sun, 04 Jan 2015 17:12:03 +0000
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