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Western philosophers have not, on the whole, regarded Buddhist thought with much enthusiasm. As a colleague once said to me: ‘It’s all just mysticism.’ This attitude is due, in part, to ignorance. But it is also due to incomprehension. When Western philosophers look East, they find things they do not understand – not least the fact that the Asian traditions seem to accept, and even endorse, contradictions.

Now, in logic, one is generally interested in whether a given claim is true or false. Logicians call true and false

To get back to something that the Buddha might recognise, all we need to do is make

*truth values*. Normally, and following Aristotle, it is assumed that ‘value of’ is a function: the value of any given assertion is exactly one of*true*(or*T*), and*false*(or*F*). 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. Thus*T*might be a value of a sentence, as can*F*, both, or neither. We now have four possibilities: {*T*}, {*F*}, {*T*,*F*} and { }.
...you might be wondering how on earth something could be both true and false, or neither true nor false. In fact, the idea that some claims are

The notion that some things might be

This statement is false.

Where’s the paradox? If the statement is true, then it is indeed false. But if it is false, well, then it is true. So it seems to be both true and false.

Many similar puzzles turned up at the end of the 19th century, to the dismay of the scholars who were then trying to place mathematics as a whole on solid foundations.

*neither*true nor false is a very old one in Western philosophy. None other than Aristotle himself argued for one kind of example. In the somewhat infamous Chapter 9 of*De Interpretatione*, he claims that contingent statements about the future, such as ‘the first pope in the 22nd century will be African’, are neither true nor false. The future is, as yet, indeterminate. So much for his arguments in the*Metaphysics*.The notion that some things might be

*both*true and false is much more unorthodox. But here, too, we can find some plausible examples. Take the notorious ‘paradoxes of self-reference’, the oldest of which, reputedly discovered by Eubulides in the fourth century BCE, is called the Liar Paradox. Here’s its commonest expression:This statement is false.

Where’s the paradox? If the statement is true, then it is indeed false. But if it is false, well, then it is true. So it seems to be both true and false.

Many similar puzzles turned up at the end of the 19th century, to the dismay of the scholars who were then trying to place mathematics as a whole on solid foundations.