Truth and Paradox: Solving the Riddles

Truth and Paradox: Solving the Riddles

Truth and Paradox: Solving the Riddles

Truth and Paradox: Solving the Riddles

Synopsis

Consider the sentence 'This sentence is not true'. It seems that the sentence can be neither true nor not true, on pain of contradiction. Tim Maudlin sets out a novel account of logic and semantics which allows him to deal with certain notorious paradoxes which have bedevilled philosophical theories of truth. All philosophers interested in logic and language will find Truth and Paradox a stimulating read.

Excerpt

I trust that I am not absolutely the last human being on the face of the Earth who might be expected to write a book on truth and the Liar paradox, but my name would not be among the first dozen, or first score, or first hundred to come to mind as a likely candidate for such an undertaking. I am not trained as a logician, or a specialist in semantics. Some explanation is in order.

I did not set out to write a book on the Liar paradox. Indeed, I did not set out to write a book at all, and the non-book I did set out to write was not about the Liar paradox. So what you have before you is the end product of a very long and difficult struggle in which one problem led to another and yet another, with the problem of truth ultimately emerging as the center of attention. The original project was concerned instead with attempts by John Lucas and, more recently, Roger Penrose to draw consequences about the structure of the human mind from Gödel's incompleteness proof. The basic line of argument is well known: suppose that human reasoning capacity can be reduced to some sort of algorithmic procedure, such that the sentences about, say, arithmetic that one takes to be provably true with certainty can be characterized as a recursively enumerable set of sentences. Gödel's procedure then shows how to identify a sentence which, if the system is consistent, is certain to be both true and not identified by the system as a truth. The idea is now this: We can recognize the Gödel sentence of the system as true even though the system itself cannot. Therefore our insight into what is certainly true outruns that of the system. But the system has not been characterized in any way except to say that it is consistent and, in some sense, algorithmic. Therefore our insight is, in principle, more extensive than that of any consistent algorithmic system. Therefore, our insight cannot be the result of any consistent algorithmic system. Therefore, the power of our minds cannot be captured by any algorithm. Therefore we are not like computers. Yet further, according to Penrose, it follows that the physics that governs our brains cannot even be computable, otherwise our insights would, in the relevant sense, be the output of an algorithm (viz. the algorithm which specifies the dynamics of the physics of the brain).

There are obviously lots of lacunae in this argument, and the foregoing sketch is only the barest skeleton of the complete defense of the conclusion. But even without going into the details, there is something extremely odd about the conclusion. It seems to rely on the idea that our insight into the truth of the Gödel sentence of a (consistent) system is evidence of some almost mystical intellectual power, a power that cannot even be mimicked by a computer. But

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