Collected Essays
“But I’ll leave the fine points of issue for other investigators to work out.Undecidability EverywhereIt often happens in the history of science that some odd-ball new category is discovered. At first nobody’s sure if any phenomena of this kind exist, but then there’s some kind of logical argument why these odd-ball things have to occur. And then, as time goes on, more and more of the curious entities are discovered until finally they’re perceived to be quite run of the mill. And I think this is... what will happen with the notion of undecidable sentences about the natural world.To dramatize this notion, I’ll present a sustained analogy between the spread of undecidability and the rise of transcendental numbers in mathematics. Brian Silverman suggested this analogy to me in an email.Transcendental Numbers. 300 BC. The Greeks worked primarily with real numbers that can be expressed either as the fraction of two whole numbers, or which can be obtained by the process of taking square roots.MoreLess
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