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The problem of induction

Posted by ducati998 under

black swans
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Recall [Russell’s famous] turkey problem. You look at the past and derive some rule about the future. Well, the problems in projecting from the past can be even worse than what we have already learned, because the same past data can confirm a theory and also its exact opposite …

For the technical version of this idea, consider a series of dots on a page representing a number through time … Let’s say your high school teacher asks you to extend the series of dots. With a linear model, that is, using a ruler, you can run only a single straight line from the past to the future. The linear model is unique. There is one and only one straight line that can project a series of points …

This is what philosopher Nelson Goodman called the riddle of induction: we project a straight line only because we have a linear model in our head — the fact that a number has risen for 1 000 days straight should make you more confident that it will rise in the future. But if you have a nonlinear model in your head, it might confirm that the number should decline on day 1 001 …

The severity of Goodman’s riddle of induction is as follows: if there is no longer even a single unique way to ‘generalize’ from what you see, to make an inference about the unknown, then how should you operate? The answer, clearly, will be that you should employ ‘common sense’.

Nassim Taleb

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