Saturday, May 10, 2008

Richard on Grue and Shepherd on Non-Difference

Richard discusses what is, in effect, the difference between natural and artificial classification, noting that, for instance, 'green' makes a better candidate for natural classification than 'grue'. I was reminded of a passage in Lady Mary:

All mathematical demonstration is built upon the notion; that where quantities, or diagrams, resemble each other, the relations which are true, with respect to ONE of each kind will be true with respect to all others of a like kind; ONLY because there is nothing else to make a difference among them. So, if in all past time, such secret powers could be shown necessarily connected with such sensible qualities; yet in future it could not thence be proved to continue so, unless supported by the axioms;--that LIKE Causes must EXHIBIT like Effects, and that DIFFERENCES CANNOT ARISE of themselves.

[Shepherd, An Essay Upon the Relation of Cause and Effect, pp. 77-78. All the weird emphasizing is Shepherd's own.]

Thus one can extrapolate what Shepherd would say about cases like grue, and it would be fairly similar to the argument Richard suggests:

One way to bring this out is to think about projectability, or what properties you can reason inductively from. All the emeralds I've seen so far have been green, so I expect the first emerald I see after 2020 will also be green. That seems a perfectly reasonable induction. On the other hand: "All emeralds I've seen so far have been grue, so I expect the first emerald I see after 2020 will also be grue" is clearly not good reasoning. This is because green is a more natural property than grue. It is an objectively better way to categorize reality.