Thursday, October 06, 2011

A fundamental failure of imagination.

Philosopher Bertrand Russell remarks on a priori knowledge, essential for deductive [mathematical] reasoning:
When Swift invites us to consider the race of Struldbugs who never die, we are able to acquiesce in imagination. But a world where two and two make five seems quite on a different level. We feel that such a world, if there were one, would upset the whole fabric of our knowledge and reduce us to utter doubt.
Children before age 3 or 4 live in this wonderful world where 2+2=5. Actually, it's quite obvious for them that you can take two pieces of playdough, add another two pieces of playdough, and out of them make any natural number of playdough pieces: 5 or 1 or whatever. Then they grow up, become adults and a simple statement like 2+2=5 throws their world into utter doubt. Amazing, how fragile the world of adults is.

tags: psychology, philosophy, logic

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