Nicholas Thompson wrote at 03/28/2012 09:38 AM: > I don't think we've been talking about psychological induction, here but > logical induction. And I think mathematical induction is actually a species > of Deduction. I am in a rush now, but I am putting in this marker in the > hope that others will help out.
I disagree. I think we've ranged over all sorts of meanings for the word "induction" ... because we're speaking English. ;-) I tried to make my perspective clear when I challenged the law of the excluded middle ... or by extension this false assumption of _crisp_ sets that underlies your example of grass being green. (RussA gives the same criticism from a different angle.) It's just a plainly flawed argument because the set we refer to as "grass" is not crisp. There are plants that are a little bit like grass and a little bit not like grass. And just because grass is dead doesn't mean it's no longer grass. And I know a few people whose _hair_ looks like grass! Etc. The same is true of the set we refer to as "green things". Ideological arguments like that fail miserably when we disambiguate and wander into math and logic. Anyway, compare and contrast that sort of rhetoric with a predicative definition of a set (like that of the Natural Numbers). That set is crisp. We are still talking about sets and set membership. And we're still talking about the ability to define a set based on "previous" (predecessor) observations and then establish the membership of a newly constructed object. That's why mathematical induction is a form of induction. Reasoning methods are not entirely disjoint. Any non-trivial act of reasoning requires all 3 forms. Hence, it's reasonable and pragmatic to think that induction and deduction aren't crisp sets either. -- glen e. p. ropella, 971-222-9095, http://tempusdictum.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
