Monday, October 09, 2006

Not that anachronistic

Kant was a constructivist of sorts. He thought one shouldn't use excluded middle for arguments that are supposed to give us knowledge. He thought that in order to have knowledge of mathematical objects they had to be made in intuition (Not sure on the phrasing of this to make it correct; we haven't gotten to that part of the Critique). He also rejected reductio arguments because they didn't bring you into acquaintance with the object/proposition of the conclusion. How delightful! One odd thing is that he didn't think modus ponens was a good rule of inference because it required infinite knowledge of the antecedent in order to affirm the consequent with certainty. But, he did think modus tollens was good since it only required one disconfirming instance. I wonder if he has a view on arguments from the contrapositive. I don't know if they were even considered then.

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