Comment author:Benquo
15 January 2008 04:59:18AM
-6 points
[-]

Sure, but recognizing that requires stepping outside of the basic structure of algebra to evaluate it. That evaluation is a function of human reason, but not one of formal logic. I think many people mean by "logic" formal logic, or the conversational equivalent, rather than what one might call natural reason.

Incidentally, that "illegal operation" is essential to the symbolization of the differential Calculus, as I'm sure you're aware. dy = K * dx, ergo dy/dx = k (i.e. 0 = K * 0, therefore 0 / 0 = K) That doesn't mean we can discard logic willy-nilly, of course (or that we can divide by zero willy-nilly; infinitesimals are an exception, because they have ratio but no magnitude). But it does mean that it's inadequate to simply plug in rules without checking occasionally to make sure they generate a map that matches the territory.

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