Friday, September 22, 2006

Kantian concepts: abstraction

I think I understand something in Kant. In his Logic, he describes three ways in which one generates concepts: abstraction, reflection, and comparison. You have your concepts, and each concept has an intension and an extension. The extension is the things that fall under the concept (anachronistically understood set theoretically). The intension is set of the differentiating things, marks. Abstraction generates concepts by fiddling with the intension, specifically by removing marks. Since the extension and intension are inversely related (according to Kant), this will increase the size of the extension. This makes sense to me. You start with a concept, say, poodle. You abstract out the breed, you get dog. you abstract out the mammal, you get quadruped, or animal. I'm not sure exactly how the hierarchy goes, but it seems like a fairly intuitive idea.

The thing I'm wondering is whether you get a strict hierarchy or if you get multiple inheritances. Kant says the most general concepts are something and nothing. You can't get any more abstract than that. Fair enough. In my toy example, could one abstract in a different order, say abstract quadruped out before mammal? Maybe there is a strict containment of mammal by animal, but there looks to be a fair amount of room to play within the concept dog. If we have a white poodle, and we abstract out white we have poodle. If, rather, we abstract out poodle, we have white dog. So far Kant hasn't set down any rules about containments and order of abstraction. Maybe white appears under poodle and under dog? Not sure.

I will have to do posts on reflection and comparison when I get through the sections on them in the Logic.

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