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Old 10-08-2008, 06:59 AM   #6 (permalink)
Jon
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Join Date: Oct 2008
Type: INTP
Location: Kanata
Posts: 43
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Ok, good. But I have a completely different way of conceptualizing: (1) russell's paradox, (2) the responses, and (3) the fate of Frege's project.

Very briefly (because I'm not sure how much you care about my version of the story):

(1) Russell's paradox is generated by the combination of (a) the Naive Comprehension Axiom (every concept has an extension), and (b) the Rule of Substitution (every open sentence which defines a condition on objects corresponds to a concept).

(2) Responses to the Paradox: The two solutions are (a) The Theory of Types (which tries to find a non ad hoc way to restrict what counts as a genuine property), and (b) Zermelo-Frankel Set Theory (denies that there is a set for every property).

(3) The Fate of Frege: Two respects in which the elements which generate the paradox are deeply entrenched in Frege's entire programme. (a) getting big enough classes (he needs there to be an infinite number of objects in order to secure the result that every number has a successor), and (b) Hume's Principle (the fact that Frege derives Hume's Principle from Basic Law 5)

I'll elaborate if asked.

lol: I posted this as a response to my thoughts regarding online threads. Most threads try to square an issue posed by a member. The benefit of the community then is to bring a group of minds together to deal with, and resolve, the issue. I found it funny that this purpose is meaningless in the face of certain issues (ie: salvaging Logicism) even though thousands could work on it. Is this medium therefore only useful for trivial issues? Depends on what you consider trivial. But read my first post with this in mind and you'll see what I mean.
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