I'm getting into the deep end of set theory, and have touched on a little group theory (although, I still don't REALLY understand it).
But I've begun to notice the Principle of Abstraction, which is how you determin the members of any particular set , seems to be a mapping of a boolean field on to a Universal Set (i.e. P(a) is a way of saying "yes" x is in the set, "no" x is not in the set) although my book doesn't say this explicitly. Anyone know if this true or is this a nieve characterization?
But I've begun to notice the Principle of Abstraction, which is how you determin the members of any particular set , seems to be a mapping of a boolean field on to a Universal Set (i.e. P(a) is a way of saying "yes" x is in the set, "no" x is not in the set) although my book doesn't say this explicitly. Anyone know if this true or is this a nieve characterization?
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Los Angeles
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Re: Formal Logic and Set Theory
Mon, September 25, 2006 - 3:38 PMWhat is the abstraction? If you show a person in culture that uses money a bit of coloured paper on that basis they may deduce that as being money; however if you show a person say from a coastal tribe that would use cowrie shells as currency, they may discern paper currency to be just a bit of coloured paper or artistic expression. The basis of imputastion is the same but due to predeliction we impute it as being something to buy food with and the other would not, although with "cowrie shells" they would. That said their is no abstraction just a differing perception of the basis of what label is imputated -
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Re: Formal Logic and Set Theory
Mon, October 2, 2006 - 7:35 PMMy only experience with set theory is in music; pitch class set theory.
I can explain how these things work, in particular, if it helps.
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Axiom of Choice?
Tue, October 24, 2006 - 10:56 PMyes, I'd say it's a similar principle. The idea is that you are trying count something, but I guess the boolean field technique relies on the mapping to pick the numbers, and I'm pretty sure requires the axiom of choice.
The Principle of Abstraction is much more pure in the sense that there are just objects and sets, and operations on that.
I dunno, I haven't done this in awhile, but that's what my intuition is telling me.
