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Originally posted by matt grime

I'm slightly curious, curiousbystander, as to why you've told me this.

I actually ran short of time and didn't reach my point before I had to leave. I was only laying out the basics before I proceeded. Without the rest of what I had planned, the quote at the top of my previous post makes it sound as if you don't understand some very basic concepts, and the tone becomes condescending. That was not my intention and you have my apologies.

My goal (in brief) was to show the interdependency of the idea of a topology with the idea of a power set, show the relation between functions and special subsets of Cartesian products, and then use the set of functions from A to the set {0,1} to build the power set P(A) out of operations that are admissable in the system described by Phoenix. I wanted to do this carefully and concisely, and then use the usual generalizaton of Kantor's argument to show the differences in cardinality between the two sets. So if you're going to give up the power set you'd have to give up not only topologies but also functions between sets, or at least functions from the Universal set to the set {0,1}.

I actually ran short of time and didn't reach my point before I had to leave. I was only laying out the basics before I proceeded. Without the rest of what I had planned, the quote at the top of my previous post makes it sound as if you don't understand some very basic concepts, and the tone becomes condescending. That was not my intention and you have my apologies.

My goal (in brief) was to show the interdependency of the idea of a topology with the idea of a power set, show the relation between functions and special subsets of Cartesian products, and then use the set of functions from A to the set {0,1} to build the power set P(A) out of operations that are admissable in the system described by Phoenix. I wanted to do this carefully and concisely, and then use the usual generalizaton of Kantor's argument to show the differences in cardinality between the two sets. So if you're going to give up the power set you'd have to give up not only topologies but also functions between sets, or at least functions from the Universal set to the set {0,1}.

This is the part where I disagree I think that implicitly he is, and when all the terms have been clarified and the logical inconsistencies straightened out, his theory will closely resemble set theory. I've not yet been convinced (though I hope you will Phoenix) that a 3 valued logic system removes any of the difficulties.You should be aware that Phoenixthoth is not using ordinary set theory.