RE: Actual Infinity in Reality?
February 15, 2018 at 3:58 pm
(This post was last modified: February 15, 2018 at 4:03 pm by The Grand Nudger.)
(February 15, 2018 at 3:35 pm)LadyForCamus Wrote: So there could be some universe where A could be both A and not A?!
We don't know, but if there were, we couldn't cogently describe it or anything about it by reference to a system of axioms derived from this universe where...so far as we know (and that's not exactly a full throated invocation of inviolable truth, now is it, lol)...such is not the case.
Logic, as a system, has all the limitations of this universe..plus whatever additional limitations arise from the axioms of the system itself -and- those who employ it.
Hell, even in -this- universe the system wasn't always formed as such. We didn't discover these "laws" all at once...and I don't know how we could know if we'd found the very last piece yet..today. Propositional logic may still be incomplete just in this world, and whatever else that's left, if there;s anything left, may invalidate some axiomatic x...just as it has in the past. The continued existence of paradox strongly implies that we haven;t gotten it quite right..somehow.
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