On 5/3/2013 2:56 PM, Dan wrote: >> Of course, when one simply works within a system of axioms, the >> problem is obscured by the presupposition of denotation. It merely >> hides itself in set theory as the question of a well-ordering for >> the reals. > > Of course.I've omitted the fact that it's often helpful to have a > standard representation in telling when things are different. > However , in general, proving they are the same is more problematic . > Deciding whether two real number-generating algorithms are equal in > general implies solving the halting problem . In a completeness sense, > decision is still possible . However, comparing arbitrary sets of real > numbers becomes less clear. > > I'm intrigued .How does denotation relate to the well ordering (or > lack thereof ) of the reals? Can you offer references? >
This is what I mean when I say that my views are non-standard. I have large pieces of the puzzle that seem to fit together. But, also, I am generally isolated from any sort of collegial interaction; thus, my own perceptions might fall on some trivial oversight or be confined to a private language. And, it has required a great deal of philosophical investigation. That has exposed the fact that I am at odds with the usual historical accounts. I have tried to be careful, but again, there is more than one person can investigate without assistance. I could be gravely in error on some matters by some mere ignorance despite my best efforts to approach matters otherwise.
I will not drag you down that path. I have already written one apology to the group as a "crank" poster this year.