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H Nathan,
Thanks for your response.
"That[, the non-existence of non-defined numbers] would make sense if one (the One) were to proceed from axiom to plenum according to an ordinal program (implying a temporal process or at least one analogous to it)."
That's what I think too. I'm glad you allowed for some variation in the "temporal process". I suspect that the Cosmic temporal dimension is not altogether like our temporal dimension which seems to be consecutive if not continuous. I think the only requirement I would demand of Cosmic Time is that it somehow allow for the possibility of change. It might be very non-consecutive, non-continuous, or chaotic.
"One of the precepts [I think] you hold is that given an algorithm, it must be processed before it's result exists."
You are right. That is a precept I hold.
"This is where I see the anthropomorphic bias. I don't grant that God must process an algorithm to it's conclusion in any iterative fashion. Later on, you claim that the math doesn't have such a bias, but you do invoke a choice of A. Choice [pi] on the basis of a Zenophobic [pi] temporal difficulty. [I crack myself up!]"
Well, now, you got me there. You are right. The math we know and love does indeed require someone to "do the math". And that someone bears a strong resemblance to a human. Very anthropomorphic I'd say.
"That's fine for finding oneself, but then we discover an apriori Universe"
I'm not so sure we have discovered an a priori Universe. In the sequence of the events we perceive, there is no doubt that thought precedes any discovery. But of course there is the possibility that the Universe preceded the thought. Most people believe that, but I don't.
"To cogitate from some ergo is putting Decartes before the horse [OK, that was lame]."
Stop! Don't shoot the lame horse, I like that kind of humor.
"However, if you would have it, I'd grant that where human sentience is insufficient for arithmogeny, God's mind is apt."
Unless I misunderstand you, I think we have shown that human sentience is sufficient for arithmogeny. (Great word!) But that only strengthens the case for God's aptness.
"This of course leads back to whether God can conceive the sum of an infinite series and whether such conceptions as the complex field over the reals have already been worked out."
I think the answers are "Yes", and "Yes".
"I just finished Russell's...The History of Western Philosophy. and was so pleased with his style that I'm going to read the Principia next. "
Prepare for a shock. The styles are nowhere near the same. "The History..." uses English words and sentences. "The Principia..." uses the most awful set of symbols you can imagine.
"I hate using the word 'believe'"
I would guess that what makes you uncomfortable is that most people use the word 'believe' without defining it or even giving any thought as to what they mean by the word. If you have read enough of these archives, you will see that I clearly define what I mean by the word. If I say "I believe a certain statement", I mean that in my estimation, the probability of the statement being true is somewhat greater than 50%. The closer that estimate is to 100% the stronger I say my belief is. So far, I acknowledge only one statement that gets the full 100% and that is that "Thought happens."
", for one, have a sense (I hate using the word 'believe') that a truly comprehensive, coherent, and closed theory of physics and reality in general will describe a supra-finite lattice of events. I use the term supra-finite to mean that from any given perspective the number of events in it's past light cone is finite, but that a transfinite cardinality is achieved when viewed from the extemporal viewpoint of total reality."
Do those transfinite cardinalities, for which you say you have a sense, bring along with them the contradictions and absurdities that Cantor, Russell, and Goedel say they must?
Warm regards,
Paul
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