Greetings Bruno and Kory, >Also, you said that your are not platonist. Could you tell me how you >understand >the proposition that the number seventeen is prime. (I want just be sure I >understand >your own philosophical hypothesis).
> A quick aside: It might be better not to even use the term "platonist" in > these discussions, because it means at least two different things. It can > be used to refer to Plato's "essentialism" - the idea that there's a world > of Forms in which exists (for instance) the Ideal Horse, and all physical > horses represent imperfect copies of this Horse. This is certainly a more > elaborate belief than "mathematical realism" (or "arithmetical realism", or > "computational realism"). One can be a mathematical realist without being > an essentialist. I am. So some people would call me a Platonist, and some > wouldn't, but that's just a disagreement about a definition. I prefer just > to use the term "mathematical realism" or "essentialism", depending on what > I'm talking about. There would seem to be some difference of opinion on this view: "Mathematical realism holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. The term Platonism is used because such a view is seen to parallel Plato's belief in a "heaven of ideas", an unchanging ultimate reality that the everday world can only imperfectly approximate. Plato's view probably derives from Pythagoras, and his followers the Pythagoreans, who believed that the world was, quite literally, built up by the numbers. This idea may have even older origins that are unknown to us." http://www.fact-index.com/p/ph/philosophy_of_mathematics.html I'd have to agree that mathematical realism smacks of "essentialism" to me as well. Thus my reservations regarding it. But my real point here is that, for myself, all "isms" including Platonism are merely maps (models?) and the world the territory, to paraphrase Korzybski. Mathematics is, I believe, one of those maps. Hard pressed for a label, I'd guess that I probably fit most well as a non-Aristotelian if anything (but I'm not sure they'd have me). But in truth I tend to be like bacterium where my "world view" is like it's genome: I take a little here, a little there from various compatible isms and assimilate the parts that seem to "fit" well, averaging across many maps to better grok the territory. Ultimately though, I suppose my "main man" would be Socrates, if I had to choose one (and apparently I just did). Plato would have done well to assimilate more of his mentor's methodology, IMHO. He might have been more competitive with the Ionians had he done so. On the science topic: Natural History magazine this month has an article on the anthropic universe, the cosmological constant and cosmology. It cites the multi-verse as one theory gaining popularity in "explaining" the constant's otherwise apparently arbitrary value. The author quotes Tegmark as well as some "soft" multi-versers and of course the skeptics who tend to see a meta-verse solution as a cop-out and, in at least one view, akin to a religious mythological tale. These last bemoan what they see as a premature abandonment of rigourous physics methodology in pursuit of an instant TOE. To this lot the rumors of the end of science are "greatly exaggerated", I would imagine. Look, all I "know" is that the world(s) apparently "proceeds" from state to state and exihibits patterns of varying degrees of order and (psuedo/) randomness. I suspect that this is likely the consequence of simple underlying "rules" or a single rule. Thus the world contains information, IMHO. That these patterns "map" reasonably (remarkably?) well to a "meme" that we call mathematics and that first appeared at a recent juncture(s) of that procession seems clear. Am I a mathematical realist? You tell me.. Cheers CMR <- insert gratuitous quotation that implies my profundity here ->