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karl
Posts:
397
Registered:
8/11/06


Re: Matheology § 068
Posted:
Jul 10, 2012 9:45 AM


Am 10.07.2012 15:37, schrieb WM: > On 10 Jul., 15:02, WM <mueck...@rz.fhaugsburg.de> wrote: >> Matheology § 068 >> >> To most mathematicians, the title of this article will, I suppose, >> appear a bit strange: it is so obvious that 265536 is a natural number >> that there would seem to be no rational basis for questioning it. Yet >> there have been objections to the claim that all such exponential >> expressions name a natural number, two of the best known being due to >> Paul Bernays and Edward Nelson. Bernays, in "On Platonism in >> Mathematics", rhetorically questions whether 67257729 can be >> represented by an "Arabic numeral" (he does not, however, press the >> discussion). By contrast, Nelson, in "Predicative Arithmetic", >> develops a large body of theory which he then advances to support his >> belief that 265536 is not a natural number or that, more generally, >> exponentiation is not a total function. [...] >> For while it does not limit the use of induction it does imply that >> the effect of induction is contextdependent. It also implies that >> when the objects of discussion are linguistic entities (and in this >> paper the position advocated is that "natural numbers" or better >> "natural number notations" are linguistic entities) then that >> collection of entities may vary as a result of discussion about them. >> A consequence of this is that the "natural numbers" of today are not >> the same as the "natural numbers" of yesterday. Although the >> possibility of such denotational shifts remains inconceivable to most >> mathematicians, it seems to be more compatible with the history both >> of the cultural growth (and of growth in individuals) of the number >> concept than is the traditional, Platonic picture of an unchanging, >> timeless, and notationindependent sequence of numbers. >> [David Isles: "What evidence is there that 265536 is a natural >> number?", Notre Dame Journal of Formal Logic, 33,4 (1992) 485480.]http://projecteuclid.org/DPubS?verb=Display&version=1.0&service=UI&ha... >> > > Of course 2^65536 and 67^(257^729) are meant. > > Regards, WM > Why, if 2^65536 is no natural number, is there any reason that 265536? You are totally confused. Please read your posts before sending them. You are making a fool of yourself if you have not noticed it already.



