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Topic: Matheology § 068
Replies: 2   Last Post: Jul 10, 2012 9:45 AM

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Posts: 397
Registered: 8/11/06
Re: Matheology § 068
Posted: Jul 10, 2012 9:45 AM
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Am 10.07.2012 15:37, schrieb WM:
> On 10 Jul., 15:02, WM <> 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 context-dependent. 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 notation-independent sequence of numbers.
>> [David Isles: "What evidence is there that 265536 is a natural
>> number?", Notre Dame Journal of Formal Logic, 33,4 (1992) 485-480.]

> 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.

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