```Date: Jun 21, 2013 9:43 AM
Author: LudovicoVan
Subject: Re: Matheology § 288

"Sam Sung" <no@mail.invalid> wrote in message news:kq1k8g\$u5d\$1@dont-email.me...> Julio Di Egidio write:>> "Sam Sung" <no@mail.invalid> wrote in message>> news:kq1ica\$juk\$1@dont-email.me...>>> Julio Di Egidio wrote:>>>>>>> << Edward Nelson criticizes the classical conception of natural numbers>>>> because of the circularity of its definition. In classical mathematics>>>> the>>>> natural numbers are defined as 0 and numbers obtained by the iterative>>>> applications of the successor function to 0. But the concept of natural>>>> number is already assumed for the iteration. >>>>>>>>>> <http://en.wikipedia.org/wiki/Ultrafinitism#Main_ideas>>>>>>> So what?>>>> You have snipped the context.>> You refer to:>>>> What does pi count?>>> Isn't it a number?>>>> pi counts pi, of course...>> ? Sorry then.The point in fact was "numbers count themselves, how else?">>> Take any (uniquely operated) iteration and count the>>> steps by whichever method you like - the result is isomorphic>>> to N in whichever 'theory'.>>>> No,>> Why not?>>> confront strict finitism.>> "Classical finitism vs. strict finitism> In her book Philosophy of Set Theory, Mary Tiles characterized those who> allow countably infinite objects as classical finitists, and those who do> not allow countably infinite objects as strict finitists. Historically, > the> written history of mathematics was thus classically finitist until Cantor> invented the hierarchy of transfinite cardinals in the end of the 19th> century.">> They may 'not allow' whatever they want, but cannot 'forbid' appliyng> endlessly an operation like a successor function to 0.Indefinitely large yet (ever) finite: there just is no set N in the strict finitist view...Julio
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