```Date: Feb 2, 2013 3:57 AM
Author: fom
Subject: Re: Matheology § 203

On 2/1/2013 9:48 AM, WM wrote:> On 1 Feb., 16:35, William Hughes <wpihug...@gmail.com> wrote:>> Let P(n) be>>   0.111...  is not the nth line>>   of>>>>   0.1000...>>   0.11000...>>   0.111000...>>   ...>>>> Clearly for every natural number n>> P(n) is true.>>>> This means there is no natural>> number m for which P(m) is true.>>>> It is not simply that we cannot find m,>> we know that m does not exist.>> More. We know that P(n) = 0.111...  = 1/0 does not exist as an> actually infinite sequence of 1's.Hmm....As I watch you make these arguments, it occurs to me...What proof do you have that some sequence is not infinitelylong?How do you prove this assertion?To even have the discussion presupposes that you ascribemeaning to the phrase "actually infinite sequence."This is an old problem.  Nevertheless, you aremaintaining your assertions relative to the factthat one cannot ostensively prove the existenceof an infinite sequence.But, one cannot prove that a sequence is notinfinite unless one can get to an end.  So,since your position entails a claim concerningall sequences, the handful of finitary sequencesthat you accept do not constitute a proofof your own claim.To assume some finite sequence of symbolsrepresents an exact real number presupposes aninfinite terminal sequence of constant 0'sin so far as that number is understoodonly in relation to a system of names (to becontrasted with understanding through the actof manipulating strings by a long division).So, you are arguing that mathematics isonly as exact as the limitations associatedwith some given acts of measurement.Every real world situation is understoodrelative to some normative ideal.  Jurisprudenceshould be just, politics should be virtuous,etc.Why is a normative ideal with respectto which acts of measurement are givena science so objectionable?
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