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Primes and I

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  • paulmillscv
    Hello, I have thought more about Page s analogy and have realised what he is trying to say. Page s analogy is that just I determine myself by noting that a
    Message 1 of 32 , Jan 29, 2002
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      Hello,
      I have thought more about Page's analogy and have realised what he
      is trying to say. Page's analogy is that just I determine myself by
      noting that a tree or a bus is not me, so a prime identifies itself
      uniquely as the number which is 'the next largest' prime having
      sieved out the composites.
      It is a very interesting (and new) analogy. What is important about
      this piece of philosophy is that it strengthens both maths and
      philosophy. For example, the old line, 'I think therefore I am', is
      seen even more clearly as 'bouncing of one's own ideas' and not off
      external realities such as trees and buses. It is possible, with
      Descartes, to infer one's own existence from one's own thought, but
      much easier with Page's method. Page says, 'I am not a bus or a
      tree,… therefore I am'. Just as the prime 17 says, I am the next
      number after prime 13 and I am not a multiple of any number less
      than myself, therefore I am' , I .e. I am a prime.
      It strengthens maths because by identifying a new prime, we also
      prove that it exists. (Page concludes his post by saying that this
      is evidence of `existence' per se.) But where does it exist? It
      must exist originally in the mind. A major blow to philosophers who
      deny the existence of ideas. However, to continue the analogy to not
      just existence , but to actions and phenomenology proper, would
      definitely be offtopic as numbers do not act. Or do they :-). Good
      stuff.

      regards,
      Paul Mills
    • Jud McCranie
      ... According to The Mathematical Experience , by Davis and Hersh, page 334, Russell and Whitehead ... after 362 pages, the arithmetic proposition 1+1=2 is
      Message 32 of 32 , Feb 1, 2002
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        > >
        > > Russell and Whitehead proved that 1+1=2, using only logic.
        >
        >1+1=2 by definition. They proved 2+2=4 though
        >(technically (1+1)+(1+1)=((1+1)+1)+1)


        According to "The Mathematical Experience", by Davis and Hersh, page 334,
        "Russell and Whitehead ... after 362 pages, the arithmetic proposition
        1+1=2 is established." and they show part of that page which says "From
        this proposition it will follow, when arithmetical addition has been
        defined, that 1+1=2."

        +--------------------------------------------------------+
        | Jud McCranie |
        | |
        | ... algorithms are concepts that have existence apart |
        | from any programming language. The word "algorithm" |
        | denotes an abstract method of computing some output |
        | from some input ... -- Donald Knuth, CACM, 1966 |
        +--------------------------------------------------------+
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