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Primes and I

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  • paulmillscv
    Hello, Good point Jud. The numeral 2 (a historical sociologically defined term) is distinct from the number 2. This is to say that the concept of 2 exists
    Message 1 of 32 , Feb 1, 2002
      Hello,
      Good point Jud. The numeral 2 (a historical sociologically
      defined term) is distinct from the number 2. This is to say that
      the concept of 2 exists first and then I can assign a term (written
      or spoken numeral) to describe it.
      However, having established that `Numbers are `out there'.
      It is time to reign in the imagination. Numbers are `out there' but
      only in relation to the human intellect. It is good time to state
      definitely that there is no intelligent life in the Universe apart
      from the rational being known as man. Sorry trekkies. Prime numbers
      appear to be a good `common knowledge' tool to explore this rational
      conclusion.
      But, gentlemen, we have found our first Realist! David
      Underbakke!
      I quote,

      This is just like the properties of mathematics, and
      prime numbers, that exist without regard to human comprehension.

      This is realism. I.e. things exist whether I think about them or
      not. Can you see how common sense says that prime numbers are
      defined and therefore a product of the intellect. Therefore they
      cannot have existed independently of the human intellect.
      If I can bring any `new-agers' on board here. Moderate realism
      (idealism) is like the intellect dipping into the stream of human
      consciousness `out there', `realising' in the intellect what already
      existed in this common stream, and in a wonderful way adding to this
      stream by its own invention or co-operation in this stream.
      Absolute realism is actually another form of Idealism or Platonism.
      Realist say that things really exist independently of the intellect,
      and idealists say that ideas exist independently of the intellect.
      Thomism is an anthropocentric philosophy, humanity and people are the
      apex of the natural world (and universe).

      If anyone would like to pursue the foundations of this
      thought, then contact me offlist. Otherwise I will confine my
      thoughts to Page's new `philosophy of primes'.
      Thanks to Page for initiating this new line of prime thought.
      I have read your last `essay' and found it very interesting. What was
      a nice surprise for myself was that your style of explanation is very
      similar to my own. (Look at the sentence construction). This is
      because you are an existential-realist-idealist, almost the perfect
      combination. Do you have classical training in philosophy? Can I
      make a suggestion. If you look through the post on this list you
      will see that many concern prime number theorems. This is not an
      accident. The theorem is a unit of knowledge. Your next step to
      participate in the mathematical discussions in this list is to learn
      some number theory, such as the properties of the prime numbers. I.e.
      A prime p = 4*k + 1 or 4*k+3. Then you will see that many of the
      primers on this list are very advanced thinkers although perhaps not
      in the form that you are familiar with.
      To conclude, live long and prosper earthmen.

      Regards,
      Paul Mills
      Kenilworth,
      England.
    • 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
        > >
        > > 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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