Spector is one who claims that numbers exist.

    "As far as mathematics is concerned, in what sense do these natural numbers exist
      -- and what do we even mean by the question?  Do we mean whether five apples or
      ten trillion stars exist?  Obviously, they do. Or do we mean that the idea of any natural
      number exists; that there is but one number 5, whose yet-to-be-named form /////, which
      is in and of mind, we recognize in things?  The mathematician Leopold Kronecker
      once observed, "God made the natural numbers.  Man has made all the rest."

      It is not necessary however to dwell on their metaphysical existence, because we have
      the clearest of models for what we call mathematical existence.  It appears in Euclid's
      Elements, where a figure -- a circle, a square -- will exist when it can be drawn.  Drawing
      it -- producing it -- confers its mathematical existence.  Defining it is not enough.  
      Moreover, statements with the word 'all' or 'every' -- such as 'All right angles are
      equal' -- refer to all which exist, that is, which have actually been drawn.

      Let us apply this to numbers.  We propose that a number will exist, mathematically,
      when it is named.  Naming will be a form of producing it.  If it is not named, whether
      in writing, speech, or thought, it does not yet exist."
      ("Do you mean to say that the number 100 does not exist mathematically until I name it?"  
      That is correct, and you have just named it!)"  [1]


    Spector claims that numbers have 'mathematical existence'. This is okay as long as he's not suggesting or implying that they
    have existence for the purposes of Science. However, the categorical way in which he phrases his opinions would seem to
    indicate that he is indeed referring to Science.

    So I will address his opinion as if he were trying to sneak a wolf in sheep's clothing... just in case. His language is simply too
    suspicious for me. I wouldn't want anyone to get the wrong impression that Spector is in any way talking about Physics or
    Science.

    For the purposes of Science, an object is 'that which has shape'. This is not because I say so. It is so because shape is the
    only definition that allows us to use the word object consistently (i.e., scientifically, rationally, logically). The word object is a
    synonym of thing, physical, material, entity, etc. Likewise, in order to use the word exist in a scientific manner we must define
    it as 'physical presence' (object + location). The 'physical' part demands a physical object. The 'presence' part requires that
    the object have location. The number 5 meets neither condition. The number 5 is not a physical object. We need not address
    location. Only objects may have location for the purposes of science.

    Allow me now to address the two justifications Spector provides for why numbers exist in Mathematics: manufacturing and
    naming. In Science, neither God nor Man can 'make' numbers. We don't manufacture or visualize concepts in Science either.
    In Science, we conceptualize and understand them. Visualize, you can visualize that which has shape. A number is an
    abstract concept. It does not posses shape.

    Also in Science, a table doesn't begin to exist simply because we name it. We can obviously mention the word table in a
    hypothetical situation. We can be referring to a table that doesn't exist, for example an imaginary one made entirely of diamonds.
    In order for a table to exist it must have location. If we name but don't point we are talking about a concept: an assumption.

    Therefore, I repeat in order to drive home the lesson. A concept doesn't exist for the purposes of Science. It is the superficial
    definitions that the mathematicians use that leads them to their supernatural world. Spector cannot use his definitions
    consistently across disciplines. He cannot say for example that the 150th chemical element  -- I'll call it 'X' --  exists simply
     because I say 'X.' Does a leprechaun exists because I say 'leprechaun'? Again, the criteria he uses to define existence has
    no possible consistent usage outside of Math. Whatever the mathematicians use within their chosen field doesn't concern
    Science. If Spector wants to extrapolate any of his conclusions onto Science, we need to review his definitions and not take
    them for granted.

    The mathematicians are also in the habit of using phrases such as 'there is or there exists a number that solves the equation'
    or 'where the function is continuous'. The use of the word exist in these contexts should be taken for what it is: ordinary
    speech. Concepts cannot exist. Mathematics deals exclusively with concepts.

    So allow me to formalize the rule:

    "If it belongs to Mathematics, it doesn't exist."

    [Unfortunately, the mathematicians themselves are the only exceptions!]

    Physics is the science that studies those things that exist. Physics is the science of existence. Mathematics is a discipline
    that exclusively studies abstract concepts. Mathematics studies only that which does not exist.
Do numbers exist?
And God said, "Let there be
numbers," and there were
numbers, and abacuses, and
slide rulers, and calculators...

And God saw that all of this was
evil because it confused the
mathematicians...

but He didn't know how to undo
the spell.
Adapted for the Internet from:

Why God Doesn't Exist

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        Copyright © by Nila Gaede 2008