Adapted for the Internet from:

Why God Doesn't Exist
The primitive point

    A mathematician begins the dissertation by saying that, as a matter of fact, some words in Geometry
    cannot or should not be defined.

    “ …math is about making definitions... If you're doing Geometry, then no amount of
      physical torture will get me to define a point; it's an undefined term, and it's undefined
      on purpose…”[1]

    “ Hilbert's axioms are a set of 20 assumptions… The undefined primitives are: point,
       line, plane.” [2]

    “ The word ‘point’ is often left undefined in geometry texts. It is pretty easy for us to
       conceptualize a point, but it is quite difficult to define exactly…” [3]  

    According to the mathematicians, the reason that words such as point and line are left undefined is that,
    if we happened to define them, this would lead to circular arguments:

    “ Points, lines, and planes are the foundations of the whole system of geometry...
       But point, line, and plane are all undefined terms. How can that be? Well, any
       definition we could   give them would depend on the definition of some other
       mathematical idea that these three terms help define. In other words, the definition
       would be circular.” [4]

    “The words points, lines, and planes are left undefined, or rather defined by usage
       in most geometries. We thus avoid circularity: where definitions circle back to one
       previously defined. This tradition was only started about 100 years ago by David
       Hilbert. However, we can form definitions using our undefined terms.”  [5]

    [Really? So if we define the word point we have circularity and if we don’t, we can
     define it in retrospect by usage. How neat! ]

    What a convenient and self-serving excuse! The mathematician tells you up front that he is afraid to
    define his key words because to do so might render his arguments circular. During his presentation he
    uses ad hoc or inconsistent definitions. Then, at the end of the dissertation he asks that you accept his
    irrational physical interpretations as if truth and law because they are founded on rigorous definitions
    and logic. They really have to be kidding!

    The true truth is that the mathematicians want their cake and to eat it too. Either the mathematicians
    CANNOT define the word point at all or they CAN define the point, but refuse to do so because it will
    invariably destroy the theory they are peddling. Make no mistake. Only non-scientists and frauds fail to
    define their language and search for excuses. There is no such thing as an indefinable word. To be on
    the safe side, always hold the presenter to the following golden rule:

    If you can’t define it, you shouldn’t use it !

          (Especially if your entire theory hinges on this definition.)

    If you can't define it, you don’t know what you're talking about! It’s just that simple. Come back and give
    the presentation when you've got your act together!

    Indeed, the countless definitions of the words point and line that float around the literature shows that
    the 'primitive' argument is absolute bunk! The other issue that cuts through the 'primitive' shield is that
    the mathematicians end up with circular reasoning and definitions anyways. They have not managed to
    avoid the predicament they wanted to avoid by not defining the terms they consider primitive. Let’s see
    what definitions the mathematicians have come up with over the years and why these definitions are
    circular.
Hmmmm! What
point mean?
I askum
Medicine Man.
Primitive Bill
The Noble Savage
?



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        Copyright © by Nila Gaede 2008