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.