Counterarguments to "Numerology"? Background:  I am interested in learning more about numerology.  In this post I am specifically interested in the arguments used by those who reject this doctrine.

My current impression of what "numerology" is:  Certain numbers in scripture have special symbolic meaning.  Examples: "7 is the number of divine perfection", "6 is the number of man", etc.  

What I am looking for:  I am sure there are "countless" examples in favor of this doctrine, but I am curious what the counterarguments are?  I am interested in maybe the top 3-5 counterarguments that a "non-numerologist" would use.

If there is no such thing as a "non-numerologist", or there are no counterarguments, please provide some sort of evidence or reference to this effect.  Thanks!
I can't answer the question in the way you're asking it, but I can 'disarm' numerology for you. When you encounter something, like say, a set of best practices in an activity, the number of units you decide to divide the information into determines the symbolic meaning you are essentially attaching to the set. This is possible with pretty much everything, so when you see 'ten commandments', if you affix too much significance to the ten, you lose sight of the fact that God could have given them four or twelve commandments with the same content, but Ten is chosen because of its symbolic meaning. 

Take the cross; it is one thing. You can divide it into the cross bar and the pole, that's two. You can divide it into the top, middle and bottom, that's three. You can divide it into each of the cardinal directions: four. You can divide it into cardinal directions plus the center: five. Or, you can get four by including more details, such as cross bar, pole, sign (above) and footrest. The cross has six elevations (forward, back, top, bottom, left, right). The five pieces before plus the footrest and the sign is seven; with the footrest and sign you get eight points. Take the seven before and include the spear of longinus and the reed with the sponge, you get nine objects. Ten if you then count the rock it was planted on. You get twelve by counting the sides in two dimensions, fourteen in three dimensions, and so on.

The problem and weakness of numerology generally is that it assumes the numbering and the content are coeval, that the ten-ness of the ten commandments is somehow essential to its content. Consider the four Gospels; four were kept because of the symbolism of four; at one time a Syriac wanted to combine them into a single gospel for accuracy (this was a long, long time ago.) 

The difficulty with numbers is teasing out the meaning of the number itself and not confusing it with the thing being numbered. All numberings aside from perhaps one and three are arbitrary; but even then the threeness of God is his decision. 

This position essentially refutes numerology because instead of seeing the numbers as a noumena, I.e a revelation of the underlying reality, it sees them as phenomena, that is, an arrangement applied to the underlying reality. Their use has a meaning, but it is not itself the meaning.