Stefan,
Thank you for your detailed review/response. And I agree with most of your analysis. Where I do not agree I do not disagree (pun intended).
I especially agree with your identification of the problem (or at least part of it) as "negation within deductive formal systems." In fact, this is one of the (many) things I had to cull from this short essay.
However, I would have a different focus. Consider a text entry field for the input of some kind of inventory. In this case I would have three distinct options; 1) enter a non-zero inventory, 2) enter a zero inventory, or 3) enter nothing (i.e., do not enter anything into the field). 2 and 3, although quite similar, are quite different. 2 could be interpreted as "no-thing" and 3 as "nothing". I will not belabor this perspective.
The perspective you presented, "1) either a mixture of both; 2) or it could be non of both" sounds something like the Buddhist catuskori that Graham Priest talks about (see, for instance, Pointing at the Moon - Buddhism, Logic, Analytic Philosophy), which (simply) says there are four options: True, False, Both True and False, Neither True or False.
Of course, no perspective could be as bad as what could be called the "probabilistic gradient" proposed by some (i.e., that there is True and False and then also shades of gray in between).
As interesting as this topic may be, I think the question of to what extent our scientific (formal) systems reflect reality or if they are simply employed (like a Pragmatist or neo-Pragmatist would) to predict reality is a more fundamental question. In that case, it doesn't matter if negation is unrealistic, only if it works. Subsequently, a more interesting question is if the two aspects mentioned, reflecting reality and predicting reality are complementary, in the sense of Bohr's principle of complementarity, which would mean that they are (intrinsically) incompatible perspectives.
What would it mean (i.e., what would it say about reality) if our scientific (formal) systems could be realistic or effective, but not both?
In any case, thanks again for your consideration and the discussion.
Jason
