Emergence: Complexity & Organization An International Transdisciplinary Journal of Complex Social Systems

Complexity is Vague and that is a Good Thing
So relating complexity to chaos as tree trunk to branch simply won’t do. And, again, I was still left with the arduous task of trying to adequately describe the tree. That brings me back to the idea of vagueness. At first impression, it might seem problematic that an entire field of study appears to be perhaps hopelessly vague. “Vague” though doesn’t necessarily entail being nebulous, ethereal, or inherently muddled. Indeed, in philosophical circles there has recently been a great deal of interest in exploring the philosophical ramifications of vagueness. In this regard, the English philosopher M. S. Sainsbury (1997) has made a good case for considering much of our ordinary discourse as composed of words that are fundamentally vague.

Thus, we find vagueness attached to the ordinary idea of “small,” demonstrated in what is called Wang’s paradox after the mathematical logician Hao Wang, a protegé of Kurt Gödel:
* By mathematical induction,0 is small, If n is small, n + 1 is small;Therefore, every number is small.

As the British philosopher of mathematics Michael Dummett (1997:101) explained about Wang’s paradox, “...since every natural number is larger than only finitely many natural numbers, and smaller that infinitely many, every natural number is small, i.e., smaller than most natural numbers.” This kind of vagueness is typically linked with the ancient conundrum of the heap known as the Sorites paradox (Sorensen, 2006): 1 grain of wheat does not make a heap.
If 1 grain of wheat does not make a heap then 2 grains of wheat do not.
If 2 grains of wheat do not make a heap then 3 grains do not. … If 9,999 grains of wheat do not make a heap then 10,000 do not.