The Sorites Paradox
The coloured strip to the left is actually made up of a series of
rectangles each about 40 times wider than it is high and each a
different colour. The top one is clearly red (its rgb specification is
"255, 0, 0"). The bottom one is absolute yellow (255, 255, 0), and
therefore clearly not red. Each ith one in between is
rgb(255, i, 0). Now each of these little rectangles is
indistinguishable to the naked eye from its neighbours, so if any one
of them looks red then so does the one immediately below it:
This is a famous old paradox, known as the sorites paradox or paradox of the heap: the applicability of a vague predicate such as "looks red" is insensitive to small changes in some respect, but sensitive to large ones, and yet the large ones are made up of small ones. There are only three ways out of it. One can:
Option 3 deserves to be taken more seriously than it usually has been: if the phenomena provide counterexamples to logical theory, perhaps it is the theory rather than the world that needs adjustment. Merely introducing "degrees of truth" into the semantics of logic, however, is not enough. I started working on a substructural logic suitable for vague reasoning in the early 1980s and have returned to it sporadically since. While I am almost the only philosopher who doesn't claim to have all the answers about this thoroughly intractable paradox, I continue to see nonclassical logic as holding the best hope for a satisfactory account.
Dominic Hyde, 'Sorites Paradox', Stanford Encyclopedia of Philosophy.
John Slaney, 'A Logic for Vagueness', Australasian Journal of Logic.
Dr J K Slaney Phone (Aus.): (026) 125 8607 Automated Reasoning Group, CSL Phone (Int.): +61 26 125 8607 Australian National University Fax (Aus.): (026) 125 8651 Canberra, ACT, 0200, AUSTRALIA Fax (Int.): +61 26 125 8651John.Slaney@anu.edu.au