Wednesday, February 02, 2005

Precision and Imprecision: Uncertainty, Probability & Proof

Aristotle, Nichomachean Ethics (trans. W.D. Ross, revised J. Urmson; Princeton U. Press, 1984) 1094b lines 24-27:
[I]t is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits: it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician demonstrative proofs.

1. The quoted language may be a bit jarring [in postmodernist jargon: "orthogonal"; in German: "quer"] to participants in contemporary debates about the relationship between probability and (forensic) proof. But, of course, Aristotle's world is different from ours and "probability" in the quoted statement (above) does not mean what it means today.

2. Despite Aristotle's insistence that in certain realms rough or imprecise reasoning is the best that we can do, can we agree that Aristotle was trying to describe precisely how rough reasoning about certain matters works? [Can we speak precisely about imprecise reasoning?]

3. Are Zadeh and Pawlak modern-day Aristotelians?