Thus spake Nicholas Thompson circa 04/28/2009 08:33 PM: > let a, b, and c > constitute macro-entity E and let the behavior of E. be controled by the > properties and intereactions of a, b and c. Now, let one of the behaviors > of E to control the behavior of a, b, or c. Is there a problem here?
There's no problem with it. It's called an impredicative definition, which basically means the application of a universal quantifier (e.g. "for all") over a set as a part of the definition of the members of that set. (IIRC, of course... ;-) Here's a quote from Barwise and Moss' "Vicious Circles" that may address the "problem" you've heard "philosophers" talk about: "In certain circles, it has been thought that there is a conflict between circular phenomena, on the one hand, and mathematical rigor, on the other. This belief rests on two assumptions. One is that anything mathematically rigorous must be reducible to set theory. The other assumption is that the only coherent conception of set precludes circularity. As a result of these two assumptions, it is not uncommon to hear circular analyses of philosophical, linguistic, or computational phenomena attacked on the grounds that they conflict with one of the basic axioms of mathematics. But both assumptions are mistaken and the attack is groundless." -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
