glen e. p. ropella wrote: > But I think Nick's answer is relevant to this point, as well. Even in a > seemingly a priori discrete system like that of the natural numbers, > "components" are psychologically induced, not necessarily embedded in > the system.
There is (actually) only *one* (closed) system, that being the universe, and "psychologically induced" "components" are *also* "embedded in the system". ... Even if you don't buy my axiom (from "There" to the following comma), you might be willing to buy the less expansive claims that (1) the intent of the question "why are there theorems?" would be better stated as "why do humans perceive/recognize theorems, and why are they interested in them?", (2) the perceived/recognized theorems are indeed "psychologically induced" AND THEREFORE *ARE* "necessarily embedded in the system" (a non-closed subsystem of the universe) that consists of the "mind" (or "minds") where the "psychology" is happening. As to "a priori", I attach an article by Konrad Lorenz in which he introduced "Evolutionary Epistemology". Nick and Eric have already had the opportunity to read it and comment on it, but as far as I can tell have done neither; perhaps it will be of interest to others here. (This version is a searchable PDF, not to mention a copyright violation.) In EE terms, one might say "theorems are there (to us) because we evolved so as to understand the world we evolved in, and (some) theorems are a damned good way to understand it (the rest have come along for the ride)". ============================================================ 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
