Roger Critchlow wrote: > No functors were deployed in the construction of these paragraphs.
I agree that the "F" isn't a functor. But, it is at the same level of discourse as functors. It's part of the definition of a category, an axiom, which means it comes from _outside_ the formalism. I.e. it comes from somewhere other than the formalism itself. Functors, being morphisms between categories are also outside of the categories they relate. So "outer entailments" involve extra information not available within the context and "inner entailments" involve only information available within the context. I think this is why Rosen links it to a discussion of final (externally imposed) cause. The whole goal is to find a way to _close_, feed back, or turn these arrows back in on themselves. The claim is that an organism will not have any efficient outer entailments (though we expect material outer entailments). To go back to parsing the notation, how about this: f => ( a => f(a)) means "f dictates that ( a dictates that f(a) )" g => ( b => g(b)) means "g dictates that ( b dictates that g(b) )" g => ( f(a) => g(f(a)) ) means "g dictates that ( f(a) dictates that g(f(a)) )" i.e. "g is defined so that the things in its co-domain (e.g. f(a)) dictate the composition g(f(a))." F => ( (f,g) => gf) means "F is defined in order to clump two functions in its co-domain so that the clumping is identified as an operation, specifically, the composition operation". p.s. I use "dictates" as opposed to "entails" just for a linguistic parallax. One might also use "specifies", "requires", "imposes", etc. -- glen e. p. ropella, 971-219-3846, http://tempusdictum.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
