Nicholas Thompson wrote at 04/12/2013 03:51 PM: > [NST ==>[...] Am I correct that you want to exclude for > "tautological" sequences of reasoning where the conclusion is entailed the > premises (or the answer in the question) but the path is so complex that we > cannot anticipate it? <==NST]
Yes. On my more flippant days, I'll point out that some people claim unanticipatable, complicated deduction reduces to tautology. And I may say it when I get frustrated at people who don't understand the difference between deduction and induction. But for the most part, yes. A purely deductive system that can hit upon true, but surprising, theorems, is not merely tautology. > [NST ==>The first time you made this distinction, I couldn't quite get it. > Can you say a bit more? It wold seem to me that recursion could happen only > once, but that iteration would require several instances. So I can imagine > an interation of recursions but not the reverse. In short, I don't know how > talk this talk, yet. <==NST] Both recursion and iteration can be infinite. The difference lies the focus of the repetition. Recursion puts more focus on the I/O of the process, what comes out of any given application must make sense going in. The input and output must be commensurate. Iteration puts more focus on the procedure, in particular the state, the conditions that obtain. As long as the conditions still tolerate it, the iteration will continue, regardless of whether the I/O is meaningful. Iteration can wander more than recursion. Recursion is less prone to the adage "garbage in => garbage out". So, in your filter metaphor, if your filter stays the same, each time the fluid is pushed through, it will filter more of the same particles out of the fluid until there are none left (or the filter fills up). With iteration, your filter might change each time it's used because of unforeseen effects. For example, if your filter is supposed to extract particles 1-100 millimeters, but you use it so much that it starts to develop densely packed regions, then it may begin to filter only particles that are 1-100 nanometers. The filter is a hysterical process. It has memory. If you replace the filter with a new one each time the fluid goes through it, then you've got recursion. If you allow the filter to get progressively dirty, then you've got iteration. Iteration is most aligned with stateful repetition. Recursion is most aligned with stateless repetition. > "P ^ M -> P" leaves out information. So, saying "P" is not the same as > saying "P^M".[NST ==>AHHHHH! So total entailment is not sufficient to > tautology, on your account. I have to think about that. So all white swans > are white is a tautology but (1) All swans are white (2) this bird is a swan > (3) this bird is white is not. <==NST] Not technically, no. But if pressed, I would consider the context of the accusation. When I'm talking to someone like you, who might actually listen to me, I'd say "no". When talking to someone who just likes to hear themselves talk, I'd say "ok, sure, 1) all swans are white plus 2) this is a swan, therefore 3) this swan is white is close enough to a tautology for me to call it that for this conversation." But when/if I allow that, I'm on a slippery slope to calling all deduction tautological. > But, as I said above, there are some people who claim that all deduction is > tautology. They would probably identify different types of tautology (e.g. > simple or minimal) versus a complicated (perhaps irreversible) deduction. > > [NST ==>OK. We are on the same page. So what term do you want to use? > <==NST] I see no problem with "deduction" or perhaps "inference", "grammatical transformation", etc. Heck, I'd even be ok with "simulation", "numerical analysis", "play it forward", "let it roll", and "Deism". > [NST ==>how about > long and short tautologies? Probably too whimsical. OK. How about .. > Tautologies for the narrow case, and analytical conclusions for the > deductions. <==NST] I like "analytical conclusions" as a synonym for "complicated deduction". The only issue is the teleological sense I get from "conclusion", I suppose. How about "analytical end state"? ;-) -- =><= glen e. p. ropella Lobsterbacks attack the town again ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
