Oh shit. Nick's in a state again. On Apr 12, 2013 9:23 PM, "Nicholas Thompson" <[email protected]> wrote:
> I have a terrible time with the word "state"; how about analytical output? > > > Otherwise we're good. > > Nick > > -----Original Message----- > From: Friam [mailto:[email protected]] On Behalf Of glen > Sent: Friday, April 12, 2013 5:40 PM > To: The Friday Morning Applied Complexity Coffee Group > Subject: Re: [FRIAM] Tautologies and other forms of circular reasoning. > > 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 > > > ============================================================ > 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 >
============================================================ 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
