Ah. Thanks glen. This is super helpful. Larding below.
-----Original Message----- From: glen [mailto:[email protected]] Sent: Friday, April 12, 2013 4:01 PM To: Nicholas Thompson Subject: Re: [FRIAM] Tautologies and other forms of circular reasoning. Nicholas Thompson wrote at 04/12/2013 02:18 PM: > See how much of the following you both can agree with: > > (1) We are talking here about a broad class of reasoning called circular, > wherein the conclusion is at least partly determined, not by any facts > about the world, but by information stated in the question. I agree completely with this. [NST ==>Lets put that in the bank <==NST] > (2) A tautology is the most narrowly defined example of such reasoning. In > tautology, we already know the answer when the question has been asked. No > doubts can be raised. This meaning can be further limited to certain > kinds of mathematical expressions. I agree mostly with this. The only exception is complicated deduction, where many premises tortuously, mechanically, crank through to "theorems" that aren't obvious in how they map back to the premises. There are some people who believe this kind of "computational" deduction is more than mere tautology. There are some who reduce it to mere tautology. [NST ==>There seem to be two issues here. (1) Whether the conclusion is entailed in the premise (or the answer in the question or (2) whether the entailed answer can be anticipated. That a white T-shirt confirms that All Ravens are Black is entailed by logic but totally unanticipated by me, and, indeed, I still don't get it. 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] > (3) In circular reasoning, (a) the conclusion can be -- at least > partly -- worked out from the question because the conclusion contains > the question embedded in it but (b) it is not entirely circular, > because it also contains other material that is not contained in the > question. So, for instance, if the question, "What selection pressure > made polar bears white?" the answer "a selection pressure that made polar bears white" is entirely circular. > It is a simple repetition of the question as an assertion. But notice > that the answer , "A selection for white fur", while highly circular, > is not entirely so because it rules out the possibility that the > selection was for some correlated trait -- conservation of melanin, > say. That information is not entailed in the question. I don't disagree or agree, here. I think this equivocates on "information" or "material not contained in the question". The only way to avoid this is to formalize the definition so that everything within the circular part and the non-circular part can be unambiguously identified. [NST ==>I see what you mean. By using this language I introduce ambiguity that really shouldn't perhaps enter a conversation about logic. Still, the make the conversation relevant, I am tempted from rigor. <==NST] > (4) Without trying to settle the question of how many forms of > semi-circular reasoning there might be, Lipton and Thompson described > a class of semi-circular reasoning called "recursive". (The idea in > the name was that the conclusion of the reasoning "runs back" to the > question for some of its information. Thus, this part of the > explanation is uninformative.) In recursive reasoning, the > uninformative part of the explanation is held within a frame that is > itself informative. If the question is, "Why is the oil in my car > clean?", then the answer, "Because it went through a clean oil filter" > is not completely circular but recursive, because the frame, "went > through _____ filter" it rules out the possibility that the oil is > clean simply because it has not yet been through the engine. The polar > bear explanation above is another example of a recursive explanation. > "His AIDS symptoms are caused by the AIDS virus" is another. We > thought that these recursive explanations play an important role in > the development of scientific explanations, because they guided > scientists as they collected data that served to revise the frame while keeping the goal of the explanation clearly in view. I agree that there are some of these filter explanations that are recursive. But some of them are not. And the more useful filter explanations are not actually recursive, but merely iterative. [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] > 4. Now where I am confused is about the relationship between > completely circular reasoning and tautological reasoning. The example > given at the dictionary of philosophy of a tautology is "Both Paul and > Mary were at the meeting; therefore Paul was at the meeting." If this > is the type-case of a tautological explanation, then I cannot see why > "A selection pressure that made polar bears white" is not another > example, given the question, "What selection pressure made polar bears white?" I disagree with your dictionary. I think of a tautology as "saying the exact same thing with different words", not saying a partly similar thing with different words. It's an if-and-only-if, not merely an if. "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] 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 think at least two of you can help me see where I am going wrong. I > think you are going to tell me that I have mixed apples and oranges > above, by talking indiscriminately about questions and answers and arguments and > conclusions. Can you straighten me out on that? Can you specify the usage > community for which your proposed usage is current? Given the FRIAM > group, can you suggest a usage convention you would recommend for our > further conversation about plurality in scientific explanation? I can't straighten anyone out. ;-) But my suggestion would be that tautology be used for the most direct, reversible, synonymous statements: "polar bears are white because polar bears are white". And anything more sophisticated should be given another name.[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] -- =><= glen e. p. ropella Oh man this egg is way too hot
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