Correction: In my last post I wrote "Your order here (result/rule/ergo case) was also recently suggested by Jon S as a possible 'inversion' of rule/case/result for abduction."
But, now I recall that Jon S gave the opposite order, ie. case/rule/result and remarked that it is the reverse of the categorial pattern for inquiry (which is correct). In my categorial vector theory I refer to the order, case/rule/result, as the vector of aspiration, and the one Ben gave, of result/rule/case as the vector of process (I often note that both inquiry and biological evolution follow this order according to Peirce). Adding these 2 to the 3 Peirce gives in the bean example, we have 5 of the 6 possible categorial vectors, the remaining one being Hegel's dialectical order. This is not to say that I'm at all sure that all these five definitely represent inference patterns. GR [image: Gary Richmond] *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *C 745* *718 482-5690* On Fri, Apr 29, 2016 at 3:31 PM, Gary Richmond <gary.richm...@gmail.com> wrote: > Ben, list, > > Thanks for your two recent posts in this thread. I've been reflecting on > them--and the whole matter of abduction--but I'm not sure exactly where to > take that reflection at the moment. Still, I believe that continuing the > inquiry might prove quite well worth the effort. > > There are clearly a number of scholars struggling with abduction in > Peirce, and they are considering it from a number of different angles, yet > with no clear cut resolution coming to the fore as far as I can tell. For > example, Sami Paavola in "Peircean abduction: instinct, or inference?" > http://www.helsinki.fi/science/commens/papers/instinctorinference.pdf argues > "that Peirce did not resolve the relationship between inference and > instinct in a clear-cut manner in his later writings." He continues: > > The interpretation that I advocate is to distinguish abductive instinct > and abductive inference, which suggests that abduction can be developed > further as a ‘pure’ form of inference: Various aspects of it can be > analyzed further, for example, the nature of its premises, the inferential > relationships within it, the strength and validity of it, how abductive > inferences are used. That is, in Peircean terms, the grammar, the critic, > and the methodeutic of abductive inference should all be further examined. > > The proposal that abductive inference should be developed further as a > mode of inference does not mean that abductive instinct should be > neglected, quite the contrary. Peirce analyzes many phenomena under the > guessing instinct that are of interest to modern cognitive sciences, > starting with the idea that human beings can use, in their problem solving, > information of which they are not conscious. Peirce, of course, did not > have at his disposal many of those conceptions that are attractive to the > modern reader from this perspective (for example the notion of ‘tacit > knowledge’, or modern conceptions of expertise). The idea of abductive > instinct could be analyzed further by using these modern notions (from the > conclusion of his paper). > > > But returning to our discussion of abduction as a mode of inference, I > think that your suggestion that we give some thought to what you referred > to as 'abductive generalization' might prove a fruitful one. You wrote: > > Also in considering the beans example, I forgot that it's just one way of > instancing Barbara and its inversions. After all, Barbara is named for its > vowels as a mnemonic for the universality and affirmativity of its > propositions - AAA. So, in a universe in which mammals are not _*defined*_ > as warm-blooded air-breathing live-young-bearers: > > *Result:* All whales are warm-blooded, breathe air, and bear live young. > > *Rule:* All mammals are warm-blooded, breathe air, and bear live young. > > Ergo *Case:* (Plausibly) all whales are mammals. > > The "case" there is itself a new rule. I'm not sure whether that's an > example of what Peirce means by abductive generalization, but there it is. > > Your order here (result/rule/ergo case) was also recently suggested by Jon > S as a possible 'inversion' of rule/case/result for abduction. I was > thinking of the bean example (which folllows the usual order: > rule/result/ergo case) when he first suggested it, but yet remarked that it > might be an interesting and valid way of looking at abduction, and your > example above would seem to support that notion. I must admit that your and > Jon S's order still strikes me as somewhat odd, while the question remains > as to whether or not it adequately represents 'abductive generalization' > (not an expression of Peirce's, I don't believe, but useful). > > One last, perhaps minor, matter is that I agree with Jon A that since > 'result' only works for deduction, that another term might be better > employed in consideration of induction and abduction. Since I associate > 'result' with 1ns, I've tended to use the term 'character' rather than > 'result' (as I did earlier in this thread and occasionally in other threads > over the past few years). But Jon has suggested 'fact' to replace 'result', > which he says has been used by others, for example, W. S. McCulloch. Since > I associate 'fact' with 2ns (which Peirce, it seems to me, does as well), > I'm going to continue to use 'character' as a substitute for 'result' > unless someone comes up with an even better term. > > Best, > > Gary R > > > [image: Gary Richmond] > > *Gary Richmond* > *Philosophy and Critical Thinking* > *Communication Studies* > *LaGuardia College of the City University of New York* > *C 745* > *718 482-5690 <718%20482-5690>* > > On Fri, Apr 29, 2016 at 6:21 AM, Benjamin Udell <bud...@nyc.rr.com> wrote: > >> Gary R., list, >> >> I got careless in my previous message. >> >> I said that "There is *F*, ergo anything is *F*" ("∃*F*∴∀*F*") would be >> abductive; however, in a stipulatedly non-empty universe, its conclusion >> entails its premiss, and so for my part I would rather call it inductive >> than abductive, at least in the "usual" universes. A better candidate for a >> toy example of an abduction to a rule would be "There is *FG*, ergo >> anything *F* is *G*" ("∃*FG*∴∀(*F*→*G*)"). These are silly examples, but >> I like the idea of being able to sort out even the simplest inference >> schemata into deductive, inductive, and abductive, in terms of entailment >> relations between the premiss set and the conclusion. In the second >> example, "∀(*F*→*G*)" is arguably a selective generalization of "∃*FG*". >> >> Also in considering the beans example, I forgot that it's just one way of >> instancing Barbara and its inversions. After all, Barbara is named for its >> vowels as a mnemonic for the universality and affirmativity of its >> propositions - AAA. So, in a universe in which mammals are not _*defined*_ >> as warm-blooded air-breathing live-young-bearers: >> >> *Result:* All whales are warm-blooded, breathe air, and bear live young. >> *Rule:* All mammals are warm-blooded, breathe air, and bear live young. >> Ergo *Case:* (Plausibly) all whales are mammals. >> >> The "case" there is itself a new rule. I'm not sure whether that's an >> example of what Peirce means by abductive generalization, but there it is. >> >> Best, Ben >> >> On 4/28/2016 3:10 PM, Benjamin Udell wrote: >> >> Hi, Gary, >> >> I agree with most of what you say, only I don't see hypothesization of a >> rule in the beans example. On the other hand, Peirce is explicit about >> hypothesizing a new general (or rule) in the 1903 quote. >> >> [....] The mind seeks to bring the facts, as modified by the new >> discovery, into order; that is, to form a general conception embracing >> them. In some cases, it does this by an act of _*generalization*_. In >> other cases, no new law is suggested, but only a peculiar state of facts >> that will "explain" the surprising phenomenon; and a law already known is >> recognized as applicable to the suggested hypothesis [....] >> (From "Syllabus", 1903, EP 2:287 >> http://www.commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-some >> ) >> >> Moreover, Peirce in a draft circa 1896 (CP 1.74) said "Kepler shows his >> keen logical sense in detailing the whole process by which he finally >> arrived at the true orbit. This is the greatest piece of Retroductive >> reasoning ever performed." Clearly, Kepler was looking for a rule, not >> merely for a special circumstance, to explain an orbit. >> >> The problem, which has been nagging at me for a while (and I have read >> too little of the secondary literature), is how to distinguish, in a >> reasonably simple way, such abductive inference from induction? >> Now, by "generalization" Peirce usually meant what many would call _ >> *selective*_ generalization. That's his hint to us there. >> >> I've tried to think in terms of the hypothesizing of a hidden special >> circumstance, e.g., a hidden mechanism, that would have to happen by a new >> rule in order to make sense at all. But, how much of this hidden special >> circumstance does one really need to conceive of, in order to conceive of a >> new rule? I've also wondered whether it's a matter of considering rules as >> special circumstances at some level of abstraction, likewise as one may >> consider integers as singulars at some level of abstraction, in an abstract >> universe of discourse. >> >> But complications make me distrustful in questions of elementary >> distinctions among inference modes. Remembering Peirce's idea of selective >> generalization as a hint, it occurs to me that maybe it's a matter of a >> need to select among the characteristics to extend. That's where some >> guessing comes in. That is, Kepler's math may represent a character of the >> appearance of orbits, but the orbits actually observed at that time might >> be accounted for in other ways, and Kepler's math might conceivably have >> worked just by accident up till then. Well, in Kepler's case, his ultimate >> solutions could hardly plausibly have worked just by coincidence, but there >> are plenty of cases where a mathematical model fits the past by accident >> and turns out to lack predictive value. >> >> So, in the schema for abductive inference to a rule, maybe there should >> be a premissual admission of characters that seemed salient, not all of >> which are extended by inference to the whole. That very selection may >> amount to an idea new to the case. Moreover, some of the characters may be >> formulated (e.g., mathematically) in a new way, the idea new to the case. >> Still, doubts nag at me. These may be patterns of abductive inference, but >> my sense is that one needs to be able to distinguish abductive inference >> (to a rule) from induction even in ridiculously crude cases. >> >> The idea of induction is that of inference from a part or fragment of a >> system to the whole. Yet it is possible to state any inference to a rule >> without any reference to a positively granted larger whole. If I conclude >> that, for any *F*, *F* is *G* , then I have not asserted or entailed in >> the conclusion the existence of a whole or even of a part of the population >> of *F* 's. Induction and testing, however, do need a positively granted >> larger whole to test. When one abduces to a rule, it may simply be that >> one "attenuates" one's focus to the rule itself, the rule as embodying a >> kind of real necessity, and _*that*_ rule, taken as itself real, >> indefinitely projectable across a population not yet contemplated, etc., is >> what is new to the case. So, the implausibly crude ampliative inference >> "There is *F*, ergo anything is *F*" ("∃*F*∴∀*F*") would be abductive, >> not inductive (in a stipulatedly one-object universe, it would be a >> reversible deduction). Well, I've been pottering around with these ideas >> for a while and I haven't gotten much farther. >> >> Best, Ben >> >> On 4/27/2016 12:42 PM, Gary Richmond wrote: >> >> Ben, list, >> >> You gave Peircean examples whereas the rule (or law) is *already known* >> either before or after the surprising fact. This seems all well and good to >> me for certain types of abductions, say, those involved in sleuthing, >> Sherlock Holmes style. >> >> But what of those inquiries in which the rule (law) is *not* known, *but >> is exactly the hypothesis* of the inquirer? This is to say that >> scientists sometimes come to uncover laws hitherto unkown or unrecognized >> (such as those hypothesized by Newton, Darwin, Einstein, Planck, etc.) >> >> I have sometimes thought that in *that* context--that is, of someone >> hypothesizing a law *not* previously known--that, modifying the 1878 >> bean example you gave: >> >> Suppose I enter a room and there find a number of bags, containing >> different kinds of beans. On the table there is a handful of white beans; >> and, after some searching, I find one of the bags contains white beans >> only. I at once infer as a probability, or a fair guess, that this handful >> was taken out of that bag. This sort of inference is called _*making an >> hypothesis* _. It is the inference of a _*case* _ from a _*rule* _ and _ >> *result* _. (CSP) >> >> the situation might look something like this (although I'm not sure that >> any bean example will quite do for this purpose. >> >> Suppose I enter a room and find a large number of bags which I know to >> contain different kinds of beans. Near one bag I find a handful of white >> beans (the surprising fact) and I make the supposition (the hypothesis) >> that *that* particular bag of beans is all white. I examine the bag of >> beans (make my experiment) and find that the bag in question does indeed >> contain only white beans (the rule). (GR) >> >> Well, it may turn out that I know beans about abduction, but it does seem >> to me that the scientifically most fruitful and significant hypotheses are >> those where the law (rule) is *not* know in advance and is only supposed >> by the scientist, again, exactly *as the hypothesis* . >> >> Peirce gives an example of that kind of hypothesis, one which is, shall >> we say, *fresh* at the time (the rule or law not being previously known): >> >> Fossils are found; say, remains like those of fishes, but far in the >> interior of the country. To explain the phenomenon we suppose the sea once >> washed over the land (CP 2.625). >> >> Now suppose that a historian of the region in which those fish fossils >> were found, himself finding documents showing that a large caravan of >> traders had brought large quantities of dried fish into that region, >> pooh-poohs my *sea washing over the land* hypothesis, which I have >> already imagined (for some good reasons) to have happened in other parts of >> the world as well. Thus, as other investigators find many other places, >> including deserts, etc., containing many fish fossils where there was no >> possibility of any fish trade occurring, my hypothesis takes hold and is in >> time accepted quite generally by the scientific community. >> >> (Another, not unrelated example, would be that of continental drift.) >> >> It seems to me that Peirce intended to cover both kinds of hypotheses >> even in his bean illustrations as he offers examples of both (the fossil >> example is preceded by what I referred to above as a sleuthing type of >> example). Any help which you or others can offer towards clarifying this >> matter--of someone hypothesizing a rule or law not previously known--would >> be appreciated. >> >> Best, >> >> Gary R >> >> [image: Gary Richmond] >> >> >> >> >> >> >> *Gary Richmond Philosophy and Critical Thinking Communication Studies >> LaGuardia College of the City University of New York C 745 718 482-5690 >> <718%20482-5690> * >> >> On Tue, Apr 26, 2016 at 11:49 AM, Benjamin Udell wrote: >> >> >> >> >> ----------------------------- >> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON >> PEIRCE-L to this message. PEIRCE-L posts should go to >> peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L >> but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the >> BODY of the message. More at >> http://www.cspeirce.com/peirce-l/peirce-l.htm . >> >> >> >> >> >> >
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