[PEIRCE-L] Re: [biosemiotics:8572] Re: Natural Propositions,
Dear Franklin, lists - It is classically described as such in the literature. The formal structure af abduction (the proposition A explains the occurrence B as a matter of necessity, therefore A can be chosen as a hypothesis to explain B) does not explain why A should be chosen over infinitely many other propositions with the same property. (see e.g. Michael Hoffmann's papers on abduction) Though Peirce did address this issue in terms of Galileo's il lume naturale, with the qualification that it has to do with a natural instinct. I have my own ideas about why we can happen upon the right hypotheses, but this is not the thread for such a discussion. That is a general explanation attempt of why humans are capable of abduction - that does not say anything about particular cases such as Wegener's. And this is where the trial-and-error phase of theorematic reasoning differs from ordinary abduction. The latter is standardly seen as a step in empirical research, from data to hypothesis. But all P's examples of theorematic reasoning are non-empirical, there is no data, for the whole problem considered is purely formal (like when selecting the right auxiliary lines in the triangle proof). That is a trial-and-error thing without procedural necessity - you may have to experiment with different lines until you find the right ones permitting you to conduct the proof. In that sense it is an "abductive" phase of theorematic reasoning. But it is not abductive in the sense that its starting point is data and its conclusion is a hypothesis. The right auxiliary lines are not at all a hypothesis explaining anything. For that reason, I do not think the proposal of saying that theorematic reasoning is just trivial deduction interspersed with abduction is satisfactory. I'm not sure about abduction being characterized as a move from data to hypothesis. Peirce's early account of abduction is somewhat close to that idea, but not so much his later account. Rather, it is typified by the move from a surprising fact, something which does not fit available data, to a hypothesis explaining the surprising fact. Correct, and that fact is a part of data. Suppose a case where the conclusion of the theorematic proof is considered the first premiss of an abductive argument, and the second premiss is the introduction of a hypothesis that would explain the conclusion of the theorematic proof. Then the conclusion of such an abduction would be the theorem introduced into the proof. So the "data" is simply the desired conclusion itself. In later discussions of abduction, Peirce does put it as something like this: There is a surprising fact. But if A were true, then the surprising fact would be a matter of course. Therefore A is true. Peirce admits though that not every case of abduction involves a surprising fact, but simply something that calls for explanation. I would suggest in this case that the desired conclusion is what is in need of explanation. It should be noticed that the way mathematicians make new discoveries is not typically through mathematical demonstrations; rather, the demonstrations are produced after the fact to communicate and prove the discovery to the satisfaction of other mathematicians. You are right that discoveries are often seen or suspected prior to demonstration - but it is too little to say demonstrations are only for communication and persuasion purposes. Considered in the larger context of the difference between discovery and demonstration in mathematics, it may very well be the case that every such major theorem in theorematic reasoning started off as a hypothesis to explain a desired conclusion, and the demonstration was produced after the fact. Of course, it would be very difficult to prove this as a general rule. But it is an alternative explanation which bears merit. It should also be noticed that all of this doesn't change the necessity of the conclusion in the theorematic reasoning, once proven. I suppose it could be replied that nevertheless, diagram experimentation would be required to develop the hypothesis. Well, my suggestion would be that, having certain propositions already, and a desired conclusion, but not being able to reach that conclusion from the given propositions alone, the diagram is put on hold while the mathematical mind starts thinking about what would explain the conclusion. Certainly - and that is where P argues that theorematic deduction is called for - Best F - 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 .
[PEIRCE-L] Re: [biosemiotics:8573] Re: Natural
Koichiro, " '. . . The path-dependent history carried by those incumbent elements in the reaction cycle, once stabilized through the successive alternation of the incumbents, must be functional in keeping the cycle in a durable manner." Is your "reaction cycle" described above different from what Prigogine called "dissipative structure" ? If so, in what way ? All the best. Sung On Sat, May 2, 2015 at 8:47 PM, Koichiro Matsuno wrote: > At 12:33 AM 05/02/2015, Benjamin Udell wrote: > > > > If there is something like evaluation or appraisal in nonliving things, > things that lack vital interests that the appraisals would reflect, then > such appraisals would seem of a rather lower grade than in living things, > > > > [KM] Ben, you shed light on the difference between physical and chemical > affinity, here. Physical affinity is operative in a manner of > space-mediated attraction like an electrostatic interaction of a > simultaneous nature carrying no memory. In contrast, chemical affinity can > exhibit a time-mediated attraction of a historical nature. The > history-dependent attraction is operative between the those atoms and > molecules visiting a reaction cycle for a while and the prospective > newcomers nearby so as to let the latter enter into the cycle subsequently. > The path-dependent history carried by those incumbent elements in the > reaction cycle, once stabilized through the successive alternation of the > incumbents, must be functional in keeping the cycle in a durable manner. > > > >Koichiro > > > > > > > -- Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net - 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 .
[PEIRCE-L] Re: [biosemiotics:8574] Re: Natural Propositions,
Frederik, lists, That is a general explanation attempt of why humans are capable of > abduction - that does not say anything about particular cases such as > Wegener's. Hmm. I'm not sure what you could be looking for here. In general, any semiotic being capable of abduction must have a natural instinct. In particular, any given abduction will be the result of that natural instinct meeting with the observation of given phenomena. On the other hand, if you mean it seems that with this idea we can't really get into a detailed analysis of just how this hypothesis was achieved and none of the others, I too share some such frustration, and would try to offer a more robust account than Peirce offered. You are right that discoveries are often seen or suspected prior to > demonstration - but it is too little to say demonstrations are only for > communication and persuasion purposes. Yes, you are right, it is too little to say. Certainly it helps to check one's work to be really convinced of the idea, and make sure it doesn't turn out somehow self-contradictory or incoherent. But I stand by the contention that the method of discovery of the idea is typically separate from its demonstration in the context of mathematical research. Certainly - and that is where P argues that theorematic deduction is called > for - Yes, I know, though of course I am saying instead that this is when abduction is called for. Theorematic reasoning should describe the whole process, both abductive and deductive, in my opinion. But I think that this is as far as we will get in discussion about it. I'll just have to agree to disagree with Charles on this one. -- Franklin On Sun, May 3, 2015 at 3:55 AM, Frederik Stjernfelt wrote: > Dear Franklin, lists - > > > It is classically described as such in the literature. The formal >> structure af abduction (the proposition A explains the occurrence B as a >> matter of necessity, therefore A can be chosen as a hypothesis to explain >> B) does not explain why A should be chosen over infinitely many other >> propositions with the same property. (see e.g. Michael Hoffmann's papers on >> abduction) > > > Though Peirce did address this issue in terms of Galileo's il lume > naturale, with the qualification that it has to do with a natural instinct. > I have my own ideas about why we can happen upon the right hypotheses, but > this is not the thread for such a discussion. > > > That is a general explanation attempt of why humans are capable of > abduction - that does not say anything about particular cases such as > Wegener's. > > > And this is where the trial-and-error phase of theorematic reasoning >> differs from ordinary abduction. The latter is standardly seen as a step in >> empirical research, from data to hypothesis. But all P's examples of >> theorematic reasoning are non-empirical, there is no data, for the whole >> problem considered is purely formal (like when selecting the right >> auxiliary lines in the triangle proof). That is a trial-and-error thing >> without procedural necessity - you may have to experiment with different >> lines until you find the right ones permitting you to conduct the proof. >> In that sense it is an "abductive" phase of theorematic reasoning. But it >> is not abductive in the sense that its starting point is data and its >> conclusion is a hypothesis. The right auxiliary lines are not at all a >> hypothesis explaining anything. For that reason, I do not think the >> proposal of saying that theorematic reasoning is just trivial deduction >> interspersed with abduction is satisfactory. > > > I'm not sure about abduction being characterized as a move from data to > hypothesis. Peirce's early account of abduction is somewhat close to that > idea, but not so much his later account. Rather, it is typified by the move > from a surprising fact, something which does not fit available data, to a > hypothesis explaining the surprising fact. > > > Correct, and that fact is a part of data. > > > Suppose a case where the conclusion of the theorematic proof is > considered the first premiss of an abductive argument, and the second > premiss is the introduction of a hypothesis that would explain the > conclusion of the theorematic proof. Then the conclusion of such an > abduction would be the theorem introduced into the proof. So the "data" is > simply the desired conclusion itself. In later discussions of abduction, > Peirce does put it as something like this: There is a surprising fact. But > if A were true, then the surprising fact would be a matter of course. > Therefore A is true. Peirce admits though that not every case of abduction > involves a surprising fact, but simply something that calls for > explanation. I would suggest in this case that the desired conclusion is > what is in need of explanation. > > It should be noticed that the way mathematicians make new discoveries is > not typically through mathematical demonstrations; rather, the > demo
