Talk:Abductive reasoning/Archive 1

Archive 1

Archive 2

Lack of clarity and lack of examples

Hello all. I was trying to learn the relationship between induction, deduction, abduction, having avoided these concepts in undergrad studies. The entries for induction and deduction make it immediately clear what these are, but after reading this, I still am not sure what is meant by abduction. Please give some examples and if there is confusion on the subject (apparently there is?) then please make that clear as well. The explanation as is mentions the *probability* of the respective observations/principles. Bringing probability into things, doesnt that put us beyond the realm of simple logic which is based on either true or false statements? —Preceding unsigned comment added by 134.95.92.236 (talk) 00:47, 19 October 2007 (UTC)

This first chapter of the referenced book by Josephson appears to be at http://www.cse.ohio-state.edu/~jj/pubs/AbdInfCh1.pdf and on page 15 starts a section that hopes to "clear up the confusion about the relationship of abduction to induction". Does anything from there help? If so, maybe it can help us improve the page. 68.9.129.213 (talk) 15:54, 29 April 2009 (UTC)

It might be helpful to define abduction, induction and deduction in layperson's terms in addition to defining them in symbolic logic. Perhaps something like: Abduction A method of logical reasoning wherein a general law is inferred from particular instances without sufficient information to guarantee their validity. Induction A method of logical reasoning wherein a general law or principle is inferred from a multiple of particular instances. Deduction A method of logical reasoning wherein a particular instance is inferred from a general law.--Rodmunday (talk) 13:16, 3 July 2010 (UTC)

One problem is that there are more than one definition of induction and more than one definition of abduction. Deduction is currently better defined in the article (e.g., "Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion") than as inference of a particular from a general (an instance from a law). For trivial example, "There is a horse, ergo there is a horse or a cow" is a valid deduction. The article's definition of abduction seems consistent with more than one picture of abduction, especially where it says "allows inferring a as an explanation of b. Because of this, abduction allows the precondition a to be inferred from the consequence b." Peirce made such remarks about abduction as deduction in reverse. I think that that has to confuse people since sometimes induction can be cast as deduction in reverse. "Premiss: As of today it has been sunny for four straight days. Conclusion: As of tomorrow it will have been sunny for five straight days." That's inductive. Reverse the premiss and conclusion, and you get deduction: "Premiss: Tomorrow it will have been sunny for five straight days. Conclusion: Today it has been sunny for four straight days." For what it's worth, my POV is that the division of inference into abductive, deductive, and inductive does get at something real, but they've never been satisfactory clarified because those kinds of inference have not all three of them been, so far as I know, defined in terms of a single set of properties or regards - which is what Peirce originally tried to do, by forming abduction and induction as transformations of a classical deductive syllogism (see Charles Sanders Peirce#Modes_of_inference. Peirce later decided that that was not the most basic way to distinguish and define them.) Your definition of induction seems clearer than the article's; but induction has sometimes been defined more broadly (to include, for example, inferring the conjunction p & q from the disjunction p v q), so your definition could be taken as a description that doesn't cover all cases. For my part, I really like for wikis to be accessible to the general reader and, failing that, at least some parts of wikis. I've just now tried adding a few things to the introductory definitions. The Tetrast (talk) 21:29, 3 July 2010 (UTC).

I agree. In fact the reason I added these definition to the discussion page and not the article page is precisely to acknowledge their provisional nature. Addressing your broader point, of course any concepts has multiple definition, moreover no article of this kind should ever imply that there is one 'royal road' to understanding. However, this article should primarily be targeting those who are initially trying to get their heads around the concept and therefore it is useful to include an understanding of abduction and how it relates to induction, deduction and hypothesis in plain English. I also think is is useful to have a sentence about these concepts here as well as linking to the full Wikipedia articles --Rodmunday (talk) 12:41, 4 July 2010 (UTC)

Well, somebody just deleted everything that I added in the definitions, and also deleted a bunch of stuff that's been there a long time and that I had not added. The editor called it "OR" - original research. So it looks like I'll have to get around to digging up references. I don't know why the text which the editor left in place is not also "original research". Ah well, when I get time, I'll fix it up. The Tetrast (talk) 00:37, 4 July 2010 (UTC).

Please post new comments at the bottom of the talkpage per WP:TALK. We can discuss why some of your additions and previous material are WP:OR here or on my talkpage, but it may suffice to review that article. D'ailleurs, a quick search through Tyler Burge's work should help clear up some common misconceptions about deduction that came up in the deleted material as well. Happy editing.--Heyitspeter (talk) 10:50, 4 July 2010 (UTC)

It's quite normal to post responses to comments within an older (but non-archived) section, as long as the comments appear at the bottom of the old section.
I had no objection to the changes in the deduction definition, none of which definition I had written.
I've looked just now at the Tyler Burge wiki which you linked. I don't think that there is anything there that would be inconsistent with the Abuctive Reasoning wiki's now-deleted claim "Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. It is true by definition and is independent of sense experience" if the now-deleted claim had been worded a little better to focus on the deduction's validity's independence from sense experience. However, such a claim, soever re-worded, about independence from sense experience still seems digressive and embroilable in arguments and I have no desire to restore it in any form. Too bad tachyons don't appear to exist, for if they did then Burge and Putnam could have talked with some topicality about the difference between what we call energy and what, for a tachyon-composed being, would work like energy - similar to two denotations "switching the socks" of their comprehensions. The Tetrast (talk) 18:33, 4 July 2010 (UTC).

That "[a valid deduction] is true by definition and is independent of sense experience" is a category error, and even if we were to concentrate on the intent behind the statement (versus on the statement itself) it would be disputed by many prominent contemporary philosophers. First, a valid deduction is not true or false. All philosophers can agree on that. Second, philosophers like Burge, Hartry Field, Laurence Bonjour and Timothy Williamson would all dispute the claim that what we call a 'truth by definition' is independent of sense experience, and some from that list would dispute that what we call a 'truth by definition' is true by definition.--Heyitspeter (talk) 00:41, 28 July 2010 (UTC)

I should add that I think that the appropriate place for discussion of your deletions from this wiki is here in this wiki's talk page, not as you suggest on your user talk page. The Tetrast (talk) 18:45, 5 July 2010 (UTC).

Off-topic and unreferenced

"Peirce stated that classification plays a major role in making a hypothesis, that is the characters of phenomenon are placed into certain categories (Peirce, 1878b). Although Peirce is not a Kantian (Feibleman 1945), Peirce endorsed Kant's categories in Critique of Pure Reason (Kant, 1781/1969) to help us to make judgments of the phenomenal world. According to Kant, human thought and enlightenment are dependent on a limited number of a priori perceptual forms and ideational categories, such as causality, quality, time and space. Also, Peirce agreed with Kant that things have internal structure of meaning. Abductive activities are not empirical hypotheses based on our sensory experience, but rather the very structure of the meanings themselves (Rosenthal, 1993). Based on the Kantian framework, Peirce (1867/1960) later developed his "New list of categories." For Peirce all cognition, ranging from perception to logical reasoning, is mediated by "elements of generality." (Peirce, 1934/1960). Based upon the notion of categorizing general elements, Hoffman (1997) viewed abduction as a search for a mode of perception while facing surprising facts." This is largely OT and full of incomplete references. Sbarthelme 12:06, 19 Jan 2005 (UTC)

Default reasoning

I have removed the following from the article:

...plan formation and default reasoning.

Negation as failure in logic programming can both be given an abductive interpretation and also can be used to implement abduction. The abductive semantics of negation as failure leads naturally to an argumentation-theoretic interpretation of default reasoning in general.

Perhaps can be reintroduced in a later section.Paolo Liberatore 12:37, 23 August 2005 (UTC)

Removed from the History section

I have removed the following:

For Peirce, progress in science depends on the observation of the right facts by minds armed with the appropriate ideas (Tursman, 1987). Obviously, the intuitive judgment made by an intellectual is different from that made by a high school student. Peirce cited several examples of remarkable correct guesses. All success is not simply luck. Instead, the opportunity was taken by the people who were prepared:

a). Bacon's guess that heat was a mode of motion;

b). Young's guess that the primary colors were violet, green and red;

c). Dalton's guess that there were chemical atoms before the invention of microscope (cited in Tursman, 1987).

By the same token, to continue our last example, the cosmological view that the atom is the fundamental element of the universe, introduced by ancient philosophers Leucippus and Democritus, revived by Epicurus, and confirmed by modern physicists, did not result from a lucky guess. Besides the atomist theory, there were numerous other cosmological views such as the Milesian school, which proposed that the basic elements were water, air, fire, earth, etc. Atomists were familiar with them and provided answers to existing questions based on the existing framework (Trundle, 1994).

This is only loosely related to abduction. Paolo Liberatore (Talk) 19:14, 30 September 2005 (UTC)

Removed parts

For the record: I just realized that the parts that have been removed by Sbarthelme and then and by me happen to be exactly those introduced by 128.107.253.41 (see diff). These paragraphs seem to come from another article [1]. Paolo Liberatore (Talk) 20:05, 30 September 2005 (UTC)

Explanatory conclusion or equivalent

This article should indicate how is named the conclusion of an abductive reasoning. I have seen the expression explanatory conclusion, but I am not an expert. I just would like to know how it is named and then I would suggest that we have a redirection from this name, whatever it is, to this article. Amrit 03:26, 10 December 2005 (UTC)

I read the article again, and maybe the name is simply the "explanation". Let me check if there is somehow a path from explanation to this article in wikipedia... Amrit 03:31, 10 December 2005 (UTC)

Nope, there is no link. So is the name of the conclusion the explanation? Should we add a link in the article Explanation? Amrit 03:33, 10 December 2005 (UTC)

Explanation is the correct term (I have also seen "solution" used sometimes). However, there is usually more than one explanation, so the "conclusion" of the abductive process is typically a set of explanations. About the link from Explanation: why not? Paolo Liberatore (Talk) 16:04, 10 December 2005 (UTC)

I added explanatory conclusion because I want to be able to point to this article with a sentence like "Your conclusion is more a XXX", where XXX is redirected to this article, and so XXX cannot be another wikipedia article. If you have another suggestion, I will be happy. If you think this extra sentence is destroying the main flow or anything like that, take it out, but then it will be less meaningful to cite this article in my context.

Adduction?

Forgive my ignorance, but isn't the proper term "adduction" or "adduce," spelled with a "d"? And not with a "b"?

  ad.duce \*-'d(y)u:s\ vt L adducere, lit., to lead to, fr. ad- + ducere to 
  lead - more at TOW : to offer as example, reason, or proof in discussion 
  or analysis SYN syn CITE, ADVANCE, ALLEGE: ADDUCE implies offering facts, 
  evidence, or instances as proof of or in support of something stated; CITE 
  implies an adducing of specific instances or authority; ADVANCE implies the 
  presenting not of facts but of a theory or claim or proposal for 
  consideration or acceptance; ALLEGE implies reciting facts intended to be 
  proved but may suggest that proof is not available or possible - ad.duc.er

In contrast:

  ab.duce \ab-'d(y)u:s\ vt [L abducere] : see ABDUCT
  ab.duct \ab-'d*kt\ \-'d*k-t*r\ vt [L abductus, pp. of abducere, lit., to 
  lead away, fr. ab- + (Xducere to lead - more at TOW 1: to carry off (a 
  person) by force 2: to draw away (as a limb) from a position near or 
  parallel to the median axis of the body; also : to move apart (similar 
  parts) - ab.duc.tor

�The preceding unsigned comment was added by 208.59.121.112 (talk • contribs) 17:11, 9 May 2006 (UTC)

JA: No, abduction, abductive inference, and abductive reasoning are the conventional terms in logic, being the Latin forms of Aristotle's α�€Î±Î³�‰Î³Î· (apagoge) for approximately the same thing. C.S. Peirce did on occasion use "adduction" for "induction", but that is rare. Jon Awbrey 17:36, 9 May 2006 (UTC)

JA: PS. The locus classicus is here: Inquiry#Abduction. Jon Awbrey 17:42, 9 May 2006 (UTC)

Examples

This article really needs examples. More people know deductive logic from the Socrates example than from any if a and if b... explanation. I will get around to adding some this weekend if no one else does. If you do thanks in advance. Quadzilla99 02:37, 18 August 2006 (UTC)

Definitely. This article needs at least two examples of abductive reasoning.

Abduction = retroduction ?

According to the link at Retroduction (http://www.cuyamaca.net/bruce.thompson/Fallacies/retroduction.asp) retroduction is (or at least has been used as) equivalent to Abductive_reasoning:

" Peirce himself originally referred to this type of reasoning as "hypothesis." He later coined the term "abduction," and used this term during the 1880s. By 1896 he had abandoned this term in favor of "retroduction," which he used for the remainder of his life. "

Should the entries to these terms be updated to indicate this equivalence?

Dinamisbo 09:09, 6 September 2006 (UTC)

JA: Not sure about the accuracy of that statement. Still, it's a first approximation truth that abduction, apagoge, hypothesis, retroduction, along with several others, are roughly equivalent for Peirce. The problem is not there, but with the fact that subsequent literatures in philosophy, psychology, and AI have piled their own accretions and hair-splittings on these terms. So, maybe some kind of note is proper, if it can be vetted against Peirce's own writings. Jon Awbrey 12:50, 6 September 2006 (UTC)

This the problems caused by Peirce’s habit at different stages of his life of assigning different neologisms to represent similar ideas. Abduction is no exception since it also went by the name of ‘retroduction’ and even ‘hypothesis’. I think the simple answer is all of these terms are subsumed under the term abduction. However, it is important to make clear that differently named terms in Peirce’s system are not necessarily conceptually synonymous, see for example the forceful argument of Deledalle (2000) makes regarding how Peirce’s thought must be interpreted in the context of the time he was writing because of the radical shifts in his own thinking that took place in his lifetime. The really daunting implication embedded in this is that one almost has to become a Pericean scholar in order to say anything about Peirce or his concepts . This is where I think the balance of reasonableness must swing towards accepting the pragmatic acceptance that anyone writing anything about Peirce is probably going to have to do some editorializing, because of the fragmentary nature of Peirce’s writings, and because he published no canonical exposition of his philosophical system in his lifetime. Rod Munday 13:20, 3 June 2009 (UTC)

Minor grammatical point about "In rare occasions"

The phrase "In rare occasions" seems awkward to me. (Speaking here of the beginning phrase in the next to last sentence of the article intro.) Suggest "On rare occasions" or "In rare instances" Any thoughts? I'm new here so I'll wait a few days for feedback before I touch anything. --Platonic Realm 17:11, 31 October 2006 (UTC)

Since no input has been given on this point, I will make a solo editing decision here. I will change "In rare occasions" to "On rare occasions." Please discuss if this is undesired. --Platonic Realm 15:55, 2 November 2006 (UTC)

Cleaned up some language

I cleaned up some of the grammar and noted that abduction as stated is formally equivalent to affirming the consequent. I'm new at this so hopefully I did it correctly. —The preceding unsigned comment was added by Killtacular (talk • contribs) 02:17, 4 February 2007 (UTC).

Heh

Fancy word for a "guess". Fatalis 13:09, 10 February 2007 (UTC)

Well

It is a fancy word for a live topic in philosophy. Killtacular 00:26, 24 February 2007 (UTC)

Proposal: Merge 'Abductive' validation into this page

The abductive validation article is brief, unreferenced, and contains information that should be on the abductive reasoning page anyway. Anarchia 00:56, 21 July 2007 (UTC)

Merge or Redirect, since the article is basically empty. ---- CharlesGillingham (talk) 10:09, 9 December 2007 (UTC)

It's already on the page, on section 6, for some reason. Exec. Tassadar (comments, contribs) 13:59, 13 April 2008 (UTC)

Evolution

"Rather, he [Peirce] pointed out that humans have an innate ability to infer correctly; possessing this ability is explained by the evolutionary advantage it gives."

Did Peirce actually use evolution in arguing for the validity of abduction, or is this a later addition by someone else? --76.205.215.91 17:45, 29 July 2007 (UTC)

Not directly, but he definitely read 'The Origin of the Species' and approved greatly of Darwin's scientific rigor and praised evolution in his writing. Here are three quotations that suggest an evolutionary approach to abduction:

Abduction is an instinct which relies on unconscious perception of connections between aspects of the world, or, to use another set of terms, subliminal communication of messages. It is also associated with, or rather produces, according to Peirce, a certain type of emotion, which sets it apart from either induction or deduction (in (Sebeok 1981).

Peirce maintained that the ability of a newly hatched chick to pick up food, "choosing as it picks, and picking what it aims to pick," while "not reasoning, because it is not done deliberately," is nevertheless "in every respect but that ... just like abductive inference," and be further traces the physical and social sciences back to the animal instincts for, respectively, getting food and reproduction (Peirce Ms. 692, quoted in Sebeok 1981).

in science... another sort of Darwinian evolution undoubtedly does take place. We are studying over phenomena of which we have been unable to acquire any satisfactory account. Various tentative explanations recur to our minds from time to time, and at each occurrence are modified by omission, insertion, or change in the point of view, in an almost fortuitous way. Finally, one of these takes such an aspect that we are led to dismiss it as impossible. Then, all the energy of thought which had previously gone to the consideration of that becomes distributed among the other explanations, until finally one of them becomes greatly strengthened in our minds. (Peirce, complete writings vols 1-6 1931-34, §1.107).--Rodmunday (talk) 16:25, 11 June 2009 (UTC)

Induction definition

I am not sure that the definition of induction given here is correct or helpful; I think that induction is the process of inferring the general rule from multiple instances - see the (linked) Logical_reasoning. The "it is snowing outside" example is misleading since it seems to suggest that the truth or otherwise of this statement is solely determined by the act of perception (which I guess it might be, but only to an extreme solipsist). --129.215.219.83 (talk) 11:00, 31 July 2008 (UTC)

The nature/definition of induction is contentious, actually. The characterization of induction as inference from particular premises to a general conclusion, however, is problematic. Note that it seems fairly uncontroversial that the following is an induction: all past fires have been hot, therefore all future fires will be hot. That's an inference from a general premise to a general conclusion. Also note that the particular-to-general characterization of induction is attractive in part b/c the general-to-particular characterization of deduction seems attractive (so some kinds of considerations of theoretical elegance seem to count for the PtG characterization of induction). But the GtP conception of deduction is clearly false--e.g. "p therefore p" is a valid deduction, as is "p and q therefore p". In neither case is either the premise or the conclusion general. --William Knorpp —Preceding unsigned comment added by 71.63.43.66 (talk) 14:27, 1 April 2009 (UTC) William Knorpp (talk) 14:43, 1 April 2009 (UTC)

What we mean by "general" will affect whether the following is particular to general, or particular to particular:

The sun rose yesterday, the sun rose today therefore the sun rises.

You could say the sun rises is general because it means the sun rises every day, or you could say it is particlaur because it relates to one particular object, i,e, the sun. The general to particalar characterisation of deduction is plainly false (no mattern how oft repeated). All As ar B All Bs are Cs ergo All As are Cs is a deduction if ever there was one, but the conclusion is as general as general can be.--Philogo (talk) 23:40, 1 April 2009 (UTC)

Abduction vs. Inference to the best explanation

Though this is somewhat contentious, it would probably be a good idea to note that abduction and inference to the best explanation (IBX) are not exactly the same thing. One way to think about it is: both are specific conceptions of the more vague and general idea hypothetical/explanatory inference.

IBX is typically conceived of as a fairly powerful type of inference--it's often characterized as somehow providing a foundation for induction (and sometimes even deduction).

'Abduction', however, is a term that began life with Peirce, and the term probably ought to be reserved for his conception of abduction-or, at least, it probably ought not to be conflated with IBX. So conceived, abduction is a very weak type of inference, not a very strong one. In a valid abduction, the conclusion follows only very weakly from the premises--valid abductions prove only that their conclusions are plausible (= worthy of testing via induction) (if their premises are true).

The big idea of IBX seems to be that we can, by employing such inferences, sort through hypotheses until we find the one most likely to be true. Such sorting is apparently conceived of as being fairly fine-grained. Abduction per se, however, only marks each inference "worthy of testing" or "not worthy of testing." That's on Peirce's conception, anyway. William Knorpp (talk) 14:42, 1 April 2009 (UTC)

Chomsky criticism

I've removed a section on criticism since it only includes a dubious quote from Chomsky. I'm gonna go back to the source, but it is not my understanding that it exactly represents Chomsky's beliefs on abductive reasoning. Feel free to add it back if you can cite me as incorrect.

Well, while I agree with you that Chomsky's criticism is not particularly meretricious, being more of an ad hominem swipe at Perice than a thoughtful critique, I think an argument can be made to include his criticism because it is important to show from historical point of view that the concept of abduction is not by any means an orthodox concept--in the sense of being part of the philosophical canon; on the same level as deduction and induction--but rather its very newness presumably made people like Chomsky feel uncomfortable. After all, guessing is offensive to an Enlightenment rationalist isn't it? And this is the real point of the Chomsky criticism, it's not its incisiveness but its very dismissiveness that is significant. I think the average person who is curious about abduction would be hard pressed to find any strong opposition to it. This is not because abduction is universally admired, but because most people are simply not aware of it, like much of Peirce's work in fact. Therefore, the problem with the absence of criticism in the article is that it implies that abduction is a universally accepted concept, which is very far from the truth. --Rodmunday (talk) 16:02, 11 June 2009 (UTC)

Well put, but I'm not sure a section on criticism would be the best way to do that. Let's simply make sure that we mention its unorthodoxy earlier in the text. I have heard Chomsky verbally agree with the validity of abduction but not necessarily Peirce's evolotionary explanation. I understand that that is original research and can't be used in the article, but my biases guide my editing and that was a red flag. Linguistixuck (talk) 23:32, 17 June 2009 (UTC)

The text:

Some people object to the tenuous nature of abduction, Noam Chomsky writes:

Peirce's ideas on abduction were rather vague, and his suggestion that biologically given structure plays a basic role in the selection of scientific hypotheses seems to have had very little influence. To my knowledge, almost no one has tried to develop these ideas further, although similar notions have been developed independently on various occasions"

—Preceding unsigned comment added by Linguistixuck (talk • contribs) 02:35, 9 June 2009 (UTC)

$\scriptstyle E\cup T$ or $\scriptstyle E\cap T$?

It is a bit surprising that in the section on Logic-based abduction the phrase E and T is symbolized according to $\scriptstyle E\cup T$ rather than $\scriptstyle E\cap T$. As far as my experience with logic goes I would expect the latter expression. Can someone explain? Or should it be corrected?WMdeMuynck (talk) 13:55, 23 February 2010 (UTC)

I'm no expert but you seem correct. The Tetrast (talk) 02:29, 26 February 2010 (UTC)

Pmurray bigpond.com 03:43, 20 Apr 2005 (UTC)

the html cup does not render on my machine, so I replaced it with math markup ... but the actual formula looks very wrong. —Preceding unsigned comment added by Pmurray bigpond.com (talk • contribs) 01:38, 20 Apr 2005 (UTC)

Fugitive quote

I'm putting this text that I've deleted from the section "History of the concept" because it no longer makes sense where it was, but maybe could be returned elsewhere in the section later.

'The processes by which we form hunches about the world are, in Peirce's conception, dependent on perceptual judgments, which contain general elements such that universal propositions may be deduced from them.' ref Sebeok, T. (1981) "You Know My Method." In Sebeok, T. "The Play of Musement." Bloomington, IA: Indiana. p 26 /ref
The Tetrast (talk) 18:10, 30 July 2010 (UTC)

Definition of abduction

I see the definition of abduction introduced here as (under scrutiny) logically equivalent to but less clear than its predecessor, though I understand how that might not be immediately obvious. Can other editors look the two versions over and agree with me before I boldly revert? or can someone explain the contrary view to me?--Heyitspeter (talk) 09:52, 27 July 2010 (UTC)

(Current first sentence) Abduction is a kind of logical inference described by Charles Sanders Peirce as the process of arriving at an explanatory hypothesis, such that to abduce a from a curious circumstance b is to determine that a may be true because then b would be a matter of course.[1] (Predecessor first two sentences) Abduction is a method of logical inference described by Charles Sanders Peirce as the process of making an hypothesis. To abduce a from b is to determine that a is sufficient but not necessary for b. Table inserted by The Tetrast (talk) 16:42, 27 July 2010 (UTC).

Please do not "boldly revert." That would be overly bold since you have provided no basis for it - no references and no argument.
The current definition is much clearer than its predecessor, especially to the general reader, who is our audience rather than a professor looking to see whether we seem to know the material, and the current definition is much more in accord with the definitions which Peirce provided, for which I have provided references and links and can provide many more. Indeed, see Peirce's definitions of retroduction, presumption, abduction, and hypothesis (Peirce's four names for this mode of inference) at the Commens Dictionary of Peirce's Terms (which dictionary consists of Peirce's own definitions). I mean actually go read them. The definitions are on average one- or two-short-paragraph quotes, often many a quote per term across the decades. It's extremely convenient and it's not like one has to read a whole essay. I've no reason to think that you in particular won't go read them, but I've learned from general experience that I need to make a point of it. Inserted note: pay special attention to the later definitions (e.g. under Retroduction), when Peirce (starting around 1900) distinguished abduction from the induction of characteristics. End of note.
Saying, as in the wiki's (currently replaced) predecessor definition, that to abduce A from B is to determine that A is sufficient but unnecessary for B, is not equivalent to the current definition, which states that to abduce is to determine, i.e., to infer to the conclusion, that A may be true, upon premisses that say or imply that then the curious circumstance B would instead be a matter of course. The predecessor definition blurs the focus on abduction's aim (to reach an explanatory hypothesis) and makes it sound as if the abduction concludes in a meta or 2nd-order statement about the logical relationships among its premisses, and as if the abducer's aim is to test for those logical relationships in a context of mathematical logic in order to say whether the inference is abductive, inductive, or deductive, rather than to simplify a complication or to make a guess worth trying out. I.e., it confuses the abductive process with a logician's concluding what is the mode of the given inference on the basis of differences between the respective implicational structures of abduction, induction, and deduction. The abducer in a given state of information does not see a necessity of A for B (so that there seems risk and opportunity) and does see that A would suffice for B in the sense of making B a matter of course - that "course" need not even consist in a strict deductive necessity; instead it could be some norm or regularity about which the abducer has little actual doubt. (If the abducer does actually doubt it yet still employs it, then we're describing a more complicated inference, perhaps a complexus of abductions in progress.) Then the abducer concludes not in an acknowledgement that A is sufficient but unnecessary for B, but instead in the hypothesis that A is true. The Tetrast (talk) 15:51, 27 July 2010 (UTC). Inserted a note. The Tetrast (talk) 16:09, 27 July 2010 (UTC).

Okay, how's this for a compromise?:
Abduction is a kind of logical inference described by Charles Sanders Peirce as the process of arriving at an explanatory hypothesis, such that to abduce the explanatory a from an observed curious circumstance b is to determine that a may be true because, though b does not imply a, still a at least strongly tends to imply b.^[1]
The Tetrast (talk) 18:14, 27 July 2010 (UTC).

Thank you for laying this out so clearly. Note that I have provided an argument, viz.: that the present version is "(under scrutiny) logically equivalent to but less clear than its predecessor." That argument stands.

Does abduction only concern events in the world? Does Peirce allow that one might abduce a statement a from, for example, "All bachelors are unmarried males"? I imagine that he does but I'm not sure.--Heyitspeter (talk) 20:26, 27 July 2010 (UTC)

Nvm Peirce answered my question (in any case I doubt he would distinguish between empirical and analytic truths). "Abduction consists in studying facts and devising a theory to explain them" (Harvard Lectures on Pragmatism, CP 5.144-145, 1903).--Heyitspeter (talk) 20:32, 27 July 2010 (UTC)

How about this for 'compromise'?

Abduction is a kind of logical inference described by Charles Sanders Peirce as the process of arriving at an explanatory hypothesis, such that to abduce a from a curious circumstance b is to determine that a may be true because then b would be a matter of course.^[1] To abduce a from a state of affairs b is to determine that a is sufficient but not necessary for b.

I'm not too worried about this. But as a random passersby, the second sentence clarifies abduction for me better than the first. No comment as to whether that would be true of most people.--Heyitspeter (talk) 20:38, 27 July 2010 (UTC)--Heyitspeter (talk) 20:38, 27 July 2010 (UTC)

You're not a random passerby or more specifically a representative specimen of the general reader. Judging by your talk page, you take some interest in participating in articles on logic. Your wording "sufficient but not necessary" in your version of the opening is (1) philosophers' and logicians' lingo - brief, to the point, and much less reliably clear and unambiguous to the general reader (who might think that "not necessary" means that there are plausible alternate explanations for b, when instead that question is unaddressed) and (2) also really not quite according to Peirce's definitions ("a matter of course" is not necessarily as strong as a matter of a deductive implication relation). Also, to abduce a is not the same as, but instead involves, determining that a is unnecessary but (more or less) sufficient for b. You say that your argument stands as to the equivalence of the two openings, but you never made an argument about that at all; go back and look; so such argument does not stand; instead you made a claim, and I made an argument refuting your claim; your claim depends on the false idea that to say or imply something (the sufficiency but unnecessity of a for b) through some premisses is equivalent to drawing a conclusion (abducing a); and to spell it out further, the sufficiency-but-unnecessity of a for b does not compel one to conclude to the hypothesis a; and one does not in fact make or select every hypothesis that one possibly could. My argument stands untouched and unaddressed. There's enough technical stuff in the article already. Its intro, at least, should be rendered clear, if possible without making it so that the reader would be better off going straight to another wiki for clarification. Still, I think that we can find wording that deals with all these issues in a reasonable way and gets our respective desired formulations in.
As to whether Peirce thought that abduction was only about the world of facts, and what did Peirce mean by "facts," Peirce held that all inquiry begins with surprising observations in the realm or realms of ideas, brute facts, and/or norms and laws - see Wikisource:A Neglected Argument for the Reality of God (1908) where he outlines his view of inquiry and scientific method. Yet, he often left mathematical reasoning to mathematics, which he defined as drawing necessary (deductive) conclusions about hypothetical objects and which he said needs no help from (philosophical) logic, which for him is the locus of the study of abduction. However in "The Logic of Drawing History from Ancient Documents" (written 1901, Essential Peirce 2, 75-114) he discusses, as a mathematical abduction, Aristotle's instance of apagôgê, sometimes translated as "abduction," which Peirce used as the name for hypothetical inference (Peirce's interpretation of Aristotle's apagôgê was unconventional).
Another try:
Abduction is a kind of logical inference described by Charles Sanders Peirce as the process of arriving at an explanatory hypothesis, such that to abduce the explanatory a from the observed curious circumstance b is to determine that a may be true because, though b does not imply a, still a would make b a matter of course. That is, to abduce a involves determining that a is not necessary, but still sufficient, as a condition for b.
(Actually, it'd be better to use em tags around the letters for automated screen readers so that the letters a and b don't get aurally lost in the sentence which is mostly words). The Tetrast (talk) 23:23, 27 July 2010 (UTC).

My relationship with logic is a lot like my relationship with sudoku. I like it, I'm good at it, but I don't take it very seriously.

I think you underestimate how familiar I am with Peirce. I've read a lot of his work and I've taken courses that rely heavily on his semiotical terminology. I've read enough of him to know that he doesn't like or perhaps isn't very good at giving clear and concise definitions of his terms, and that in those rare cases where he does give single-sentence definitions of a term he often defines that term using other terms for which he has idiosyncratic definitions. Therefore, when explaining a Peircean term I think it's fair to paraphrase his definition using more common phraseology. I think that for many people, the phrasing utilized here will help. With the disambiguation of "necessary and sufficient" it probably won't do much to confuse the rest. I think you do know more about Peirce's conception of abduction than me, though. Would you mind explaining further how "if a is true then b is a matter of course" might differ from "a is sufficient but not necessary for b"?--Heyitspeter (talk) 23:44, 27 July 2010 (UTC)

By that link to where you had written "In other words, to abduce a from b is to determine that a is sufficient but not necessary for b," you reassert your claim that it's the same thing to say or imply something (the sufficiency but unnecessity of a for b) through some premisses, and to draw a conclusion (abducing a). That claim is mistaken on Peirce's or anybody else's definition of abduction. I've offered some very clear arguments against it. Why do you repeat your claim without ever offering an argument? This is, after all, a question about inference, in an article on inference and reasoning. So I replace "is" with "involves." Meanwhile, I reword to "not necessary but still sufficient" in order for parallelism with the sentence that is currently included before your sentence. That's in order to make it easier for the general reader - the same ideas in the same order instead of reverse order.
I think that your ideas of common phraseology are those of common phraseology in logic and philosophy classrooms, books, etc. There is no reason to confine the intro to academic connect-the-dots lingo when that confinement amounts to stinginess toward the general reader. We can spell things out a little for the general reader, at least in the intro. Logical senses of "not necessary" and "sufficient" are unusual senses in everyday English and it takes practice to be at ease with a sentence compounding them like "a is sufficient but not necessary for b." So I add "as a condition" into it. "Implies" is more common in roughly its logical senses in everyday English. So there's a sentence using "implies" to talk about these things first. So, in sum, say it in a less technical way, then restate it in a more technical way. And that's what we're doing. Wikipedia is supposed to be addressed, when possible, to the general reader, though it often fails to take the opportunity. I remember once a top Peirce scholar told me in a hilarious, yet scathing way, that I had made a Wikipedia Peirce passage so technical that only an expert would understand it and the expert would agree with it but wouldn't care, and that at least it could do no harm since nobody else would understand it or be reading it. That brought me back to my usual senses.
The difference between "matter of course" and a matter of deductive implication seems to be when one believes that, given a, b would be a matter of course but one can't frame it in a convincingly deductive way. I think that, basically, Peirce wanted to play down the rigid forms when it comes to abduction. Excessive attention to them had, he felt, slowed his understanding of abduction and gotten it stuck in a confusion with induction of characteristics, and I guess that he decided that the rigid forms didn't help him in actually using abduction (he had some experience with using it in science). The Tetrast (talk) 01:30, 28 July 2010 (UTC).

I like the direction of your edits of the wiki today, they're helpful to the general reader. But I must insist on not flatly equating the formation or selection of A as a hypothesis, with determining A's implication relations with a premiss, since in fact one rejects many a hypothesis that one determines technically to have just such implication relations of sufficiency and non-necessity. The Tetrast (talk) 04:21, 28 July 2010 (UTC).

Could one say that abduction is relying on circumstantial evidence? If so this could make the discussion less technical.WMdeMuynck (talk) 06:28, 28 July 2010 (UTC)

@Tetrast (not to discount WMdeMuynck's remark, but only because that's where my current train of thought is stationed). I see what you mean now, that one can abduce a from c, and decide against abducing b from c, though both a and b are sufficient and not necessary for c. That ruins most of what I've said and I like it. We need a new definition of abduction.

I wonder, though, how either a and b can be favored in any act of abduction. Is it pure whimsy? I'm trying to figure how to define abduction given this remark.--Heyitspeter (talk) 09:50, 28 July 2010 (UTC)

WMdeMuynck, that's a thought, for my part I'll have to think about it, but the thing is, if we decide that abduction depends in some essential way on circumstantial evidence, then that's our "original research" - we can't just put it into the wiki.
Heyitspeter, the situation isn't as bad as you think. It's the same in deduction. We can note that B implies C without proceeding to deduce C from B. We don't deduce everything that we see that we could deduce, and this is clear when it matters what we deduce, for example in deducing predictions from a hypothesis. Many deducible propositions would fail to place the premisses in an aspect either new or nontrivial - but usually we won't define deduction by novelty or nontriviality - those characteristics instead contribute to making a deduction not valid or sound, but valuable (in usual situations, not logical-axiom selection situations - "A is A" is a truism till somebody might deny it, then it is a capital-T Truth; well, objective truth properties don't behave like that, but you know what I mean). At this point, I rambled on and it becomes inappropriate for this talk page. So I'm copying the above and moving the rest to User talk:The Tetrast#Definition_of_abduction_(cont'd) (edited The Tetrast (talk) 17:39, 28 July 2010 (UTC)), if anybody is interested. (If we get back to stuff that'll affect how the wiki is edited, that should, I think, still be on the Abductive inference talk page.) The Tetrast (talk) 16:53, 28 July 2010 (UTC).

Okay, but deductions that you don't personally carry out are still deductions. Similarly, abductions that you don't personally carry out (e.g., b from c) are still abductions. This makes me think that abduction doesn't "involve determining" but rather "is to determine."--Heyitspeter (talk) 17:02, 28 July 2010 (UTC)

They may still be deductions and abductions in an ideal realm, but you didn't perform them. That they have certain implication relations also doesn't mean that you determined that they have those implication relations. To top it off, implication is not inference, and determining an implication "A implies B" is not making an inference "A, ergo B". I go into further differences between implication and inference on my talk page. The Tetrast (talk) 17:34, 28 July 2010 (UTC).

Here's something more. A: "Every day this week is sunny." B: "Today is sunny." You determine that A is sufficient but unnecessary for B. Have you abduced A from B? Perhaps you might abduce A from B if A is not already a premiss. But it doesn't seem like abduction, and furthermore whether B is a premiss is unaddressed by the implication relations. Also you could deduce B from A - but only if A is the premiss. Here's another. C: "The last six days have been sunny." D: "Tomorrow will mark a solid week of sunny days." You determine that D is sufficient but unnecessary for C. Have you abduced D from C? Only if D C is a premiss. But the implication relations don't address that. Moreover "The last six days have been sunny, ergo tomorrow will mark a solid week of sunny days" looks like an induction. The Tetrast (talk) 17:50, 28 July 2010 (UTC).

More. If we ignore the question of deciding which proposition is the premiss, then, by your reasoning, to determine that A is sufficient but unnecessary for B is simultaneously to abduce A from B and to deduce B from A. So you define abduction in such a way that you cannot distinguish it from deduction. The Tetrast (talk) 17:56, 28 July 2010 (UTC). Corrected. The Tetrast (talk) 18:00, 28 July 2010 (UTC)

That's not true. To deduce A from B is to determine that B implies A. To abduce A from B is to determine that A implies B. I'm going to add back the original text: "to abduce a from b is to determine that a is sufficient but not necessary for b." Think about what it says carefully. It fully respects your distinction between inferring and implying.--Heyitspeter (talk) 17:29, 31 July 2010 (UTC)

"pq is sufficient but unnecessary for p" and "p is insufficient but necessary for pq" are equivalent and mean the same thing. But "pq, ergo p" and "p, ergo pq" are not equivalent and do not mean the same thing. The Tetrast (talk) 18:18, 28 July 2010 (UTC) Correction further above (using del and ins tags). The Tetrast (talk) 19:02, 28 July 2010 (UTC)

They're equivalent to someone that hasn't read Necessary_and_sufficient_conditions or who isn't thinking about what he or she is saying very carefully. If p is sufficient but not necessary for q, then p implies q but q does not imply p. If p is insufficient but necessary for q, then p does not imply q but q does imply p.--Heyitspeter (talk) 17:36, 31 July 2010 (UTC)

But that's not what I said. Go back and read carefully. Here, I'll arrange it to facilitate visual comparison:
"pq is sufficent but unnecessary for p"
      is equivalent to
"p is necessary but insufficient for pq"
Got it?
Actually, if both statements are formally true, then they're already formally equivalent just for that reason, but the point is not just that they're both formally true (schematically valid) but that they're saying the same specific thing.
As to your remarks in your comment begiinning "That's not true," your problem is that a statement such as "A implies B" says nothing about whether A, B are: premisses—or conclusions—or premiss, conclusion—or conclusion, premiss.
Now, for convenience, I'll use the phrase "strictly deduce" in an old-fashioned sense of "to deduce to a conclusion necessary but insufficient for the premiss(es)", and "strictly implies" in the parallel sense of "is sufficient but unnecessary for".
  If to abduce A from B is to determine that A strictly implies B, then to abduce B from A is to determine that B strictly implies A.
  And if to strictly deduce B from A is to determine that A strictly implies B, then to strictly deduce A from B is to determine that B strictly implies A.
  (And if to deduce B from A is to determine that A implies B, then to deduce A from B is to determine that B implies A.)
But given all that, then:
  to determine that A strictly implies B is both to strictly deduce B from A and to abduce A from B;
  and to determine that B strictly implies A is both to strictly deduce A from B and to abduce B from A.
So your reduction of inference to sheer implication relations fails, because sheer implication relations, among propositions qua propositions, don't include info on premiss/conclusion status. Instead you have to introduce the inference relation of premiss and conclusion. So maybe you could say that to determine that premiss A implies conclusion B is to deduce B from A, and so on; but most people will prefer to say that deduction is the inference of a implied conclusion from a premiss, rather than the determination that a conclusion is implied by its premiss, as if to infer were to anatomize an inference that has already been performed. At that point it just seems a pointlessly roundabout, even temporally circular, phrasing that makes no practical difference. Moreover you still have the problem of distinguishing abduction from induction, because induction too can involve inferring A from B where A is unnecessary but sufficient for B. The Tetrast (talk) 04:52, 1 August 2010 (UTC). Edited The Tetrast (talk) 05:12, 1 August 2010 (UTC). Edited The Tetrast (talk) 05:15, 1 August 2010 (UTC). Corrected and I'm trying to call it a night. The Tetrast (talk) 05:26, 1 August 2010 (UTC).

Neither statement is formally true, if by formally true you mean tautologous. They're completely different statements, and they're completely not true by logic alone. I'm sorry if I'm being curt, and I do believe that truth is a kind of vocabulary, but I think we're both trying to use the same vocabulary and I'm going to make the change now.--Heyitspeter (talk) 07:35, 2 August 2010 (UTC)

The two statements are both true, formally or not, and are formally equivalent. I would expect an editor here to know that much about implication relations in elementary propositional logic. pq implies, but is not implied by, p. And that's just to say that p is implied by, but does not imply, pq.
Do you really not know that if (and only if) A is sufficient for B, then B is necessary for A? And that if (and only if) A is unnecessary for B, then B is insufficient for A? Ergo, if (and only if) A is sufficient but unnecessary for B, then B is necessary but insufficient for A. QED.
You have failed to respond to the rest of the argument; and you have introduced your own mistaken original theory of reduction of inference to implication relations among propositions, and you have applied your theory to Peirce's definition and provided no reference to show that Peirce regarded your kind of reformulation as a statement of his definition. It can be shown that he did regard abduction as involving a premiss set which does not imply, but is implied by, the conclusion; but you will not find him saying that abduction flatly is a relation between any propositions A and B such that A is implied by, but does not imply, B; and Peirce's definition involves the explanandum's being a some "very curious circumstance"; in the later years he incorporates that idea of surprise into the abductive form itself. That aspect of surprise fails to appear in the implication relations which you specify, so your paraphrase of Peirce's definition is false already right there. You omit reference to that aspect without defending the omission because you're stuck on your idea of reducing inference to implication relations among propositions, and you don't want to admit that your idea is not just obvious, which a defense would require you to admit. Your theory also leaves you unable to clearly distinguish abduction from induction, since both can involve a conclusion which implies, but is not implied by, the premisses. I myself would prefer to be able to define all the basic modes in terms of premisses, conclusions, and their implication relations (e.g., without reference to a curious or surprising observation in a premiss), but that's my POV or OR and I don't incorporate it into the wiki itself. You want to define them in terms of simply the implication relations, not even along with the premiss/conclusion statuses, and you do insist on incorporating your POV or OR into the wiki. Since you admit to finding Peirce "unclear" and admit to not taking logic "seriously", why are you so insistent in your edits and so unresponsive in your arguments? And, no, I won't let your new edit stand. Please prove your point and quote your sources here first. The Tetrast (talk) 14:08, 2 August 2010 (UTC). Edited The Tetrast (talk) 14:14, 2 August 2010 (UTC). Edited The Tetrast (talk) 14:17, 2 August 2010 (UTC). typo The Tetrast (talk) 14:29, 2 August 2010 (UTC) Edited The Tetrast (talk) 14:49, 2 August 2010 (UTC). Typo. The Tetrast (talk) 16:07, 2 August 2010 (UTC). Edited The Tetrast (talk) 16:22, 2 August 2010 (UTC).

You are simply wrong (I didn't comment on the entirety of your post earlier because it wasn't especially relevant to the discussion). You clearly aren't familiar with formal logic and its terminology. There's not much more I can say than that. I suggest browsing through some of the pages on wikipedia's logic project and rereading my comments here with a more open mind. Just as I admitted to having less familiarity with Peirce's work than you and have sat back and watched you add valuable information to those sections of the article, I'd like for you to have the humility to allow that you're less familiar with logic than another editor and allow that editor to edit those sections of the article without edit warring. (e.g., [2] [3] [4])--Heyitspeter (talk) 00:25, 6 August 2010 (UTC)

You have made no arguments, only assertions. You have not responded with arguments versus my arguments either. You say that I said some irrelevant things but you don't attempt to argue or explain their irrelevance. It's apparent that you see no real difference between implication and inference. You state that "pq is sufficient but unnecessary for p" is "completely different" (your words) from "p is necessary but insufficient for pq" and you think that I'll somehow realize it if I look at some logic wikis, saving you the trouble of articulating a difference that isn't there. No, I don't think that they're first-order tautologies, but they are about valid schemata such as "if pq, then p" and "p if pq" and about consistent but invalid schemata such as "if p then pq" and "pq if p". Moreover you have been unwilling to recognize that Peirce did not define abductive inference entirely in terms of implication relations - you desire instead to pursue your pet theory of definition of inference modes by implication relations among propositions (or statements or, Quine's final favorite, sentences, but anyway whatever reassuringly contemporary terminology you like). Why is thaat irrelevant? Peirce also didn't define abductive inference entirely in terms of implication relations between premiss set and conclusion set - why is that irrelevant? - but as far as I can tell you do not recognize the ideas of premiss and conclusion as relevant to any definition of a mode of inference, leading you to be unable to distinguish abduction from deduction, a problem which you flatly don't recognize or address - why is it irrelevant? - and maybe you rebel against the use of phrase "strict implication" in the old-fashioned sense (adapted from set theory's ideas of "strict subset" and "strict superset", before the days of relevance logic) in which I stipulated that I was using it. But who knows? You never get down to brass tacks, but only make assertions. You haven't noticed that a determination of the (more-or-less) sufficiency despite unnecessity of some A for some C is a premiss in Peirce's 1903 definition of abductive inference, and not his whole 1903 definition of abductive inference. Why is it irrelevant? By the way, Peirce was quite clear; the hypothetical explanation does not need (even in combination with some already-granted rule) to be deductively sufficient to account the surprising observation. Why is it irrelevant? I'm sorry that these criticisms don't seem to you to be made using contemporary terminology (where did I get that word "unnecessity"? - I simply formed it for convenience), but I must take your silence on pretty much all those issues as signs not of some superior knowledge of yours but rather of your grasping few if any of the ideas. You think that they're mostly wrong or irrelevant, though you can't explain or argue as to why. You also can't distinguish abduction from all induction, with your emphasis on nothing but implication relations among propositions, which seems the only thing relevant to you. As for edit-warring, you're the one who proceeded to edit without resolving things here first. And as for appreciation of each other's better editing, you talk as though I hadn't said nice stuff about your making the definitions of the various inference modes more accessible via examples for the general reader. The Tetrast (talk) 03:48, 6 August 2010 (UTC). Edited The Tetrast (talk) 04:03, 6 August 2010 (UTC)

I am losing the thread of the argument. Are you still in disagreement about the first two sentences? I edited the introduction by replacing "determine" by "surmise" which seems to capture the spirit of "abduction" better. "sufficient but not necessary" seems too formal in this context. Tkuvho (talk) 07:50, 6 August 2010 (UTC)

I can understand how anybody would lose the thread of this argument. It's about one sentence.
Heyitspeter wants to say: "To abduce a from b is to determine that a is sufficient but not necessary for b".
I say keep it at: "To abduce a from b involves determining that a is sufficient but not necessary for b".
- Implication is not inference. To determine an implication relation is not to draw an inference marked by that implication relation.
- If to determine that a is sufficient but not necessary for b were to abduce a from b, then it would also be to deduce b from a (in the sense of 'forward-only' deduction). It could also be to induce a from b. For example, by noting that pq is sufficient but unnecessary for p, we would be both abducing pq from p and deducing p from pq (and also inducing pq from p). So such a definition simply degenerates into glop. Likewise if we note that p is necessary but insufficient for pq - same result, since it says the same thing as "pq is sufficient but unnecessary for p".
- One needs to consider implication relations between premiss set b and conclusion set a, and not merely implication relations between sets b and a of propositions. But even if one does take premiss/conclusion relations into account, then abductive inference resists being defined as an inference in which the premiss set is necessary but insufficient for the conclusion set. Peirce defined abductive inference as involving something more or less like sufficiency, despite unnecessity, of the hypothetical explanation for the surprising/curious observation. But the sufficiency didn't need to be strong, deductive, etc. - he said that the explanation could suffice to make the surprising phenomenon seem merely likely, not fully necessary. It just gets rid of the surprisingness, or most of it. In the 1903 form, the determination of that more-or-less sufficiency is one of the premisses ("But if A were true, C would be a matter of course") and is not the whole inference:
The surprising fact, C, is observed;
  But if A were true, C would be a matter of course,
  Hence, there is reason to suspect that A is true
as Heyitspeter knows, since he has read the "History" section of the wiki. And to top it off, Peirce's idea of abduction always involved the idea of a "very curious circumstance" or "surprising fact" or the like in a premiss. That aspect of surprise can't be reduced to sheer implication relations, whether between propositions per se or between premisses and conclusions, in the abductive forms (or in any of the inference forms). If it can, somebody please show me how.
I keep going into all these details in the belief that argumentation makes a difference, but the entirety of his response has seemed poor in specifics and full of talk about who knows logic, my not sounding like textbooks in classes that he's taken, my saying things that are wrong or irrelevant (which he mostly avoids specifying, and never argues or explains), his being "good at" logic, his not taking logic "very seriously," his being a "random passerby" (rather than somebody interested in participating in logic wikis, as evidenced by his talk page) etc. - an odd combination of CYA and arguing from his own authority. The Tetrast (talk) 14:54, 6 August 2010 (UTC).

Is the current version of the introduction acceptable to everybody? Tkuvho (talk) 20:50, 7 August 2010 (UTC)

It seems okay to me, except that the section on probabilistic abduction is unclear to me, so it's not clear to me whether it involves a weakening of a requirement of deducibility of explanandum from the explanation. (Peirce in 1903 didn't strictly require such deducibility and said that the explanation needs to make it so that "the phenomenon, under that assumption, would not be surprising, but quite likely, or even would be a necessary result"). I once made my way successfully through a problem about test reliability, false positives, etc., but the "Probabilistic abduction" section in this wiki doesn't say what the explanandum is and what the abduced hypothesis is (at least not clearly), and I'm not accustomed enough to the notation to figure out what the longer formulas are saying. So it's not clear to me what's abductive about it, though the section starts off by calling probabilistic abduction a form of abductive validation. Also the section discusses the use of Bayes rule - is probabilistic abduction then a Bayesian kind of inference? Well, insofar as I don't understand the section, I don't have a specific objection to the introduction's reference to it. And I do like the indication that the sufficiency doesn't need to be strict and deductive. The Tetrast (talk) 22:11, 7 August 2010 (UTC). Edited The Tetrast (talk) 22:22, 7 August 2010 (UTC).

I can't say I have studied the probability section any more closely than you have. I added the parenthetical remark only as a way of illustrating the adverb "typically". If there is a better example, then replace it by all means. Can you think of quick example from Peirce? Obviously the parenthetical remark should not be long. If there is a convincing concrete example that one can quote from Peirce that's longer than a parenthetical remark, one could add a subsection to that effect. Tkuvho (talk) 07:01, 8 August 2010 (UTC)

Actually, perhaps the "rain" example from the "history of the concept" section would do. Tkuvho (talk) 18:18, 8 August 2010 (UTC)

I didn't see your last comment before I edited. In editing, I figured, play it safe, keep it simple. The rain example might be good, though. The Tetrast (talk) 19:48, 8 August 2010 (UTC).

I've added the rain example. Thank you! I think it works like a charm. The Tetrast (talk) 20:14, 8 August 2010 (UTC).

The current version of the sentence is not acceptable to me. I want the article to include a definition of abduction, not a vague outline of what it sometimes involves. It seems to me that (save for probabilistic abduction, grace à Tkuvho),

(1) to abduce a from b is to determine that a is sufficient but not necessary for b.

If we are to account for Tkuvho's considerations we may say, as per the current version of the intro, that

(2) to abduce a from b is to determine that a is sufficent (or nearly sufficient) but not necessary for b.

I like (2) a lot. In none of The Tetrast's several lengthy essays have I heard a counterexample, or even a quote to the contrary from Peirce, and so I'd like to see (2) included.

I would also like to reiterate that this article is not about Peirce except insofar as he coined the word 'abduction'. Peirce did not coin per impossibile the concept associated with that word. (Putting this in your terms, The Tetrast, this article is not about the representamen [specifically the rhematic symbol] 'abduction', it's about its interpretant.) So, for example, just because Peirce states that abduction is accompanied by surprise does not mean that abduction is accompanied by surprise and we should not state as much in the article without the qualification that "Peirce wrote [etc.]" (If you respond please keep it on point. Length and scope are not virtues at best they're foreboding.)--Heyitspeter (talk) 11:24, 9 August 2010 (UTC)

— Everything that I've said has been "on point," and I've been carefully responding to your claims, and have ended up repeating myself in the process, since you simply don't engage, rather you ignore. Since you don't provide either arguments or source quotes, you end up being much briefer than I am, while my arguments become all the longer as I try to make answers to your possible arguments or ideas. Then you sit back behind the opacity of your underlying views and venture an occasional pot shot at my good-faith efforts. It's a lousy division of labor but it's the one that you're making.
— You want "counterexamples" from Peirce when in fact he talks about premisses and conclusions when it comes to inference, and many of the quotes from him now in the footnotes and in the "History of the concept" section are good examples; he's talking about curious circumstances, surprising observations (premisses) and conclusions drawn from them. All his examples of abductive forms are in premiss-conclusion format.
— It's up to you to find a quote from him, or from anybody else, that reduces abduction or any mode of inference to implication/entailment relations among propositions or statements per se. You think it doesn't matter whether they are premisses or conclusions, and that's just wrong.
In fact his 1903 definition of abduction is counterexample to your definition, for there he includes some determination of implication relations as a premiss in the abduction itself - it's there in the definition as linked in the footnote "Peirce, C. S. (1903), Harvard lectures on pragmatism, Collected Papers v. 5, paragraphs 188–189.Peirce, C. S. (1903), Harvard lectures on pragmatism, Collected Papers v. 5, paragraphs 188–189" and as quoted in the "History of the concept" section.
The surprising fact, C, is observed;
  But if A were true, C would be a matter of course,
  Hence, there is reason to suspect that A is true.
Ergo, the implication relations can hardly be the inference itself; some of them are an explicit premiss within it (and he often states that an abductive conclusion is not necessitated by its premisses). Moreover in the definition he includes things, such as the idea of the surprising, which your definition omits. So there's your counterexample.
— Moreover your definition doesn't distinguish abduction from deduction or induction. If to abduce A from B is, as you say, to determine that A is sufficient but not necessary for B, then it's also to deduce B from A and even to induce A from B. That kind of nonsense is "unacceptable" (to borrow your word from somewhere) in the wiki.
— You seem to take your own first thought as presumptively true and stick to it by tenaciously ignoring counterarguments and source quotes. Now that you're finding that Peirce doesn't support you, you want to tamp the Peirce down instead of "paraphrasing" him where you find him "confusing." But you can't have your cake and eat it too. Either you're paraphrasing Peirce and drawing an implication from his idea of abduction, or your doing so with somebody else's idea of abduction. Whose? Yours? What support do you have for your definition of abduction? Sources and quotes, please.
That you "like" a version "a lot" is not an argument for using it. As I've pointed out repeatedly, if to abduce A from B is simply to determine that A is sufficient but not necessary for B, then to abduce A from B is also to deduce B from A and could also be to induce A from B. Adding "(or nearly sufficient)" in that case compounds the original confusion, turning a good point into further murk. It is ironic that you consider such a definition less "vague" than also specifying the premiss/conclusion relations of A and B independently of their implication or entailment relations - an issue which you tenaciously ignore because of your exclusive focus on implication/entailment relations; you seem to want the difference between implication and inference to be trivial, merely formal, perhaps because of the focus of much modern formal deductive logic on implication relations between statements, terms, etc., as being "where the action is." However, the location of such action has nothing to do with whether inference is in fact reducible to implication relations. Your definition degenerates into glop and leaves you unable to distinguish any of the modes of inference, and is, to borrow your word, "unacceptable." You may also not "like" the broader practical context - really, the broader methodological context, as I now have edited it to say, but that context is real and helps the general reader to understand what this stuff is all about; and AI researchers are interested not just in individual abductions but in strategies. More in the next section. The Tetrast (talk) 17:07, 9 August 2010 (UTC). Edited. The Tetrast (talk) 17:15, 9 August 2010 (UTC). Edited. The Tetrast (talk) 17:18, 9 August 2010 (UTC). Much edited The Tetrast (talk).