Ben, list,
No problem with the delay in response, Ben, except to say that there is a way in which I've moved on to other vectorial considerations since my last message. I'll leave those to another post and just respond to a few of your several interesting points and intriguing analyses here below. Meanwhile, thank you for reminding me that even such 'games' as we've been playing with "All men are mortal" may "help develop the ability to deal with Peirce's categories in terms of the permutations to which they certainly seem to lead." It's likely that this will eventually happen--which your last phrase seems to suggest. Still, it would be nice to see it happen sooner than later. . .
Now, on to the "All men are mortal" permutations game. You wrote (and, btw, you're the only philosopher I know who could coin a phrase like "less Procrustean-beddishly"):
[BU] "I'd have thought that the retroductive-syllogistic version of the man-mortal-Socrates syllogism would, less Procrustean-beddishly, be:
Retroduction:
Rule: All men are mortal.
Result: (It is observed that) Socrates is mortal.
Ergo: (Hypothetical) Case: Socrates is a man."
Hm. I'm not quite sure about this formulation. For example, if my cat is named 'Socrates', using the above formulation we arrive at the hypothetical case that she's a man! That certainly can't be right!
I'd earlier offered something to this effect:
Rule: It is hypothesized that it is a law that all men must die,
Result (that is, observed character), we see that the character 'mortal' appears to apply to all men
Ergo: it is the case that Socrates, a man, may possibly die.
Again, this only works as an abduction in the sense that in the future my contemporary Socrates may be the beneficiary of some immortality treatment, say, brought to Earth by some alien species.
You also gave what you called a "compromise with Peirce's 1903 form" putting the results first.
[BU] "Result: (surprisingly) Socrates is mortal. (Subtext: Yes, it came as a surprise to us. Please don't be surprised at us!)
Rule: All men are mortal. (Subtext: so, if Socrates were a mere man, then it would follow as a matter of course that he is mortal.)
Ergo: (possibly) Case: Socrates is a man."
At first glance this seems preferable. But which of the three inference patterns is this? It seems to follow the structure of something following the vector of process, that is, like evolution or inquiry, beginning at 1ns, passing through 3ns, and arriving at 2ns. So, firstly, this seems to me not to be an abduction, and so, secondly, I'm not sure how this represents a "compromise" with what you've been calling the 1903 formulation (btw, it may be that I see the year 1903 as much richer in regard to abduction than you've been suggesting it is, rather limiting it to the "surprising" observation formulation, a formulation I find in itself somewhat limiting). These questions also pertain to your representation of "the 'strategic' abduction, in the syllogistic semi-1903 form" as well, so I won't consider that just now even given your quite interesting real-world analysis of the "education reduces prejudice" topic.
So, continuing, after summarizing rather neatly how I see the three inference patters "with reference to the three stages of Peirce's scientific method" as:
[BU] "(a) [Abduction concludes] It is hypothesized that education (the right education, a rich education, etc.) about anti-Semitism will reduce anti-Semitism.
(b) [Deduction concludes] A rich education has the characters M, N, etc.
(c) [Induction concludes (for the time being)] An education with the characters M, N, etc., if tried out on a sufficient scale, "may possibly show" a measurable reduction of anti-Semitism.
The word "possibly" in (c) is certainly in error and should have been "probably". You note quite correctly that as originally written that I "make (c) seem an abductive conclusion, but I thought that (c) was supposed to be the stage of induction. I think that there has to be some actual experience referenced, for it to be the inductive stage in scientific method. So I would re-word it to say something like "shows a reduction [or increase or unchanged state] of anti-Semitism with a statistical significance of X," etc. (Assuming that we had good ways to measure and whatever.)"
Your formulation here is good and better even than how I intended to phrase it, which was simply to write something like "what may *probably* show. . . " But, again, your phrasing, "with a statistical significance of X," is more precise and, perhaps, clearer than simply to point to a probability (although Peirce uses that expression in such instances quite often).
Your tale of a man you knew who was "disappointed and annoyed" after taking a course in logic because what he really desired in taking that course was to learn, in the expressions you suggested to him:
[BU] "How to argue in real life? How to reason about practical things? [The man] said, Yes, exactly. Probably there are many like him. Everyday people who use the word "logic" pretty much in Peirce's sense."
Well, this story suggests many things to me so that I agree with the general thrust of it and, a fortiori, for Pragmaticism. In a sense, discoveries, insights, advances, etc. in theoretical logic, logica docens, ought to impact on clear thinking in the realm of practical logic, logica utens. Yet, I think that "Peirce's sense" of the word 'logic' is not quite so simple since I would imagine that Peirce would argue that logica docens, as a pure, theoretical investigation, needs to be free of all practical considerations, something he holds for all theoretical science. Yet, the findings of pure science will--and indeed should--filter down to the practical arts/sciences. I think that you're suggesting, and I completely agree, that "everyday people" expect logic and philosophy to accomplish much more in their practical lives than they seem now to be doing.
Finally, I'll be very interested to learn more of your thinking about the categories in light of, for example, the ""Prolegomena to an Apology for Pragmaticism." You wrote, parenthetically:
[BU] "(I don't feel that I understand the categories better than many "three-ists" as you suggest - at least, better than any authentic three-ists. I think that I may _like_ the idea of _pervasive, patterned categories_ as much as any three-ist likes them, and possibly I like them more than some do, so maybe occasionally I seem to plunge more readily into them than some do.)
I wish that at least some others would plunge into the categories as readily as you do. Meanwhile, I will only say that your work on them (3's and, yes, even 4's!) has been most useful to my own categorial thinking. I encourage those who haven't yet taken a look at your blog to do so.
http://tetrast.blogspot.com/
Best,
Gary
>>> "Benjamin Udell" <budell <at> nyc.rr.com> 7/5/2010 12:49 AM >>>
Gary, list,
Sorry for the delay. Now that I'm started, I'll try to get this done before NYC gets too far into a week of 95-degree (Fahrenheit) weather that I suspect will be too much for the local power grid. It just snowed somewhere in New Hampshire, I'd prefer that!
You sound a little too down on the "harmless game" appearance that vectorial analysis might take on for some people. Well, it's "only" a procedure for taking the bull by the horns! Whether it's a game or an exercise or whatever, such exercises help develop the ability to deal with Peirce's categories in terms of the permutations to which they certainly seem to lead.
I'd have thought that the retroductive-syllogistic version of the man-mortal-Socrates syllogism would, less Procrustean-beddishly, be:
Retroduction:
Rule: All men are mortal.
Result: (It is observed that) Socrates is mortal.
Ergo: (Hypothetical) Case: Socrates is a man.
A compromise with Peirce's 1903 form would put the result first.
Result: (surprisingly) Socrates is mortal. (Subtext: Yes, it came as a surprise to us. Please don't be surprised at us!)
Rule: All men are mortal. (Subtext: so, if Socrates were a mere man, then it would follow as a matter of course that he is mortal.)
Ergo: (possibly) Case: Socrates is a man.
So, in the "strategic" abduction, in the syllogistic semi-1903 form:
Sought, not observed, result: (surprisingly) Prejudice will decrease.
Rule: Education about X reduces ignorance about X. (Subtext: so, if prejudice about X is a form of ignorance about X, then it would follow as a matter of course that education about X will reduce prejudice about X).
Ergo: (possibly) Case: Prejudice about X is a form of ignorance about X. (Subtext: so, education about X will reduce prejudice about X.)
That isn't quite how I did it before, I've been forced to become more exact. It exposes one of the weaker parts of the argument, the idea that prejudice about people, prejudice which we normally regard as having strong components of long-standing emotion and habitual conduct, is merely a lack of some appropriate cognitions. Such prejudice might possibly have been nipped in the bud by some appropriate cognitions, but such prejudice becomes something a little more formidable, and may have started formidably enough, imparted by parents or schools or popular TV shows to children who, let's suppose that they grow up to be personally honest, compassionate, etc., may go on believing nevertheless some silly things to destructive effect.
Also the "rule" "Education about X reduces ignorance about X" needs to be extendible to "For any given form of ignorance about X, there is a form of education about X that reduces said ignorance" etc. Would it be mere hand-waving of me to say that we should be glad to seem to have landed in the right problematics?
Meanwhile you proceeded to something interesting. You introduce this with reference to the three stages of Peirce's scientific method, and then say essentially (I've summarized somewhat):
(a) [Abduction concludes] It is hypothesized that education (the right education, a rich education, etc.) about anti-Semitism will reduce anti-Semitism.
(b) [Deduction concludes] A rich education has the characters M, N, etc.
(c) [Induction concludes (for the time being)] An education with the characters M, N, etc., if tried out on a sufficient scale, "may possibly show" a measurable reduction of anti-Semitism.
I quoted the "may possibly show" directly from you because you thereby make (c) seem an abductive conclusion, but I thought that (c) was supposed to be the stage of induction. I think that there has to be some actual experience referenced, for it to be the inductive stage in scientific method. So I would re-word it to say something like "shows a reduction [or increase or unchanged state] of anti-Semitism with a statistical significance of X," etc. (Assuming that we had good ways to measure and whatever.)
You go on to say:
[GR] My point for now would be that using vector analysis in such a way could strengthen thinking about, for example, the optimal kind of social-psychological-historical inquiry needed here , that a clearer grasp of what is involved in each of the inference patterns when employed in inquiry, might result in better inquiries being made, greater economy of inquiry, etc.
That could be. I'm so out of it nowadays when it comes to psychology and social studies, but they're certainly the Usual Suspects when it comes to wondering where inquiry could be improved. Then there's philosophy itself, of course. I can think of a further need. I knew a man who told me of taking a course on logic and being disappointed and annoyed. I figured that he had found himself plunged into something like Quine's _Methods of Logic_ and so I said something like, All those forms and schemata, that's not what you were interested in? He said, Right. I asked, What were you interested in? He had momentary trouble saying, so I said, How to argue in real life? How to reason about practical things? He said, Yes, exactly. Probably there are many like him. Everyday people who use the word "logic" pretty much in Peirce's sense.
As regards the Categories (Peirce) wiki, I may bring up some questions related to it here at peirce-l. It contains a long quote from Peirce which I first had read years ago and had assumed at the time that it was "early Peirce" but instead it's from 1906, "Prolegomena to an Apology for Pragmaticism" (which I did not adequately read because I kept skipping over parts especially when he gets into detail about the Existential Graphs and if I read most of it years earlier, I probably forgot when it was written or anyway I wasn't thinking about the "Categories (Peirce)" wiki) and it seems to me a quote from a problematic passage, not the thing for an introductory wiki, though maybe I'm just confused. (I don't feel that I understand the categories better than many "three-ists" as you suggest - at least, better than any authentic three-ists. I think that I may _like_ the idea of _pervasive, patterned categories_ as much as any three-ist likes them, and possibly I like them more than some do, so maybe occasionally I seem to plunge more readily into them than some do.)
You wrote,
[GR] the relationship of "conjecture" and "surprise" especially needing to be examined, imho.
That would be interesting.
Best,
Ben
----- Original Message -----
From: Gary Richmond
To: Peirce Discussion Forum
Sent: Thursday, June 24, 2010 5:47 PM
Subject: Re: [peirce-l] Induction, Deduction, or Abduction: was Deduction versus Induction
Ben, List,
There's not much in your philosophically and psychologically rich post that I don't rather agree with, Ben. For example, your discussion of why, if we may assume that some people take Peirce's categories seriously, and the categorial vectors clearly addressing genuine issues in Peirce's work, these vectors--or paths through categorial relations--have been neglected. Be that as it may, I like your suggestion as to a way to move this categorial vector analysis forward, namely, that I should more and more show a 'need' for vector analysis. Yes, one can play the harmless game of watching those "categorially double-tracking vectors refracting various modal/categorial possibilities," but where does that get one? In any case, one can spin this crystal on even a version of the mother of all syllogisms, "All men are mortal" (note: I recently had a young student with the first name of Socrates, so that I will assume that there are Socrates (plural) living today, especially as an already dead Socrates will not do for this bit of crystal gazing). So:
Deduction: (3ns) It is a law that all men die, (2ns) it is the case that Socrates is a man; (1ns) so Socrates necessarily will (eventually) express the character 'mortal'.
(c) (1ns) so Socrates necessarily will (eventually) express the character 'mortal'.
|> (a) (3ns) It is a law that all men die,
(b) (2ns) it is the case that Socrates is a man;
Now, the other two inference patterns. OK, the hypothetical form is a Procrustean bed of sorts, but it is possible:
Retroduction: (3ns) It is hypothesized that it is a law that all men die, (1ns) observing how the character 'mortal' seems to apply to all men; (2ns) it is the case that the man, Socrates, may possibly die (note: we can't be totally certain; some future advance of science, or this brought to earth by some alien species, might do away with man's mortality).
(b) (1ns), observing how the character 'mortal' seems to apply to all men;
|> (a) ( 3ns), It is hypothesized that it is a law that all men die,
(c) (2ns), it is the case that the man, Socrates, may possibly die.
Induction: (2ns) It is the case that Socrates is a man, (1ns) men have (so far) always exhibited the character 'mortal'; (3ns) it is most probable that Socrates, like all men so far, will succumb to the law 'human-mortality' and die.
(b) (1ns) men have (so far) always exhibited the character 'mortal';
|> (c) (3ns) it is most probable that Socrates like all men so far, will succumb to the law 'human-mortality' and die.
(a) (2ns) It is the case that Socrates is a man,
But, of course, this kind of thing is merely a game and hardly worth the effort. In a certain sense, such analyses as the above, as well as the parallel ones I attempted on J's syllogism, may have a legitimate place in that they are either stated logically correctly or not. That legitimate place is, I believe, critical logic, the 2nd, so the penultimate branch of Peirce's science of logic as semeiotic.
But your remarks suggested to me what I have always tended to think at this moment, namely, that the more important use of vector analysis-synthesis could be in how these three inference patterns might play out in the third, ultimate, branch of semeiotic, namely logical rhetoric seen as theory of inquiry. As you know, Peirce prescribes these three to be taken up in this order: (a) (1ns) Hypothesis formation, (b) (3ns) deduction of the implications of the hypothesis for the purpose of devising an adequate test of it; and (c) (2ns) the actual inductive testing of the hypothesis built on the deduction.
(a) 1ns, Abduction
|> (b) 3ns, Deduction
(c) 2ns, Induction
So, spring-boarding off J's S, I begin by offering an hypothesis:
(a) It is hypothesized that a rich education into the history of and psychological-social causes of anti-Semitism (type of prejudice for the purposes of this inquiry), in reducing ignorance about that issue will, in turn reduce anti-Semitism, (b) so that carefully characterizing what we mean by 'rich education', 'psychological-social causes', etc; (c) we will devise and execute a well-designed, sufficiently large experiment which may possibly show a measurable reduction of anti-Semitism as the result of authentic education occurring.
[3ns/1ns/2ns]
(b) 1ns, so that carefully characterizing what we mean by 'rich education', 'psychological-social causes', etc;
|> (a) 3ns, It is hypothesized that a rich education into the history/causes of anti-Semitism, in reducing ignorance about that issue will, in turn reduce anti-Semitism,
(c) 2ns, let us devise and execute a well designed, sufficiently large experiment which may possibly show a measurable reduction of anti-Semitism as the result of authentic education occurring.
According to Peirce, this ought be followed by a deduction of the hypothesis' implications for testing such an hypothesis, the subsequent devising of a suitable experiment, and the actual testing of a suitably large and appropriately selected population in order to see the extent to which the hypothesis proves true (that is, conforms to reality; I won't attempt any of that here).
My point for now would be that using vector analysis in such a way could strengthen thinking about, for example, the optimal kind of social-psychological-historical inquiry needed here , that a clearer grasp of what is involved in each of the inference patterns when employed in inquiry, might result in better inquiries being made, greater economy of inquiry, etc.
Moving now to this comment of yours:
[BU] "I'm a fine one to be talking in that way about categories when I've left the "Categories (Peirce)" wiki in the state that it's in."
Well, I hope you eventually do find the time to work on the "Categories (Pierce)" wiki as I don't know anyone better suited to that work. As you also wrote,
[BU] ". . .categorization long ago became 90% of why I'm interested in philosophy, so, while I'm not a three-ist, I hardly want people to give up on trying to advance philosophy of categories and categorial patterns."
It has always been my sense that, even while you reject Peirce's 3 universal categories, that you yet understand them better than many a "three-ist," and this applies to the vectorial part as well. So, again, I know you will continue to do work on categorization, and I hope that at some point you'll complete and perfect the "Categories (Peirce)" wiki. Of course, if there's any way in which I could help in that matter, I'd be delighted to do so.
As for the discussion re: abduction/retroduction/hypothesis, you wrote:
[BU] "Regarding my "strategic abduction," I wasn't countering what you said, I was just taking the opportunity for a "do-over" to elucidate in just what sense I saw it as parallel to explanatory abduction,"
and, similarly, I wasn't countering you. That said, I believe that this topic needs much more discussion, the relationship of "conjecture" and "surprise" especially needing to be examined, imho.
At the moment, I haven't much more to say on the "begging the question" issue brought up here--and this post is already way too long!
Best,
Gary
Gary, List,
I agree tha it's not too much to expect, that people find the categorial vectors of genuine interest, since, after all, the vectors address genuine issues. While iconistic expressions like my occasional ones might help as you suggest, let's note that they haven't won any interest among people in my fours. You've focused on establishing the categorial vectors' legitimacy and reasonableness as extensions of something that Peirce was already doing. You might want to focus also on the _need_ for them as solutions, or the beginnings of solutions, to categorial ordering problems or complexities which they address and which they didn't create. They're not solutions in themselves, rather they're a way of being systematic (and diagrammatic) about the permutations of the ordering, so that the reasons for the permutations can be brought to light, explicated, in a generalizable way. The three inference modes are a good case in which to study them. Other cases are the order of semiotic determination (obviously) and some of the broader structures in Peirce's classification of the sciences, such as the nomological-classificatory-descriptive trichotomy. I think that people may be thinking of it as working with "vague" paradigms just to watch the crystal refract as it turns, when what they want are results, when, to the contrary of all of that, you're pointing to problems and talking about a framework for their analysis, a way to keep track of categorial double patterns, glean a pattern in the double patterning itself. I suppose that one could call it a "paradigm" but really it's just a method for focusing on some pre-existent unresolved issues. It's as if people didn't see the problems as problems. Now, I would guess that, among people interested in Peirce, a strict subset, but a sizable one, takes the categories seriously, and I don't know why they don't take more interest in dealing with categorial ordering issues, except to guess that they have done so in the past, have felt that they made little headway, and have switched to other aspects of Peirce. That can't happen to me unless I give up on philosophy, since categorization long ago became 90% of why I'm interested in philosophy, so, while I'm not a three-ist, I hardly want people to give up on trying to advance philosophy of categories and categorial patterns.
I'm a fine one to be talking in that way about categories when I've left the "Categories (Peirce)" wiki in the state that it's in.
Regarding my "strategic abduction," I wasn't countering what you said, I was just taking the opportunity for a "do-over" to elucidate in just what sense I saw it as parallel to explanatory abduction. Well, the strategic version is still explanatory; it explains how a surprising phenonemon (though not yet observed) could be brought about. In both cases the abduction charts a kind of course of determination. In Peirce's definition of abduction as reasoning from consequent to antecedent, I think that it's worth noting that he was referring to reasoning from consequent to antecedent in a rule that serves as a premiss in the syllogistic forms of both deduction and abduction, even though the abduction does also involve reasoning from the corresponding deduction's conclusion, taking as a premissual observation the result which would be the deduction's conclusion. Peirce does talk about surprise in connection with inquiry and abduction in the paragraph (CP 6.469) from "A Neglected Argument" (1908) from which you quote, but he goes into some detail so the discussion gets a bit spread out. The retroduction proceeds from consequent (the surprising phenomenon) to the supposed antecedent (which would make the phenomenon less surprising). The paragraph on colligation from which you quote, from 1898 Lecture 3 (CP 5.581), and the nearby paragraphs, do not mention surprise. He's talking about the (unpermuted) sequence colligation-iteration-erasure in all three inference modes, and so we can see that Peirce thought it reasonable to discuss abductive inference without mentioning surprise; but that predates the 1903 form of abduction, which included the surprising observation as a premiss. Still, he discusses abduction or retroduction in later years without mentioning surprise
http://www.helsinki.fi/science/commens/terms/retroduction.html, and he did not quite stick with the 1903 form for abduction. Peirce said, in a letter to J. H. Kehler, NEM 3:203-204, 1911:
I do not, at present, feel quite convinced that any logical form can be assigned that will cover all "Retroductions". For what I mean by a Retroduction is simply a _conjecture_ which arises in the mind.
For my part, I'm willing to allow as an abductive premiss the sheer possibility of a surprising observation (in that which I've called strategic abduction). Anyway, though I think that it's worth noting that it's quite arguable that surprise became a standing part of his conception of abduction (especially given his 1908 remarks), I agree that the 1903 form for abduction is not the "canonical" one. It's just the one that I used. I think that it remains also illuminating to use, as you sometimes do, the earlier syllogistic form as well. (I was real glad to get the syllogistic versions of the three inference modes into the Peirce wiki!) I don't think that the idea of surprise was entirely absent from his earlier conceptions of abduction, but he didn't incorporate the idea explicitly into the form, and anyway syllogistic forms are usually kept bare and simple. (Likewise, for induction, he didn't formally incorporate "randomly selected" into the syllogistic premiss "these beans are from this bag," even though at least sometimes in his discussion back then he did put the idea of random selection into the foreground). To look at the syllogistic forms of induction and abduction, which come across at first glance simply as bad deductions, and to experience one's own coming to see how with some turns of context (that turning crystal again) they could lead, as inferences, to the truth, is a worthwhile bit of intellectual education, and I can't help thinking that Peirce prized it partly for that reason.
Anyway, I've gotten kind of rusty in the past six months, and I said some things in my last post that reflect that. I addressed Irving's question about whether all deductions are syllogisms as if he were wondering for his own part rather than asking somebody else for their opinion. He probably has a definite opinion on it and he's certainly knowledgeable enough. I forgot about a pre-Boolean form called immediate inference which was not considered syllogism and most of which is swept away under Boolean assumptions. Meanwhile, modus ponens and the rest don't look on the surface like syllogisms but I was thinking vaguely of how Peirce might be flexible about it, with his equating if-thens to copulas, P-->Q is like A(G-->H), etc. Maybe he'd even count immediate inference, or what survives of it, as a degenerate kind of syllogism. But I don't know enough about how Peirce regarded these things or even about how they are regarded generally nowadays. Another odd thing that I did in my last post was talk about equivalence properties in connection with syllogizing a mathematical induction, when those equivalence properties depend on postulates, standing givens, which takes the question outside the usual classification of syllogisms. So it's apples and oranges.
Meanwhile I was getting myself confused about begging the question since a little over six weeks ago. I had thought about the "subjective" novelty of a deductive conclusion (a Neo-Scholastic called it "psychological novelty"; Peirce called it placing the premisses in a "new aspect"; and I once read online about an effort, that didn't get very far, to quantify such psychological novelty from a 2nd-order standpoint) versus the objective novelty which is information as in information theory. I was thinking likewise about subjective versus objective simplicity/efficiency/etc. (facility/feasibility and naturalness), likeliness, and nontriviality/depth/complexity. Initially I thought that the difference between between circular and non-circular deduction was "subjective" by such a standard and I reacted, no way! and decided to call it "aspectual." Then I changed my mind again, and thought it was non-aspectual. Yep, I have to blame this on six months of rusting. Finally I realized (my current but still nervously stated view) that the question of whether it's circular simply is not to be characterized based either on the deduction's aspect ("aspectual") or on what's really in it in terms of information or data (for which I made up the word "transpectual," i.e., that which one will see in it if one looks through it enough). Instead it's based on whether one actually has looked through it (and the postulates or standing givens on which it is based) enough. Whether we actually already know or don't know that a conclusion is implied or contradicted simply does not depend directly either on whether it is implied or contradicted or on whether it somehow bears the aspect of something implied or contradicted in the manner that "Socrates is mortal" has a (notably persistent) novel aspect in view of its usual premisses. (I retained the "aspectual/transpectual" terminology because, in the case of probability, the phrase "subjective probability" suggests incorporation of subjective estimates of amount of probability into the reasoning itself, whereas one considers whether an inductive estimate seems likely or reasonable without pointing toward quantifying the induction's probability, likewise as one considers whether a deduction's conclusion has a novel or informative aspect, without pointing toward quantifying that informativeness.)
That's clearly enough for the time being! I'm at my prolix stage of de-rusting. Hope soon I regain my previous hard-won concision.
Best, Ben
----- Original Message -----
From: Gary Richmond
To: Peirce Discussion Forum
Sent: Thursday, June 17, 2010 7:39 PM
Subject: Re: [peirce-l] Induction, Deduction, or Abduction: was Deduction versus Induction
Ben, Irving, list,
Ben wrote:
[BU] Gary, I think you're right. The argument is expressed in such a general way that to ask whether it is deductive, inductive, or otherwise, is to ask which mode's "canons" appear to be being followed in the argument's expression. So we can turn it around like a crystal, as you have with your categorially double-tracking vectors, and watch it refracting various modal/categorial possibilities.
Ben, you have such a wonderful knack for expressing subtle logical and other philosophical ideas in poetic language which represents, as I see it, a "more iconic" way of expressing things. You spoke of such a very general syllogism as is Burke's that "we can turn it around like a crystal, as you have with your categorially double-tracking vectors, and watch it refracting various modal/categorial possibilities." This way of putting it seems to me to make at least my most general point in that post most succinctly, while at the same time suggesting some of the richness of possibility of using Peirce's trichotomic understanding for considering anything--here, a syllogism--which may be so analyzed.
I say 'Peirce's, not mine as you suggested above, because the connection of the three categories with vectorial movement through them is explicated in Peirce's own writing, something which I've argued here as well as in several papers. So, at most, I attempt to systematize vectorial movement through the categories and try to offer various examples of such movement; while, at least, I provide a more iconic diagrammatic form for analyzing anything which can be tri-categorially analyzed. Burke's syllogism offered a good opportunity to try that out with the three patterns of inference.
To tell the truth, I've always been somewhat surprised that more folk on this list haven't found Peirce's tri-category theory, and especially the vectorial part of it, of the greatest interest. For example, it seems to me that trikonic, as a visual diagram for analyzing trichotomic objects and ideas, might help clarify many an issue where the Three Universes of Experience are involved--in Peirce, most everywhere. In addition, it can do this with fewer words, something which more iconic visual diagrams--also poetry--are famous for doing.
Perhaps, though, it's more a matter of my faulty voice. Perhaps I sound dogmatic in my presentation of and claims about vector analysis. I certainly don't mean to be as I myself have often corrected a tri-categorial analysis of my own; I would look forward to others' corrections of my analyses. And, as just stated, I consider trichotomic to be Peirce's invention which I have only attempted to begin to systematize, diagram, and extend. So, perhaps if I had a more poetic voice I'd be able to sound less didactic and dogmatic.
But returning now to the recent trikonic analysis prompted by Burke's syllogism, I certainly did make one grave error. I unquestionably should have made clearer that when linking rule/case/result to the categories it is better (at least it seems to me) to associate 'result'--the 1ns here---with 'character', a term much more closely associated with 1ns. So, revised:
character, 1ns
|> rule, 3ns
case, 2ns
Now all three elements are, I hope, associated with the categories in a way which could facilitate the understanding of any syllogistic analysis by this method. But for now, Let's just look at one of the three analyses in the earlier post, that of deduction applied to J's S. I analyze this as follows [adding some material for further clarification]:
(a) 3ns, It is a socio-psychological law that authentic education reduces ignorance which in turn reduces prejudice ['rule' == 'law'],
(b) 2ns, so that when we sample a large enough population so educated [and the sampling of a population clearly puts us into the realm of 2ns];
(c) 1ns, we will necessarily find that there has been a reduction in prejudice [prejudice being the character being considered in J's S]
[GR] [3ns/2ns/1ns]
(c) we will necessarily find that there has been a reduction in prejudice.
|> (a) It is a socio-psychological law that authentic education reduces ignorance which in turn reduces prejudice,
(b) so that when we sample a large enough population so educated;
So, again, in the trikonic analysis of a deductive syllogism the result is a character, just as the middle term of induction and abduction are also characters.
Turning now to another point of your post regarding abduction you wrote:
[BU] As to my suggestion of [J's S] being regardable as abductive, let me show it in a way that aligns it with Peirce's 1903 form.
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.
I'm so glad you brought this up. While Peirce undoubtedly uses this "surprising fact" expression of abduction in considering hypothesis formation, when he analyzes hypotheses as retroductions he is looking at the matter somewhat differently. In the very late "Neglected Argument" he defines retroduction as "reasoning from consequent to antecedent" [CP6.469]. Here a prepared scientific mind iterates all that is relevant to the problematic situation in a colligation of his experiences in regard to it, then he creates an internal diagram in order to mentally observe and manipulate the diagram (just as he does with his Existential Graphs).
So, moving from consequent to antecedent, "Retroduction [ . . . ] begins with colligation. Something corresponding to iteration may or may not take place. And then comes an Observation"[CP 5.581]. The third step, the conclusion, is that this hypothesis does strongly suggest to the abducing scientist that the hypothesis will, if tested, explain the existential (or quasi-existential) question put to nature, etc.
I won't add more to an already long post except to say that you've pretty much convinced me that the deductive version of J's S begs the question, at least as you put it at the conclusion of your post:
[BU] Burke asked only whether his argument was deductive or inductive, not whether it was a deductive or inductive proof (that its conclusion is actually true). So I'd say that the question of whether it begs the question doesn't arise.
But I was thinking, as my final quotations from Nott's book might suggest, less about syllogistic per se than of inquiry per se. So, I analyzed the deductive form as expressing a settled rule such that inquiry had ceased. I'm not sure what I'd call that.
Best,
Gary
>>> "Benjamin Udell"> 6/15/2010 7:09 PM >>
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