1 Jul 12:16 2010

### Re: Deduction versus Induction

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5 Jul 06:49 2010

### Re: Induction, Deduction, or Abduction: was Deduction versus Induction

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'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.

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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5 Jul 22:21 2010

### Re: Induction, Deduction, or Abduction: was Deduction versus Induction

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'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.

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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6 Jul 13:58 2010

### Re: Deduction versus Induction

```
Vinicius,

Several days ago I did find the following words of Peirce regarding
Mill's conception:

"This is, as it happens, in strict accordance with Mill's account of
the proposition; he says (Logic, eighth edition, p. 135) that it
asserts that "all things which have a certain attribute have along with
it a certain other  attribute," which is exactly what is asserted in D.
Either D or D1 amounts to a statement of the dictum de omni (in one the
s =(=. p plays the part of a major premise, in the other of a minor
premise); and Mill agrees with De Morgan that to give any real meaning
to the dictum de omni, we must consider it not as an axiom but as a
definition. In speaking of the relation s < p in words, it is necessary
to use the language either of the term or of the proposition; but
everything that has just been said of subject and predicate must be
taken as having also been said, in terms of premise and conclusion, or
of antecedent and con-sequent (for it makes no difference for this
purpose whether, in 'S-is-followed-by P,' the following is of a logical
or of an extra-logical nature)."

Being distracted with other issues, I did not, regrettably, record the
source, however. So, if anyone recognizes this, would they please post
the bibliographic data.

----- Message from viniroma <at> yahoo.com ---------
Date: Thu, 1 Jul 2010 03:16:47 -0700 (PDT)
From: Vinícius Romanini <viniroma <at> yahoo.com>
Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
Subject: Re: [peirce-l] Deduction versus Induction
To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>

> That´s very interesting, Irving.
> I would argue on the same lines as Mill, if I understood his claim correctly.
> I attach a unpublished paper that I delivered last year at the
> Pragmatism meeting in São Paulo in which I build this argument on a
> Peicean basis.
>
> Best,
>
> Vinicius Romanini, Ph.D.
> Professor of Sciences of Communication
> School of Communications and Arts
> University of Sao Paulo, Brazil
> www.minutesemeiotic.org
>
> --- On Thu, 6/17/10, Irving <ianellis <at> iupui.edu> wrote:
>
>
> From: Irving <ianellis <at> iupui.edu>
> Subject: Re: [peirce-l] Deduction versus Induction
> To: "Peirce Discussion Forum" <peirce-l <at> lyris.ttu.edu>
> Date: Thursday, June 17, 2010, 6:17 PM
>
>
>
> Tom,
>
> I apparently missed one of the initial points, which I thought was
> whether every syllogism is a petitio principia. I know that Mill
> asserted both that the syllogism is de facto a petitio principii, and
> that all logical inferences, including those that pass for syllogisms,
> are ultimately
> empirical.
>
> I think it was probably also Mill who perhaps conflated the these two
> claims, to argue, consequently, that all arguments that are
> information-producing, rather than merely peitios, are inductive --and
> that Mill was seeking to render deductive argument as a subclass of
> inductive logic, i.e., attempting to establish an ars inveniendum.
>
>
> ----- Message from tgollier <at> gmail.com ---------
>     Date: Thu, 17 Jun 2010 12:11:52 +0200
>     From: Tom Gollier <tgollier <at> gmail.com>
> Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
> Subject: Re: [peirce-l] Deduction versus Induction
>       To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>
>
>> Irving,
>>
>> Those are intriguing questions and contrasts, but my concern remains with
>> Burke's argument. Is it ? as it appears to me to be ? a question-begging
>> induction masquerading as a deduction?
>>
>> Tom
>>
>> On Tue, Jun 15, 2010 at 8:49 PM, Irving <ianellis <at> iupui.edu> wrote:
>>
>>>
>>> Mill wanted to claim that the syllogism is a petitio principii. That
>>> was my only point in my response to Burke's assertion that the
>>> particular argument being discussed "is masquerading as a deduction by
>>> begging the question". I was at this conjucture neither defending nor
>>> contesting Mill's assertion, but merely rendering an historical point.
>>> (Mill's other point in this regard was that, at bottom, all logical
>>> inferences, including those that pass for syllogisms, are ultimately
>>> empirical.)
>>>
>>> If we rewrite the BARBARA syllogism as an implication, as Peirce,
>>> MacColl, Frege, and Russell did; thus: If A implies B and B implies C;
>>> therefore A implies C; or as a subsumption, as Peirce and Schroeder
>>> did: If A is included in B and B is included in C, therefore A is
>>> included in C. In that case, there are those (e.g. Mill) who would
>>> argue that the conclusion is already inherently included in the
>>> conjunction of the premises.
>>>
>>> Now Tom Gollier asks: "if "EVERY syllogism is question-begging," what
>>>
>>> better way to masquerade as a deduction?"
>>>
>>> My questions -- as an historian who is not a philosopher -- now are:
>>> (1) Is the point of Gollier's question to suggest that question-begging
>>> syllogism is identical with deduction (or that the set of syllogisms is
>>> coextensive with the set of deductions)?; (2) assuming that every
>>> question-begging syllogism is a deduction, does it necessarily follow
>>> that every deduction is a question-begging syllogism?; and (3) are
>>> there syllogisms which are not question-begging, and are there some
>>> deductions that are not syllogisms? (Note that this not necessarily the
>>> same as asserting, as Frege, e.g. did, that there are syllogisms that
>>> are valid which are not valid in, say, first-order functional calculus.)
>>>
>>>
>>>
>>> ----- Message from tgollier <at> gmail.com ---------
>>>    Date: Mon, 14 Jun 2010 09:35:59 +0200
>>>
>>>
>>
>> -----
>> **
>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>> ** the central pointer and guide for Peirce resources on the web:
>> **            http://csp3.blogspot.com/
>> ** -------
>> **
>> ** If you want to cancel your subscription to PEIRCE-L
>> ** send a message to the list manager at:
>> **
>> **      joseph.ransdell <at> yahoo.com
>> **
>>
>>
>> joseph.ransdell <at> yahoo.com
>
>
> ----- End message from tgollier <at> gmail.com -----
>
>
>
> Irving H. Anellis
> Visiting Research Associate
> Peirce Edition, Institute for American Thought
> 902 W. New York St.
> Indiana University-Purdue University at Indianapolis
> Indianapolis, IN 46202-5159
> USA
> URL: http://www.irvinganellis.info
>
>
> -----
> **
> ** Click on the following URL link for THE PEIRCE BLOG, which is
> ** the central pointer and guide for Peirce resources on the web:
> **            http://csp3.blogspot.com/
> ** -------
> **
> ** If you want to cancel your subscription to PEIRCE-L
> ** send a message to the list manager at:
> **
> **      joseph.ransdell <at> yahoo.com
> **
>
>
> joseph.ransdell <at> yahoo.com
>
>
>
>
> -----
> **
> ** Click on the following URL link for THE PEIRCE BLOG, which is
> ** the central pointer and guide for Peirce resources on the web:
> **            http://csp3.blogspot.com/
> ** -------
> **
> ** If you want to cancel your subscription to PEIRCE-L
> ** send a message to the list manager at:
> **
> **      joseph.ransdell <at> yahoo.com
> **
>
>
> joseph.ransdell <at> yahoo.com

----- End message from viniroma <at> yahoo.com -----

Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info

-----
**
** Click on the following URL link for THE PEIRCE BLOG, which is
** the central pointer and guide for Peirce resources on the web:
**            http://csp3.blogspot.com/
** -------
**
** If you want to cancel your subscription to PEIRCE-L
** send a message to the list manager at:
**
**      joseph.ransdell <at> yahoo.com
**

joseph.ransdell <at> yahoo.com

```
6 Jul 14:32 2010

### Re: Deduction versus Induction

```Hi Irving,

A Google search of the phrase

"This is, as it happens, in strict accordance with Mill's account of
the proposition"

brought up the following result:

http://www.archive.org/stream/nsmindrev01edinuoft/nsmindrev01edinuoft_djvu.txt

which I was then able to look up in JSTOR.  The full reference refers
to a book review by Ladd-Franklin of Schroder (the passage you cite
appears to be her own words):

Review: Vorlesungen iiber die Algebra der Logik (Exakte Logik). By Dr.
ERNST SCHRODER. Leipzig: B. G. Teubner. Vol. I.
Pp. 717
Source: Mind, New Series, Vol. 1, No. 1 (Jan., 1892), pp. 126-132
Stable URL: http://www.jstor.org/stable/2247407

Best,
Jonathan DeVore

Quoting Irving <ianellis <at> iupui.edu>:

>
> Vinicius,
>
> Several days ago I did find the following words of Peirce regarding
> Mill's conception:
>
>
> "This is, as it happens, in strict accordance with Mill's account of
> the proposition; he says (Logic, eighth edition, p. 135) that it
> asserts that "all things which have a certain attribute have along with
> it a certain other  attribute," which is exactly what is asserted in D.
> Either D or D1 amounts to a statement of the dictum de omni (in one the
> s =(=. p plays the part of a major premise, in the other of a minor
> premise); and Mill agrees with De Morgan that to give any real meaning
> to the dictum de omni, we must consider it not as an axiom but as a
> definition. In speaking of the relation s < p in words, it is necessary
> to use the language either of the term or of the proposition; but
> everything that has just been said of subject and predicate must be
> taken as having also been said, in terms of premise and conclusion, or
> of antecedent and con-sequent (for it makes no difference for this
> purpose whether, in 'S-is-followed-by P,' the following is of a logical
> or of an extra-logical nature)."
>
>
> Being distracted with other issues, I did not, regrettably, record the
> source, however. So, if anyone recognizes this, would they please post
> the bibliographic data.
>
>
> ----- Message from viniroma <at> yahoo.com ---------
>     Date: Thu, 1 Jul 2010 03:16:47 -0700 (PDT)
>     From: Vinícius Romanini <viniroma <at> yahoo.com>
> Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
> Subject: Re: [peirce-l] Deduction versus Induction
>       To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>
>
>> That´s very interesting, Irving.
>> I would argue on the same lines as Mill, if I understood his claim
>> correctly.
>> I attach a unpublished paper that I delivered last year at the
>> Pragmatism meeting in São Paulo in which I build this argument on a
>> Peicean basis.
>>
>> Best,
>>
>> Vinicius Romanini, Ph.D.
>> Professor of Sciences of Communication
>> School of Communications and Arts
>> University of Sao Paulo, Brazil
>> www.minutesemeiotic.org
>>
>> --- On Thu, 6/17/10, Irving <ianellis <at> iupui.edu> wrote:
>>
>>
>> From: Irving <ianellis <at> iupui.edu>
>> Subject: Re: [peirce-l] Deduction versus Induction
>> To: "Peirce Discussion Forum" <peirce-l <at> lyris.ttu.edu>
>> Date: Thursday, June 17, 2010, 6:17 PM
>>
>>
>>
>> Tom,
>>
>> I apparently missed one of the initial points, which I thought was
>> whether every syllogism is a petitio principia. I know that Mill
>> asserted both that the syllogism is de facto a petitio principii, and
>> that all logical inferences, including those that pass for syllogisms,
>> are ultimately
>> empirical.
>>
>> I think it was probably also Mill who perhaps conflated the these two
>> claims, to argue, consequently, that all arguments that are
>> information-producing, rather than merely peitios, are inductive --and
>> that Mill was seeking to render deductive argument as a subclass of
>> inductive logic, i.e., attempting to establish an ars inveniendum.
>>
>>
>> ----- Message from tgollier <at> gmail.com ---------
>>     Date: Thu, 17 Jun 2010 12:11:52 +0200
>>     From: Tom Gollier <tgollier <at> gmail.com>
>> Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>> Subject: Re: [peirce-l] Deduction versus Induction
>>       To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>>
>>
>>> Irving,
>>>
>>> Those are intriguing questions and contrasts, but my concern remains with
>>> Burke's argument. Is it ? as it appears to me to be ? a question-begging
>>> induction masquerading as a deduction?
>>>
>>> Tom
>>>
>>> On Tue, Jun 15, 2010 at 8:49 PM, Irving <ianellis <at> iupui.edu> wrote:
>>>
>>>>
>>>> Mill wanted to claim that the syllogism is a petitio principii. That
>>>> was my only point in my response to Burke's assertion that the
>>>> particular argument being discussed "is masquerading as a deduction by
>>>> begging the question". I was at this conjucture neither defending nor
>>>> contesting Mill's assertion, but merely rendering an historical point.
>>>> (Mill's other point in this regard was that, at bottom, all logical
>>>> inferences, including those that pass for syllogisms, are ultimately
>>>> empirical.)
>>>>
>>>> If we rewrite the BARBARA syllogism as an implication, as Peirce,
>>>> MacColl, Frege, and Russell did; thus: If A implies B and B implies C;
>>>> therefore A implies C; or as a subsumption, as Peirce and Schroeder
>>>> did: If A is included in B and B is included in C, therefore A is
>>>> included in C. In that case, there are those (e.g. Mill) who would
>>>> argue that the conclusion is already inherently included in the
>>>> conjunction of the premises.
>>>>
>>>> Now Tom Gollier asks: "if "EVERY syllogism is question-begging," what
>>>>
>>>> better way to masquerade as a deduction?"
>>>>
>>>> My questions -- as an historian who is not a philosopher -- now are:
>>>> (1) Is the point of Gollier's question to suggest that question-begging
>>>> syllogism is identical with deduction (or that the set of syllogisms is
>>>> coextensive with the set of deductions)?; (2) assuming that every
>>>> question-begging syllogism is a deduction, does it necessarily follow
>>>> that every deduction is a question-begging syllogism?; and (3) are
>>>> there syllogisms which are not question-begging, and are there some
>>>> deductions that are not syllogisms? (Note that this not necessarily the
>>>> same as asserting, as Frege, e.g. did, that there are syllogisms that
>>>> are valid which are not valid in, say, first-order functional calculus.)
>>>>
>>>>
>>>>
>>>> ----- Message from tgollier <at> gmail.com ---------
>>>>    Date: Mon, 14 Jun 2010 09:35:59 +0200
>>>>
>>>>
>>>
>>> -----
>>> **
>>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>>> ** the central pointer and guide for Peirce resources on the web:
>>> **            http://csp3.blogspot.com/
>>> ** -------
>>> **
>>> ** If you want to cancel your subscription to PEIRCE-L
>>> ** send a message to the list manager at:
>>> **
>>> **      joseph.ransdell <at> yahoo.com
>>> **
>>>
>>>
>>> joseph.ransdell <at> yahoo.com
>>
>>
>> ----- End message from tgollier <at> gmail.com -----
>>
>>
>>
>> Irving H. Anellis
>> Visiting Research Associate
>> Peirce Edition, Institute for American Thought
>> 902 W. New York St.
>> Indiana University-Purdue University at Indianapolis
>> Indianapolis, IN 46202-5159
>> USA
>> URL: http://www.irvinganellis.info
>>
>>
>> -----
>> **
>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>> ** the central pointer and guide for Peirce resources on the web:
>> **            http://csp3.blogspot.com/
>> ** -------
>> **
>> ** If you want to cancel your subscription to PEIRCE-L
>> ** send a message to the list manager at:
>> **
>> **      joseph.ransdell <at> yahoo.com
>> **
>>
>>
>> joseph.ransdell <at> yahoo.com
>>
>>
>>
>>
>> -----
>> **
>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>> ** the central pointer and guide for Peirce resources on the web:
>> **            http://csp3.blogspot.com/
>> ** -------
>> **
>> ** If you want to cancel your subscription to PEIRCE-L
>> ** send a message to the list manager at:
>> **
>> **      joseph.ransdell <at> yahoo.com
>> **
>>
>>
>> joseph.ransdell <at> yahoo.com
>
>
> ----- End message from viniroma <at> yahoo.com -----
>
>
>
> Irving H. Anellis
> Visiting Research Associate
> Peirce Edition, Institute for American Thought
> 902 W. New York St.
> Indiana University-Purdue University at Indianapolis
> Indianapolis, IN 46202-5159
> USA
> URL: http://www.irvinganellis.info
>
>
>
> -----
> **
> ** Click on the following URL link for THE PEIRCE BLOG, which is
> ** the central pointer and guide for Peirce resources on the web:
> **            http://csp3.blogspot.com/
> ** -------
> **
> ** If you want to cancel your subscription to PEIRCE-L
> ** send a message to the list manager at:
> **
> **      joseph.ransdell <at> yahoo.com
> **
>
>
> joseph.ransdell <at> yahoo.com
>
>
>
>

-----
**
** Click on the following URL link for THE PEIRCE BLOG, which is
** the central pointer and guide for Peirce resources on the web:
**            http://csp3.blogspot.com/
** -------
**
** If you want to cancel your subscription to PEIRCE-L
** send a message to the list manager at:
**
**      joseph.ransdell <at> yahoo.com
**

joseph.ransdell <at> yahoo.com

```
6 Jul 15:13 2010

### Re: Deduction versus Induction

```
Thank you, Jonathan,

As it happens, I had been looking at Ladd-Franklin's review just a few
days ago; I just hadn't taken the time to record that that is where I
saw tose lines.

----- Message from devorejd <at> umich.edu ---------
Date: Tue, 06 Jul 2010 08:32:46 -0400
From: Jonathan DeVore <devorejd <at> umich.edu>
Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
Subject: Re: [peirce-l] Deduction versus Induction
To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>

> Hi Irving,
>
> A Google search of the phrase
>
> "This is, as it happens, in strict accordance with Mill's account of
> the proposition"
>
> brought up the following result:
>
> http://www.archive.org/stream/nsmindrev01edinuoft/nsmindrev01edinuoft_djvu.txt
>
> which I was then able to look up in JSTOR.  The full reference refers
> to a book review by Ladd-Franklin of Schroder (the passage you cite
> appears to be her own words):
>
> Review: Vorlesungen iiber die Algebra der Logik (Exakte Logik). By Dr.
> ERNST SCHRODER. Leipzig: B. G. Teubner. Vol. I.
> Pp. 717
> Source: Mind, New Series, Vol. 1, No. 1 (Jan., 1892), pp. 126-132
> Published by: Oxford University Press on behalf of the Mind Association
> Stable URL: http://www.jstor.org/stable/2247407
>
> Best,
> Jonathan DeVore
>
> Quoting Irving <ianellis <at> iupui.edu>:
>
>>
>> Vinicius,
>>
>> Several days ago I did find the following words of Peirce regarding
>> Mill's conception:
>>
>>
>> "This is, as it happens, in strict accordance with Mill's account of
>> the proposition; he says (Logic, eighth edition, p. 135) that it
>> asserts that "all things which have a certain attribute have along with
>> it a certain other  attribute," which is exactly what is asserted in D.
>> Either D or D1 amounts to a statement of the dictum de omni (in one the
>> s =(=. p plays the part of a major premise, in the other of a minor
>> premise); and Mill agrees with De Morgan that to give any real meaning
>> to the dictum de omni, we must consider it not as an axiom but as a
>> definition. In speaking of the relation s < p in words, it is necessary
>> to use the language either of the term or of the proposition; but
>> everything that has just been said of subject and predicate must be
>> taken as having also been said, in terms of premise and conclusion, or
>> of antecedent and con-sequent (for it makes no difference for this
>> purpose whether, in 'S-is-followed-by P,' the following is of a logical
>> or of an extra-logical nature)."
>>
>>
>> Being distracted with other issues, I did not, regrettably, record the
>> source, however. So, if anyone recognizes this, would they please post
>> the bibliographic data.
>>
>>
>> ----- Message from viniroma <at> yahoo.com ---------
>>     Date: Thu, 1 Jul 2010 03:16:47 -0700 (PDT)
>>     From: Vinícius Romanini <viniroma <at> yahoo.com>
>> Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>> Subject: Re: [peirce-l] Deduction versus Induction
>>       To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>>
>>
>>> That´s very interesting, Irving.
>>> I would argue on the same lines as Mill, if I understood his claim
>>> correctly.
>>> I attach a unpublished paper that I delivered last year at the
>>> Pragmatism meeting in São Paulo in which I build this argument on a
>>> Peicean basis.
>>>
>>> Best,
>>>
>>> Vinicius Romanini, Ph.D.
>>> Professor of Sciences of Communication
>>> School of Communications and Arts
>>> University of Sao Paulo, Brazil
>>> www.minutesemeiotic.org
>>>
>>> --- On Thu, 6/17/10, Irving <ianellis <at> iupui.edu> wrote:
>>>
>>>
>>> From: Irving <ianellis <at> iupui.edu>
>>> Subject: Re: [peirce-l] Deduction versus Induction
>>> To: "Peirce Discussion Forum" <peirce-l <at> lyris.ttu.edu>
>>> Date: Thursday, June 17, 2010, 6:17 PM
>>>
>>>
>>>
>>> Tom,
>>>
>>> I apparently missed one of the initial points, which I thought was
>>> whether every syllogism is a petitio principia. I know that Mill
>>> asserted both that the syllogism is de facto a petitio principii, and
>>> that all logical inferences, including those that pass for syllogisms,
>>> are ultimately
>>> empirical.
>>>
>>> I think it was probably also Mill who perhaps conflated the these two
>>> claims, to argue, consequently, that all arguments that are
>>> information-producing, rather than merely peitios, are inductive --and
>>> that Mill was seeking to render deductive argument as a subclass of
>>> inductive logic, i.e., attempting to establish an ars inveniendum.
>>>
>>>
>>> ----- Message from tgollier <at> gmail.com ---------
>>>     Date: Thu, 17 Jun 2010 12:11:52 +0200
>>>     From: Tom Gollier <tgollier <at> gmail.com>
>>> Reply-To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>>> Subject: Re: [peirce-l] Deduction versus Induction
>>>       To: Peirce Discussion Forum <peirce-l <at> lyris.ttu.edu>
>>>
>>>
>>>> Irving,
>>>>
>>>> Those are intriguing questions and contrasts, but my concern remains with
>>>> Burke's argument. Is it ? as it appears to me to be ? a question-begging
>>>> induction masquerading as a deduction?
>>>>
>>>> Tom
>>>>
>>>> On Tue, Jun 15, 2010 at 8:49 PM, Irving <ianellis <at> iupui.edu> wrote:
>>>>
>>>>>
>>>>> Mill wanted to claim that the syllogism is a petitio principii. That
>>>>> was my only point in my response to Burke's assertion that the
>>>>> particular argument being discussed "is masquerading as a deduction by
>>>>> begging the question". I was at this conjucture neither defending nor
>>>>> contesting Mill's assertion, but merely rendering an historical point.
>>>>> (Mill's other point in this regard was that, at bottom, all logical
>>>>> inferences, including those that pass for syllogisms, are ultimately
>>>>> empirical.)
>>>>>
>>>>> If we rewrite the BARBARA syllogism as an implication, as Peirce,
>>>>> MacColl, Frege, and Russell did; thus: If A implies B and B implies C;
>>>>> therefore A implies C; or as a subsumption, as Peirce and Schroeder
>>>>> did: If A is included in B and B is included in C, therefore A is
>>>>> included in C. In that case, there are those (e.g. Mill) who would
>>>>> argue that the conclusion is already inherently included in the
>>>>> conjunction of the premises.
>>>>>
>>>>> Now Tom Gollier asks: "if "EVERY syllogism is question-begging," what
>>>>>
>>>>> better way to masquerade as a deduction?"
>>>>>
>>>>> My questions -- as an historian who is not a philosopher -- now are:
>>>>> (1) Is the point of Gollier's question to suggest that question-begging
>>>>> syllogism is identical with deduction (or that the set of syllogisms is
>>>>> coextensive with the set of deductions)?; (2) assuming that every
>>>>> question-begging syllogism is a deduction, does it necessarily follow
>>>>> that every deduction is a question-begging syllogism?; and (3) are
>>>>> there syllogisms which are not question-begging, and are there some
>>>>> deductions that are not syllogisms? (Note that this not necessarily the
>>>>> same as asserting, as Frege, e.g. did, that there are syllogisms that
>>>>> are valid which are not valid in, say, first-order functional calculus.)
>>>>>
>>>>>
>>>>>
>>>>> ----- Message from tgollier <at> gmail.com ---------
>>>>>    Date: Mon, 14 Jun 2010 09:35:59 +0200
>>>>>
>>>>>
>>>>
>>>> -----
>>>> **
>>>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>>>> ** the central pointer and guide for Peirce resources on the web:
>>>> **            http://csp3.blogspot.com/
>>>> ** -------
>>>> **
>>>> ** If you want to cancel your subscription to PEIRCE-L
>>>> ** send a message to the list manager at:
>>>> **
>>>> **      joseph.ransdell <at> yahoo.com
>>>> **
>>>>
>>>>
>>>> joseph.ransdell <at> yahoo.com
>>>
>>>
>>> ----- End message from tgollier <at> gmail.com -----
>>>
>>>
>>>
>>> Irving H. Anellis
>>> Visiting Research Associate
>>> Peirce Edition, Institute for American Thought
>>> 902 W. New York St.
>>> Indiana University-Purdue University at Indianapolis
>>> Indianapolis, IN 46202-5159
>>> USA
>>> URL: http://www.irvinganellis.info
>>>
>>>
>>> -----
>>> **
>>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>>> ** the central pointer and guide for Peirce resources on the web:
>>> **            http://csp3.blogspot.com/
>>> ** -------
>>> **
>>> ** If you want to cancel your subscription to PEIRCE-L
>>> ** send a message to the list manager at:
>>> **
>>> **      joseph.ransdell <at> yahoo.com
>>> **
>>>
>>>
>>> joseph.ransdell <at> yahoo.com
>>>
>>>
>>>
>>>
>>> -----
>>> **
>>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>>> ** the central pointer and guide for Peirce resources on the web:
>>> **            http://csp3.blogspot.com/
>>> ** -------
>>> **
>>> ** If you want to cancel your subscription to PEIRCE-L
>>> ** send a message to the list manager at:
>>> **
>>> **      joseph.ransdell <at> yahoo.com
>>> **
>>>
>>>
>>> joseph.ransdell <at> yahoo.com
>>
>>
>> ----- End message from viniroma <at> yahoo.com -----
>>
>>
>>
>> Irving H. Anellis
>> Visiting Research Associate
>> Peirce Edition, Institute for American Thought
>> 902 W. New York St.
>> Indiana University-Purdue University at Indianapolis
>> Indianapolis, IN 46202-5159
>> USA
>> URL: http://www.irvinganellis.info
>>
>>
>>
>> -----
>> **
>> ** Click on the following URL link for THE PEIRCE BLOG, which is
>> ** the central pointer and guide for Peirce resources on the web:
>> **            http://csp3.blogspot.com/
>> ** -------
>> **
>> ** If you want to cancel your subscription to PEIRCE-L
>> ** send a message to the list manager at:
>> **
>> **      joseph.ransdell <at> yahoo.com
>> **
>>
>>
>> joseph.ransdell <at> yahoo.com
>>
>>
>>
>>
>
>
> -----
> **
> ** Click on the following URL link for THE PEIRCE BLOG, which is
> ** the central pointer and guide for Peirce resources on the web:
> **            http://csp3.blogspot.com/
> ** -------
> **
> ** If you want to cancel your subscription to PEIRCE-L
> ** send a message to the list manager at:
> **
> **      joseph.ransdell <at> yahoo.com
> **
>
>
> joseph.ransdell <at> yahoo.com
>
>

----- End message from devorejd <at> umich.edu -----

Irving H. Anellis
Visiting Research Associate
Peirce Edition, Institute for American Thought
902 W. New York St.
Indiana University-Purdue University at Indianapolis
Indianapolis, IN 46202-5159
USA
URL: http://www.irvinganellis.info

-----
**
** Click on the following URL link for THE PEIRCE BLOG, which is
** the central pointer and guide for Peirce resources on the web:
**            http://csp3.blogspot.com/
** -------
**
** If you want to cancel your subscription to PEIRCE-L
** send a message to the list manager at:
**
**      joseph.ransdell <at> yahoo.com
**

joseph.ransdell <at> yahoo.com

```
7 Jul 00:09 2010

### Re: Induction, Deduction, or Abduction: was Deduction versus Induction

Ben, list,

I'd like to shift the emphasis for now to a consideration of some other questions relating to the 6 possible paths (vectors) through the categories. For anyone not familiar with the six vectors, but interested in this aspect of tri-categorial analysis, you might take a look at my paper outlining vector analysis. http://www.cspeirce.com/menu/library/aboutcsp/richmond/ccsarisbe.pdf

Remembering that (for good reason, I believe) the three categories are invariably placed by me around the trikon in this way:

1ns
|> 3ns
2ns

here's a diagram of the six vectors with the descriptive names I've given them. Note that since I last used this diagram in a paper in 2006, I've tended to refer to 'analysis' (which here refers in particular to tri-categorial analysis) as the vector of 'involution'. Peirce used both terms interchangeably in "The Logic of Mathematics" paper.

So far we've only been discussing the vectors/paths of the three inference patterns. One question which immediately comes to mind is why do the three inference pattens follow just these paths: deduction--vector of 'involution'; induction--'determination'; abduction--'representation? It is perhaps helpful here to consider what else follows each of these same three paths.

Not only deduction, but categorial analysis and involution (in Peirce's sense, as in the derivation of the categories in "The Logic of Mathematics") follow the path of analysis/involution. And like induction, semiosis (in the sense of the object determines the sign for the interpretant sign) follows the vector of determination. Abduction follows the vector of representation, where my favorite examples are the creation by a scientist or logician of a diagram of relations pertaining to some universe of experience, or an artist's creation of some work referencing the real or some imaginary world. While you can imagine that I have more to say on this matter, to keep this message short, both here and below I'll make just the most cursory observations.

Before moving from the inference patterns to the three other vectors, it may be interesting to observe how induction ('determination' vector) and abduction  ('representation') "point in opposite directions," as Peirce remarks. While in terms of their visually opposite direction this is rather obvious in the diagram above, the logical question is, what does this imply for the relationship holding between the two? (I have some ideas about this, but won't get into it here.) One can also clearly see that deduction ('analysis') and abduction ('representation') mirror each other's path. This might hint as to how the deductive path is related to the other two (which, again, are the reverse of each other)? I have elsewhere suggested that it also seems significant that each of the inference patterns either commences at or, in the case of induction, arrive at 3ns (while the remaining three vectors, not yet discussed, either commence at or arrive at 1ns).

While there is much more to be said here, I'd like to move on to the three other vectors, these being: the vector of 'order' (where the quintessential example is Hegelian dialectic, or Peirce's "something, other, medium"); the vector of 'process' (the most important examples in Peirce being evolution and inquiry); and finally, the vector of 'aspiration' (I finally must admit that this is the only one of the 6 which Peirce does not explicitly connect to a tri-categorial path, although there are hints and suggestions throughout his work that this vector exists and is important). My principal example of 'aspiration' is a community hoping that its concerted efforts--one has to assume pragmatism or critical commonsense undergirding this effort--will lead to its success.

So the remaining three vectors (with examples) are as follows (the small letters, a, b, c, showing the path):

Vector of order (ex: dialectic);

(a) 1ns, something (thesis),
|> (c) 3ns, medium (synthesis).
(b) 2ns other (antithesis);

Vector of process (ex: evolution, or, inquiry:)

(a) 1ns, chance sporting, or, abduction,
|> (b) 3ns, new habit formation, or, deduction;
(c) 2ns evolutionary change, or, induction.

Note that only these two of the six vectors commence at 1ns, but I won't now comment on what I see to be the implications of this except to say that there is one sense in which both the vectors of 'order' and 'process'--quite clearly the vector of order, can be seen to be logically primitive in relation to the others. Order, in the sense of ordinal, is exactly this primitive: firstly, 1ns, secondly, 2ns, thirdly, 3ns. Peirce himself makes this point in his discussion of the logical derivation of the categories in "The Logic of Mathematics."

In a  tri-categorial Universe there is, however, a way in which, given the reduction thesis which denies 4ns, etc., 3ns can be seen, and even necessarily, to be 1st, since it involves both the other universal categories. For this reason this path represents categorial analysis and acts as the vector of 'involution'. For Peirce, unlike Hegel, the other categories, 2ns, and 1ns, are NOT Aufheben, and so, the vector of involution:

(c) 1ns.
|> (a) 3ns, involves 2ns, and 1ns,
(b) 2ns, involves 1ns;

Again, this is exactly the path used to analyze deduction in the earlier discussion of the three inference patterns. Now how is it that the Peircean categories are derived in just this way, that is, in consideration of involution? And what is the relationship holding between 'involution' and 'order' (which, like abduction and induction "point in opposite directions").

This sixth and final vector is, as far as I can tell, the only one that Peirce didn't explicitly connect to the categories, nor, a fortiori, analyze vectorially. This is, in a sense, the "missing" vector which, however, represents a thread running through much of Peirce's work; namely, that it is possible for us, the community of seekers after "the evolution of consciousness" or "the fulfillment of our human destiny" or "the growth of scientific and other knowledge" (or however one might want to characterize a shared world-meaning evolving because we've incorporated enough pragmatic logic and critical discipline into our acting as human beings who would and do put their shoulders to such a great human task, that is, wherever and whenever it is "up to us" to do so, as Peirce puts it).

Perhaps a simpler way of saying this is that there is, for Peirce, the hope that humanity may become more and more pragmatistic with all the intellectual, critical, ethical, etc. growth that that term implies.  Although most signs aren't very promising, there remains for Peirce the hope that we may yet begin to apply critical commonsense to our consideration of those things which are of greatest importance to us (this is why pessimism in this matter is decidedly illogical and counter-productive). So this vaguest of the six vectors appears to be one involving our own human striving, and so this is why I call it the vector of 'aspiration'. For if we do have a vocation, a true "calling" as a species (and this is by no means certain), we may some day be able to conceive together something like a human summum bonum. It is my sense that if we cannot do that together, then it is practically inconceivable that we could ever make much progress on such "wicked problems" that everywhere surround and haunt us. So, in this sense, the vector of aspiration may represent--in a diagram completing, in a way, all the rest--why I am a Peircean pragmatist.

Vector of aspiration:

(c) 1ns, in order to achieve our summum bonum.
|> (b) 3ns, to define and connect our shared intelligent purpose;
(a) 2ns, The community of common human purpose strives,

Rather, this represents the ultimate form this path might take. Meanwhile, smaller communities of interest can achieve small goals which might help lead us to this ultimate one. The vector of aspiration reverses the direction of evolution in one sense, and I believe that it is precisely in the sense that we have the potential to influence our own human evolution of consciousness by the kinds of self- and other-control which follow from the deepest meanings implied by Pragmaticism as a principle and method of right thinking and conduct.

Best,

Gary

>>> "Gary Richmond" <richmondga <at> lagcc.cuny.edu> 7/5/2010 4:21 PM >>>
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'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.

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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### Re: Deduction versus Induction

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13 Jul 23:51 2010

### Re: Induction, Deduction, or Abduction: was Deduction versus Induction

Gary, list,

It would be a lot to respond to both of your recent posts at once, so I'll start with the earlier one. There was an older post in which I forgetfully spoke of "syllogism" while thinking of "categorial syllogism." I've been boning up on the terminology again! Anyway, sometimes transformations across inference modes get like hopskotch, and I think it's good to keep those things straightened out. But I kept running into at least mildly interesting side lights along the way, thing on which I hadn't focused before.

Taking things not in their original order:
>> [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."

>[GR] 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.
You're right. I was careless in my wording. I was thinking that Peirce includes in logic not only deduction and induction but also hypothetical inference which is hard to formalize in detail. The full sweep across inference modes was what I had in mind, but I mistakenly made it sound like exact deductive logic was not part of Peirce's conception of logic. On top of that, I simply forgot about the logica utens/docens distinction, which to the contrary is relevant in exactly the way that you describe.

>[GR] 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."
Thank you. It'll take a while. At this stage, I'm caught up in what I don't understand about it, not in what I'm coming to understand.

>>[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."

>[GR] 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 think that I got the retroductions right in Peirce's terms. The problem which you see with the retroduction, the problem of the possibility that Socrates could turn out to be a cat or, more generally, that the retroduction's conclusion could prove false even if its premisses are true, just reflects that which Peirce always emphasized, the insecurity of hypothetical inference a.k.a. abduction a.k.a. retroduction. It sounds like you're thinking of deduction.

Now, in the categorical-syllogistic formulations for example in 1878 in "Deduction, Induction, and Hypothesis," one can transform a deduction into a hypothetical inference by making the result a premiss and making the case the conclusion. In short, result and case switch places. And that's what I did.

 Deduction: Rule: All men are mortal. Case: Socrates is a man. Ergo: Result: Socrates is mortal. Retroduction: Rule: All men are mortal. Result: (It is observed that) Socrates is mortal. Ergo: Case: (Hypothetically) Socrates is a man.

One could trace this out in terms of the beans examples. There are at least two ways to schematize them, which gets into some possibly interesting aspects of Peirce's expository aims. Rather than taking "beans from this bag" as the syllogistic predicate term as one usually would, one might take it as the compound of "from this bag" as the predicate, and "beans" as a kind of extra term appearing in all three of the syllogism's propositions. (Note, "beans" is the grammatical subject, but I'm talking about subjects, predicates, and middle terms in the sense traditional for categorical syllogisms. I've been boning up on the terminology since my recent forgetfulness about it.)

P = (predicate). S = (subject). M = (middle term). Z = ("extra" term). Propositional schemata are underlined (gmane won't render the underlines). (Note: if we treat "beans" as a separate and extra term, then it's not a categorical-syllogistic term, since then it appears as a separate term in all three propositions in the syllogism.)

 Deduction:   Rule: All (M) beans-from-this-bag are (P) white. All M is P. Case: (S) These-beans are (M) from-this-bag. All S is M. Ergo: Result: (S) These-beans are (P) white. All S is P.   Or (schematized in a less usual way):   Rule: All (Z) beans (M) from-this-bag are (P) white. All ZM is P. Case: (S) These (Z) beans are (M) from-this-bag. All ZS is M. Ergo: Result: (S) These (Z) beans are (P) white. All ZS is P. Retroduction:   Rule: All (M) beans-from-this-bag are (P) white. All M is P. Result: (S) These-beans are (P) white. All S is P. Ergo: Case: Hypothetically,  (S) these-beans are (M) from-this-bag. All S is M.   Or (schematized in a less usual way):   Rule: All (Z) beans (M) from-this-bag are (P) white. All ZM is P. Result: (S) These (Z) beans are (P) white. All ZS is P. Ergo: Case: Hypothetically,  (S) these (Z) beans are (M) from-this-bag. All ZS is M.

The restriction to beans across the board makes the examples of induction and hypothetical inference more immediately appealing and plausible, and reflects at least somewhat the reality that, in practice with induction and hypothetical inference, one typically will need more restrictions and qualifications than just those of simplest subject, predicate, and middle in order to make a reasonably good inference. Well, this has included one of those "mildly interesting side lights" that I mentioned at the start.

In the mortal-Socrates-men syllogism one can add a word such as "philosophical" or "Athenian" to play the role of the word "beans" (whether we count the word as an extra term or instead weave it into subject, predicate, etc.) The choice of the word "philosophical" seems to steer us away from the Socrates-the-cat problem in particular (unless, say, E.T. aliens land and teach our cats philosophy), but that problem would resurge if we were to use the word "Athenian" instead. But, again, the _general_ problem of an insecure conclusion from true premisses remains throughout yet is not a problem that disqualifies an inference from being a hypothetical inference. Hypothetical inference does not claim to be secure. The hypothetical conclusion that _these beans_ are _from this bag_ could well be false too, even when the premisses are true.

We should remember that the ordering of premisses in those syllogisms does not affect the syllogisms' validity (or invalidity).In the classification of (deductive) categorical syllogisms in all four figures, it's a matter of tradition to put the _major_ premiss (which always contains the deductive conclusion's _predicate_ and the middle term in some order and in some quantification) before the _minor_ premiss (which always contains the deductive conclusion's _subject_ and the middle in some order and in some quantification). As far as validity/invalidity goes, one could put the minor premiss first and the major premiss second.  On the first page http://books.google.com/books?id=u8sWAQAAIAAJ&pg=PA470 of "Deduction, Induction, and Hypothesis," Peirce instances Barbara with the minor premiss first and the major premiss second. (To erect separate classifications for each of the two ways would usually be trivial, leading merely to repeating the classificational structure of the moods.)

In Bocardo (OAO in the 3rd figure) and in Disamis and Dimaris (IAI in the 3rd and 4th figures, respectively), the major premiss is particular, and seems to be the _case_ while the minor premiss is universal and seems to be the _rule_.

 Bocardo: Some M is not P. All M is S. Ergo, some S is not P. Disamis: Some M is P. All M is S. Ergo, some S is P. Dimaris: Some P is M. All M is S. Ergo, some S is P.

For the purposes of your vectors, I think that you could:
• Simply switch the order of the premisses in Bocardo, Disamis, and Dimaris.
• Or you could hold that there are two vectors for deduction, perhaps indeed two vectors per inference mode. This could pertain to what vectorial significance you might see in the roles of syllogistic predicate, subject, and middle.
• Another possibility is to consider cases where a deductive categorial syllogism lends itself to interpretation as a kind of _timid form_ of another inference mode, as Peirce says of Baroco and Bocardo http://books.google.com/books?id=u8sWAQAAIAAJ&pg=PA474 in "Deduction, Induction, and Hypothesis." I don't know how that would take care of all three currently "unused" vectors, but it's just a thought that I just had. Maybe there's also a case where an induction seems like a timid retroduction (induction of characteristics?). If this pans out, then it comes from another one of those interesting side lights that I mentioned. If it doesn't pan out, well, then - hey, quick, look over there!
If you don't want to assign all six vectors to inference modes or sub-modes, then it might be useful to make explicit why, for vectorial purposes (and not just syllogistic tradition with Barbara and the like), the deductive categorial syllogism proceeds rule-case-result rather than case-rule-result, and, _mutatis mutandis_, likewise for the other two inference modes. Maybe you've already given a reason somewhere, I don't remember. In the deductive and retroductive modes, the reason seems like it could be that, if one already knows a rule and either a case or a result, then one will at least in simple or normal situations have already known the rule before learning of the result or case. In that sense, the rule would come first. If the reasoner learns the rule _after_ the case in deduction or _after_ the result in retroduction, that suggests that a whole lot of relevant concurrent reasoning by the reasoner (to obtain the rule) is being omitted from the formulation - the situation seems complicated just under the surface.

>[GR] 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.

>[GR] 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, rathe limiting it to the "surprising" observation formulation, a formulation I find in itself somewhat limiting).
 1903 formulation (so that readers don't need to scroll elsewhere to find it) 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.
There's nothing wrong with _presenting_ an inference's propositions in various orders as long as it is clear what one is doing. In the 1903 formulation Peirce put 1st the surprising observation and 2nd the proposed application of an already-known rule or norm. In 1878 he put 2nd the very curious circumstance and 1st the already-known rule or law of which said curious circumstance will appear as a case in the conclusion. In your vectors for all three inference modes the premisses' ordering is (I take it) in accordance with what was known first, or at least what is supposed to be known first in normal or maybe simplest situations. In the 1903 formulation Peirce (intentionally or not) complies with that sense of ordering by replacing the already-known rule/norm with a proposal for its result as "a matter of course" given a case, a proposal that, in the formulation, only alludes to the applied rule/norm (the "course"). I simply make the reference explicit.

I think that the compromise or wedding between the two forms is feasible insofar as Peirce did not radically revise his conception of retroduction, except for such radicalness as might be considered to be involved in his coming to distinguish retroduction firmly from the induction of characteristics, a form of inference which the 1878 hypothetical inference form seems capable of including (which capability of inclusion may be part of why in 1902 he said about the syllogistic forms that he had made them "more fundamental than they really are." ('Minute Logic', CP 2.102, c. 1902 http://www.helsinki.fi/science/commens/terms/hypothesis.html )).

But there's continuity between the two forms. Even back in 1878 in "Deduction, Induction, and Hypothesis" he characterized hypothetical inference as arising from the observation of "some very curious circumstance." He keeps the idea of the curious, the surprising, etc. In 1911 in that context he speaks of the "incomprehensible," the "extremely complicated" and the "at least surprising." (Quotes further down.). His mention of _complication_ seems to reflect the emphasis which he had come to put on a hypothesis's plausibility as having to do with (complication's opposite) _simplicity and naturalness_. The point of all those things is not some emotion like that of puzzlement or surprise per se at complication or unusualness. The point for Peirce, I think, is that retroduction's purpose is _to explain_, and to explain observations about which one _actually_ feels that they need to be explained. Its purpose is to answer - or to propose answers to - questions involved in actual doubts, not mere verbal doubts which, in "The Fixation of Belief" and elsewhere, he held to be fruitless. That coheres with his putting retroduction as inquiry's first stage - his view (as expressed in "A Neglected Argument for the Reality of God") is that all genuine inquiry begins with surprising observations, observations that cause actual doubts.

You said that you find the 1903 formulation limiting. If by that you meant its particular _expression_, then Peirce in 1911 expressed a tendency to agree with you, and I suspect that he agreed with you earlier than that about it. But the general idea of a connection between surprise and retroduction should not seem too limiting as a rendition of Peirce's view, given that it is an aspect of Peirce's idea that retroduction aims to explain things that one actually feels need to be explained. As to Peirce's having more to say about retroduction in 1903, well, yes, of course, and I never suggested otherwise. But, what did he say in 1903 (or in any year) that _countervails_ against his seeming to hold as a simple rule (i.e., not as only sometimes true) that retroduction is inference trying to explain actually surprising or puzzling observations?

1903 1878, with premisses' order reversed
The surprising fact, C, is observed; Result: These beans are white ("very curious circumstance")
But if A were true, C would be a matter of course, Rule: All the beans from this bag are white.
Hence, there is reason to suspect that A is true. Ergo Case: (Possibly) These beans are from this bag.

The surprising fact (C) that (result) these beans are white is observed ("very curious circumstance").
But, if (A) these beans were from this bag ((rule) all of whose beans are white), then it would be a matter of course (C) that these beans are white.
Hence there is reason to suspect (A) that (case) (possibly) these beans are from this bag.

"Hypothesis is where we find some very curious circumstance, which would be explained by the supposition that it was a case of a certain general rule, and thereupon adopt that supposition. Or, where we find that in certain respects two objects have a strong resemblance, and infer that they resemble one another strongly in other respects."
In the second sentence in the above quote, he seems to have inference by analogy and/or induction of characteristics in mind.

Peirce, 1911 in 'A Logical Criticism of the Articles of Religious Belief', MS 856: 3-4, 1911) http://www.helsinki.fi/science/commens/terms/retroduction.html
By Retroduction I mean that kind of reasoning by which, upon finding ourselves confronted by a state of things that, taken by itself, seems almost or quite incomprehensible, or extremely complicated if not very irregular, or at least surprising; we are led to suppose that perhaps there is, in fact, another definite state of things, because, though we do not perceive any unequivocal evidence of it, nor even of a part of it, (or independently of such evidence if it does exist,) we yet perceive that this supposed state of things would shed a light of reason upon that state of facts with which we are confronted, rendering it comprehensible, likely (if not certain,) or comparatively simple and natural.
I could multiply the quotes but also pertinent remains the strong link of the beginning-in-surprise/puzzlement/etc. idea with the idea that abduction's purpose is to explain things about which one actually feels that they need to be explained - thus, to offer resolutions of actual doubts, not merely verbal doubts, an important issue for Peirce (e.g., his opposition to Cartesian foundationalism).

If we reverse the order of the 1903 premisses, like so:

If A were true, C would be a matter of course.
The surprising fact, C, is observed.
Hence there is reason to suspect that A is true.

we get something that may remind us of the deduction of consequences of a hypothesis. Then C seems not the original surprising observation, instead it seems some predicted consequence from the hypothesis A, a consequence which would _also_ be surprising except on the hypothesis A, thus tending to support hypothesis A which was formed in order to explain some original surprising observation. (So one might prefer to say, "hence there is _further_ reason to suspect that A is true.") But the inference is not a deduction, it's still a retroduction. One might object that it combines retroductive and deductive stages or parts of stages of inquiry in a way that is not helpful to clarity. On the other hand it gets at the deduction's resting on the retroductive conclusion, and it gets at the idea that the hypothesis is helped by predicting not only things which we already know to be true, but also testable would-be-surprising things that we don't already know to be false. That's what happened with Hamilton's prediction of external conical refraction, Einstein's prediction of light bending around stars, etc. So, though it doesn't count as representing one of the three inferential stages of inquiry, it still casts light. I'd argue that what I'm doing with this is in the Peircean spirit of looking at permutations and seeing what they mean, seeing what they resemble, etc., even if the lookings that I'm doing are not so well carried out as his were.

Best, Ben

----- Original Message -----
From: Gary Richmond
To: Peirce Discussion Forum
Sent: Monday, July 05, 2010 4:21 PM
Subject: Re: [peirce-l] Induction, Deduction, or Abduction: was Deduction versus Induction

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

[For previous posts, see
or

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14 Jul 12:55 2010

### Help with a quote

Hi everybody,

I am having difficulties to confirm the quote bellow from the original source. Does anyone have the book at hand and could help?

Thanks a lot,
Vinicius

“We stipulate that the following is a necessary and sufficient condition for something to be a semiosis: A interprets B as representing C. In this relational characterization of semiosis, A is the Interpretant, B is some object, property, relation, event, or state of affairs, and C is the meaning that A assigns to B.” (Posner et al., 1997, p 4).

From: Posner, Roland; Robering Klaus and Sebeok Thomas (1997). Semiotik/Semiotics: A Handbook on the Sign-Theoretical Foundations of Nature and Culture. Volume 1. Berlin: Walter de Gruyter, p 4.

Vinicius Romanini, Ph.D.
Professor of Sciences of Communication
School of Communications and Arts
University of Sao Paulo, Brazil
www.minutesemeiotic.org

--- On Wed, 7/7/10, Vinícius Romanini <viniroma <at> yahoo.com> wrote:

From: Vinícius Romanini <viniroma <at> yahoo.com>
Subject: Re: [peirce-l] Deduction versus Induction
To: "Peirce Discussion Forum" <peirce-l <at> lyris.ttu.edu>
Date: Wednesday, July 7, 2010, 2:26 AM

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Gmane