Helmut, You wrote:
HR: What I find interesting, is, that between deduction, induction and abduction, there are inversions in the sequence of rule-case-result: Deduction: Rule-case-result Induction: Case-result-rule Abduction: Result-rule-case. This is like in music, like with a trichord and its inversions. Yes, it is like a trichord in music, and I like your laying it out in this way. You continued: HR: You can do the same with the beans-in-a-bag-example, though originally, in Peirces version, it is not written in this way that shows the inversions. Actually, Peirce does show the inversion, although not in the same way that you or I did in diagrams at 2.622 (for induction), and for all three types of inference 2.623. HR: I hope i did not mess everything up, like the nesses and the middle term and the vectors. Sorry if i did. Perhaps I just chose a different way of arranging things- good or bad, i dont know. Not at all! What I like about my trikonic diagrams is that, besides showing inversions (no doubt better shown by broken arrows connected to the three vertices of the triangle which I can't produce in ordinary type but which I've included in certain ppt shows accompanying talks I've given), my diagrams in addition show categoriality, vectorial movement through the categories (paths or orders through them), show the place of the middle term in each inference pattern, and offers the conclusions of each as either necessary, possible, or probable--all of this in a single diagram. I think there are possibly many ways of laying these inference patterns out (I've experimented with several myself) which can help us understand them in relation to deduction and to each other. Best, Gary R [image: Gary Richmond] *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *C 745* *718 482-5690* On Thu, Apr 28, 2016 at 1:22 PM, Helmut Raulien <[email protected]> wrote: > Gary, list, > in my understanding, the conclusion is always the last of the three lines, > and the three lines are written underneath each other according to time, in > the sense of what comes first to mind, what then and what then, so for me > it would go like this: > > Deduction: > Rule: All men die > Case: Jesus was a man > Result: Jesus has died, necessarily (necessary conclusion) > > Induction: > Case: Jesus is a man > Result: Jesus has died > Rule: All men die (probably, as one more example is added to all the > previous examples of men having died- probable conclusion) > > Abduction: > Result: Jesus has died > Rule: All men die > Case: Jesus was a man (possibly- possible conclusion). > > What I find interesting, is, that between deduction, induction and > abduction, there are inversions in the sequence of rule-case-result: > Deduction: Rule-case-result > Induction: Case-result-rule > Abduction: Result-rule-case. > > This is like in music, like with a trichord and its inversions. You can do > the same with the beans-in-a-bag-example, though originally, in Peirces > version, it is not written in this way that shows the inversions. > > I hope i did not mess everything up, like the nesses and the middle term > and the vectors. Sorry if i did. Perhaps I just chose a different way of > arranging things- good or bad, i dont know. > Best, > Helmut > > *Gesendet:* Mittwoch, 27. April 2016 um 23:45 Uhr > *Von:* "Gary Richmond" <[email protected]> > *An:* Peirce-L <[email protected]> > *Betreff:* [PEIRCE-L] Three inference patterns > List, > > Not to be taken too seriously--as this was just a bit of play which > occupied me for an hour or so today-- but based on the bean example, here's > how I see the three inference patterns and their paths (vectors) through > the 3 categories. > > *Inference patterns and categoriality:* > 1ns, Result (for deduction only) == 'Character' (for abduction/induction) > |> 3ns, Rule > 2ns, Case > > Middle term: That which is the middle term in deduction is put in *bold *in > all 3 patterns > Vectorial order: In each case start at * and conclude at *** > > *Deduction* (vector of involution): > ***3rd, 1ns: *conclusion*-It is NECESSARY that Jesus die. > |> *1st, 3ns: All *men* die, > **2nd, 2ns: Jesus is a *man*; > > *Abduction* (vector of representation): > **2nd, 1ns: Jesus died; > |> *1st, 3ns: I make the supposition that all *men* die, > ***3rd, 2ns: *conclusion*-It is POSSIBLE that Jesus was but a *man*. > > *Induction* (vector of determination): > **2nd, 1ns: Jesus dies; > |> ***3rd, 3ns: *conclusion*-It is PROBABLE that all *men* die. > *1st, 2ns: Jesus is a *man, * > > Well, again, one doesn't want to make too much of this except to note that > both deduction and abduction begin with a rule (in abduction, a mere > 'supposition'), while induction concludes with a rule (which has some > probability). > > Best, > > Gary R > > ----------------------------- PEIRCE-L subscribers: Click on "Reply List" > or "Reply All" to REPLY ON PEIRCE-L to this message. 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