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
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
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