Dear list members (esp. Jerry, Jon, Gary...)
I have started a new thread, because this is a different way of sequencing the inferences, I have tinkered out, and I dont know how it might fit into the other threads, and if it is interesting. So far, I have not compared it yet to Peirce and to vectors. The starting point is deduction, with two possible sequences: rule-case-result (I suggest categorically rule with 2, and case with 1, so it would be 2-1-3). And 1-2-3, that would be case-rule-result.
The second point from which I start is, tentatively making inversions, like those of a musical trichord: The first inversion of 1-2-3 wold be 2-3-1, and the second 3-1-2.
The third starting point is the hypothesis, that induction and abduction are both degenerate deductions, and that you can make a deduction out of an induction by adding a "probably" to the conclusion (the third term), and out of an abduction by adding a "possibly". Now lets see, what all this leads to. I have chosen Abraham (A) instead of Socrates or Jesus for the example, because I thought it might be better to choose somebody who has died of old age and not of killing. So:
Deduction with rule-case-result:
Rule: All men die
Case: Abraham was a man (to be overcorrect, something about possible age and time of birth should be mentioned...)
Result: Abraham has died
First inversion of this:
Case: Abraham was a man
Result: Abraham has died
rule: all men die
This is induction. Can we now de-degenerate it into a deduction?
Rule: Abraham was a man- (well, not really a rule, but you may say, a definition. So a kind of rule, far fetched)
Case: Abraham has died (A case? Yes, why not.)
Result: Abraham probably was a man (Result of concluding. The statement is a necessary one, ok.)
second inversion:
Result: Abraham has died
Rule: All men die
Case: A. was a man
This is abduction. Now trying to de-degenerate it into deduction:
Rule: Abraham has died
Case: All men die
Result: A. possibly was a man
This does not work. We have to turn around the first and the second line:
Rule: All men die
Case: Abraham has died
Result: A. possibly was a man
Now it works. it is a deduction. The rule is arule, the case is a case, and it is necessary that Abraham possibly was a man.
So the inversion thing does not work with abduction. With abduction you have to swap the first with the second premise to de-degenerate it into deduction.
Now to the second possible sequence of deduction: Case-rule-result. I do not do all this again now. Try yourself if you like. What comes out of it is: The first inversion is abduction, and the second inversion is induction. And again it is with abduction, that the first and the second premise have to be changed with each other to de-degenerate it into a deduction.
Well, all this probably is pure sophism, but to give it a philosophic turn, one might guess two things: First: Gladly we cannot get a grip at nature too easily, eg. by just making inversions. Second: there is something special about abduction.
So much for that, I hope I did not write too confusing.
Best,
Helmut
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
