Hi again!
Deduction, I think, is a matter of subsets-transitivity: Three sets: those who die (D), all men (M), Abraham (A)." M is element of D" is written "M E D". M E D + A E M --> A E D . For better understanding, I call the smallest set (Abraham): A, the next largest set (men) AA, and the largest set (those who die) AAA. Now the general form of deduction is: AA E AAA (rule) + A E AA (case) --> A E AAA (result).
To show that the de-degenerated induction is 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: All men probably die
Rule: Abraham is a man = AA E AAA with AA= Abraham, and AAA = men who die and men who dont die
Case: Abraham has died = A E AA with A = death and AA = Abraham. The set "Abraham" has only one element, so "death" is a nenessary trait of Abraham.
Result: All men probably die = A E AAA with A= death, and AAA = men who die and men who dont die. The probability lies in the fact, that AAA now contains one example of men who died.
Now to show, that the de-degenerated abduction is a deduction:
Rule: All men die = AA E AAA with AA = death, and AAA = possibility of being a man (set with one element, so "death" is a necessary trait of this element)
Case: Abraham has died = A E AA with A = Abraham and AA= death
Result: Abraham possibly was a man = A E AAA with A = Abraham and AAA = possibility of being a man
All a bit far fetched, I admit. What does not fit is being made to fit.
Best,
Helmut
Gesendet: Samstag, 07. Mai 2016 um 23:26 Uhr
Von: "Helmut Raulien" <[email protected]>
An: Peirce-L <[email protected]>
Betreff: [PEIRCE-L] rule-case-result, deduction, induction, abduction
Von: "Helmut Raulien" <[email protected]>
An: Peirce-L <[email protected]>
Betreff: [PEIRCE-L] rule-case-result, deduction, induction, abduction
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 (corrected): All men probably die (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
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