Frederik, lists, In the famous 'beans' example, Peirce make induction and abduction to be the obverse of each other.
Note: below I've substituted "Character" for result since "Result" only works for Deduction. [Indeed, Peirce comments: "But, because all inference may be reduced in some way to Barbara, it does not follow that this is the most appropriate form in which to represent every kind of inference. On the contrary, to show the distinctive characters of different sorts of inference, they must clearly be exhibited in different forms peculiar to each. Barbara particularly typifies deductive reasoning; and so long as the is is taken literally, no inductive reasoning can be put into this form. *Barbara, is, in fact, nothing but the application of a rule. The so-called major premiss lays down this rule; as, for example, All men are mortal. The other or minor premiss states a case under the rule; as, Enoch was a man. The conclusion applies the rule to the case and states the result: Enoch is mortal. All deduction is of this character; it is merely the application of general rules to particular cases.* (emphasis added, CP 2.630] DEDUCTION. Rule.--All the beans from this bag are white. Case.--These beans are from this bag. .·.[Character].--These beans are white. INDUCTION. Case.--These beans are from this bag. [Character].--These beans are white. .·.Rule.--All the beans from this bag are white HYPOTHESIS. Rule.--All the beans from this bag are white. [Character].--These beans are white. .·.Case.--These beans are from this bag. I have occasionally argued this obverse relationship of induction to abduction from the standpoint of categorial vector analysis, associating 1ns with Character, 2ns with Case, 3ns with Rule. With Induction one begins at 2ns (some, existential case, say, these particular beans are from *this* bag), moves through 1ns (all of, say, a large sample of these beans have the character 'white'), arriving at 3ns (the 'rule' that *probably *all the beans in this bag are white). Abduction is the obverse. One begins at 3ns, the rule (we know the beans in this bag to be all white), moves through 1ns (the, perhaps, large number of beans we find on the table near it are *all *white--note: there may be other bags with other known mixtures of black and white beans), arriving at 2ns (it is the case that *possibly *all the beans found are from *this* bag). Interestingly, as does Abduction, Deduction also begins at 3ns (we know the beans in this bag to be all white), moves through 2ns, the case (we take a sampling of the beans from this bag), arriving at 1ns (all of this sample are *necessarily* white). So, all three inference patterns either commence or conclude at 3ns, the Rule. This may be of mere historical interest, but I thought I'd throw it into the mix of this quite interesting exchange. Best, Gary [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 Fri, Apr 24, 2015 at 5:38 PM, Frederik Stjernfelt <[email protected]> wrote: > Dear Howard, lists - > Not a bad description - > F > > Den 23/04/2015 kl. 15.24 skrev Howard Pattee <[email protected]>: > > At 12:57 AM 4/23/2015, Joseph Brenner wrote: > > Peirce's 'lumping' of the alleged opposites of induction and abduction is, > rather the recognition that the opposition between them is not so absolute, > and indeed they have 'a common feature'. Further, if the criterion for > judgement is only the effectiveness of the arguments they yield, this is > not the difference between yes and no. This is my answer to Howard's > question. > > > Thank you, Joseph, for a very pragmatic answer with which I agree. I still > prefer to think of induction and abduction as a case of *complementarity* -- > two logically incompatible views, both irreducible one to the other, but > both necessary in the search for truth.. > > >
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