Jon, List, At CP 2.619, after commenting that "It is capable of strict proof [. . .] that all arguments whatever can be put into [*Barbara*]" Peirce gives a rather tortured example of an induction taking that form, putting it in the Procrustean bed of *Barbara*.
These beans are two-thirds white, But, the beans in this bag are (represented) by these beans; Ergo, The beans in the bag are two-thirds white. But then in the very next sentence he pointedly 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*." 2.620 Throughout this discussion I have been maintaining that this is precisely what he does--or, rather, is just about to do in the next paragraphs of this piece--in outlining the three inference patterns as he does at 2.623. But continuing the passage just quoted above, Peirce writes: "*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*." So, looking at the syllogism you quoted from 2.619 and your comment: Enoch and Elijah were men, all men die; Hence, Enoch and Elijah must have died. Here the order is Case/Rule/Result, as confirmed by how Peirce assigns these labels to the three propositions in CP 2.620, even though he there presents the Rule first. I would say that the passage I just quoted above makes clear that deduction *properly* (that is, as showing "the distinctive character" of its underlying logical structure) commences at the rule (the major premise), continues with a case (the minor premise), and concludes by stating the result. One can loosely (and I'd say, confusedly, even as Peirce sometimes does) reverse the order of major and minor premise as he does at 2.619. But for deduction "The so-called major premiss lays down this rule [and] the other or minor premiss states a case under the rule." NB: "a case *under* the rule," which is to say that one doesn't arbitrarily offer a case, but precisely one *under a rule*. Or one might say, it's clear that the rule *rules *in deduction no matter in what order you may informally set out the major and minor premises. And this is so as well for the other example you gave and commented on: All quadrangles are figures, But no triangle is a quadrangle; Therefore, some figures are not triangles. But here the reasoning is really this: *Rule.*--Every quadrangle is other than a triangle. *Case.*--Some figures are quadrangles. *Result.*--Some figures are not triangles. These two arguments are logically equivalent, and although the "translation" is given as Rule/Case/Result, the original is given as Case/Rule/Result. In other words, as I have said before, the order of the two premisses is irrelevant to the underlying logic. I continue to disagree as to what constitutes "the underlying logic." Again, I would say that it is important to keep in mind that when you finally lay out "the distinctive logical form" of deduction, as Peirce does in what you referred to as his "translation," that the Case will *necessarily *fall under the Rule, the first the minor, the second the major premise. *That* as I see it *is* the underlying logic which Peirce is at pains to make clear by translating the confused form into that which clearly shows the *subordination* of a case under a rule (and *not* the reverse). So, in this manuscript Peirce then next does what he had more or less promised to do at 2.260, namely, "to show the distinctive characters of different sorts of inferences [by clearly exhibiting the] different forms peculiar to each." And he does this by now laying out the *logical form* of all three inference patterns, inverting the deductive syllogism to arrive at the two synthetic inference patterns of induction and abduction. In sum, as I read him, Peirce lays out the *problem* (that while all arguments can be put into *Barbara*, that "they must clearly be exhibited in different forms peculiar to each") at 2.619-620, then offers his *solution* (revealing the "distinctive characters" of the three forms of inference by exactly offering the "different forms peculiar to each") at 2.621-624, most especially in the chart of deduction, induction, and hypothesis at 2.623. 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 <718%20482-5690>* On Thu, May 5, 2016 at 11:42 PM, Jon Alan Schmidt <[email protected]> wrote: > Gary R., List: > > I do not believe that we are talking past each other, just > sharing thoughts from our different perspectives. > > I acknowledge that CP 2.623 presents the Rule as the first premiss of both > Deduction and Hypothesis. However, does Peirce say anything there--or > anywhere else, for that matter--to indicate that this is the only "correct" > or "proper" sequence? On the contrary, that whole section on the three > forms of inference begins in CP 2.619 with a different example of deduction. > > Enoch and Elijah were men, all men die; > Hence, Enoch and Elijah must have died. > > Here the order is Case/Rule/Result, as confirmed by how Peirce assigns > these labels to the three propositions in CP 2.620, even though he there > presents the Rule first. > > *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. > > Then Peirce gives yet another example. > > > All quadrangles are figures, > But no triangle is a quadrangle; > Therefore, some figures are not triangles. > > But here the reasoning is really this: > > *Rule.*--Every quadrangle is other than a triangle. > *Case.*--Some figures are quadrangles. > *Result.*--Some figures are not triangles. > > These two arguments are logically equivalent, and although the > "translation" is given as Rule/Case/Result, the original is given as > Case/Rule/Result. In other words, as I have said before, the order of the > two premisses is irrelevant to the underlying logic. > > Now, note Peirce's statement after the Enoch example that the Rule is > general (Thirdness) and the Case is particular (Secondness). If we > then attribute Firstness to the conclusion, the deductive vector is either > 3ns/2ns/1ns (as you advocate) or 2ns/3ns/1ns--which, interestingly, is the > same as what I have been suggesting as the abductive vector based on CP > 5.189. The difference is that the Case and Result switch places, and thus > they also switch categories; hence why I wondered earlier if there is a > good reason why the three propositions must (or at least should) be > assigned to the same categories for all three inference types. > > As for CP 2.624, my reading of the text is that "the supposition" is > not the Rule itself, but rather "that the [curious circumstance] was a case > of a certain general rule." This phrasing--not just any rule, or a > supposed rule, but a *certain* rule--suggests strongly to me that the > Rule is already known to the one drawing the abductive inference. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Thu, May 5, 2016 at 6:46 PM, Gary Richmond <[email protected]> > wrote: > >> Jon, >> >> I've based my analysis on CP 2.623 and what I gave as the order of >> hypothesis is exactly Peirce's there. In his diagram he clearly outlines >> "Hypothesis" (and Deduction) as commencing at a Rule. There can be no >> question of the text there. So, are you saying that he's wrong in that >> outline? >> >> At 2.624 he further remarks: "Hypothesis is where we find some very >> curious circumstances, which would be explained by the supposition that it >> was the case of *a certain general rule*, and there upon adopt that >> supposition." That 'supposition', that 'general rule' is why Hypothesis >> commences at a Rule at CP 2.623: "It is the inference of a *case* *from* >> a *rule* and a *result*." >> >> We seem to be talking past each other. >> >> Best >> >> Gary R >> >
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