Ben, Christina, List, Referring to the first half of Christina's question, namely "where does Peirce suggest that all syllogisms may be reduced to Barbara," this article https://en.wikipedia.org/wiki/Charles_Sanders_Peirce#cite_note-137 (see:"Modes of inference")--composed at least in part by Ben, I believe, gives a well-known 1878 example of Peirce's transformations of Barbara to include 'induction' and 'hypothesis'. There may be earlier examples, but I can't quickly locate them.
[Peirce] sometimes expounded the modes of inference by transformations of the categorical syllogism Barbara (AAA) <https://en.wikipedia.org/wiki/Syllogism#Barbara_.28AAA-1.29>, for example in "Deduction, Induction, and Hypothesis" (1878).[137] <https://en.wikipedia.org/wiki/Charles_Sanders_Peirce#cite_note-137> He does this by rearranging the *rule* (Barbara's major premise), the *case* (Barbara's minor premise), and the *result* (Barbara's conclusion): Deduction. *Rule:* All the beans from this bag are white. *Case:* These beans are from this bag. [image: \therefore] *Result:* These beans are white. Induction. *Case:* These beans are [randomly selected] from this bag. *Result:* These beans are white. [image: \therefore] *Rule:* All the beans from this bag are white. Hypothesis (Abduction). *Rule:* All the beans from this bag are white. *Result:* These beans [oddly] are white. [image: \therefore] *Case:* These beans are from this bag. He makes this point much earlier--in the '60's--but makes it explicit here. 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 <718%20482-5690>* On Wed, Oct 28, 2015 at 12:45 PM, Benjamin Udell <[email protected]> wrote: > Here's one place where Peirce says that *Barbara* is not enough: > "Relatives (logic of)" in Baldwin's _Dictionary of Philosophy and > Psychology_, New York: Macmillan, 1902, DPP 2:447-450; CP 3.636-643 > http://www.gnusystems.ca/BaldwinPeirce.htm#Relatives > > [....] Since Kant, especially, it has been customary to say that deduction > only elicits what was implicitly thought in the premisses; and the famous > distinction of analytical and synthetical judgments is based upon that > notion. But the logic of relatives shows that this is not the case in any > other sense than one which reduces it to an empty form of words. Matter > entirely foreign to the premisses may appear in the conclusion. Moreover, > so far is it from being true, as Kant would have it, that all reasoning is > reasoning in _*Barbara*_, that that inference itself is discovered by the > microscope of relatives to be resolvable into more than half a dozen > distinct steps. In minor points the doctrines of ordinary logic are so > constantly modified or reversed that it is no exaggeration to say that > deductive logic is completely metamorphosed by the study of relatives. > [End quote] > > Best, Ben > > On 10/28/2015 12:17 PM, Christina Da Silva wrote: > > I am finishing up a masters that focuses on Medieval Islamic philosophy, > and this list has been an inestimably useful resource for me, so thank you > to all who post here. I am now trying to find the source for some > information I have in my notes, and my hope is that someone on the list can > help me. > > Here is my question: where does Peirce suggest that all syllogisms may be > reduced to Barbara, and where does he later renounce this idea? > > Thank you, > Christina da Silva > > > > > ----------------------------- > 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 > . > > > > > >
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