1. Hypothesis (Abduction) 2. Induction 3. Deduction But isn't it also the case that we can mix firsts, seconds and thirds if we think it appropriate. As in Terms Propositions Symbols. Best, S *ShortFormContent at Blogger* <http://shortformcontent.blogspot.com/>
On Fri, Mar 2, 2012 at 12:25 PM, Catherine Legg <cl...@waikato.ac.nz> wrote: > Thanks for the thoughtful reply, Gary! > > The issue you raise about how deduction and induction should be > categorised is an interesting one. I had always thought of deduction > as falling clearly under secondness, due to the compulsion involved. > But you are right to note that in theorematic deduction the mind is > not passive but active, and that this form of reasoning was very > important to Peirce. > > I don't see how one might interpret induction as secondness though. > Though a *misplaced* induction may well lead to the secondness of > surprise due to error. Hmmmm... > > Cheers, Cathy > > On Thu, Feb 23, 2012 at 1:49 PM, Gary Richmond <gary.richm...@gmail.com> > wrote: > > Cathy, list, > > > > When I first read your remark suggesting that "the birth, growth and > > development of new hypostatic abstractions" should be in the position > > of 3ns rather than argumentative proof of the validity of the > > mathematics as I had earlier abduced, I thought this might be another > > case of the kind of difficulty in assigning the terms of 2ns and 3ns > > in genuine triadic relations which had Peirce, albeit for a very short > > time in his career, associating 3ns with induction (while before and > > after that time he put deduction in the place of 3ns as "necessary > > reasoning"--I have discussed this several times before on the list and > > so will now only refer those interested to the passage, deleted from > > the 1903 Harvard Lectures--276-7 in Patricia Turrisi's edition--where > > Peirce discusses that categorial matter). > > > > I think his revision of his revision to his original position may have > > been brought about by the clarification resulting from thinking of > > abduction/deduction/induction beyond critical logic (where they are > > first analyzed as distinct patterns of inference), then in methodeutic > > where "a complete inquiry"--in which hypothesis formation is 1ns, the > > deduction of the implications of the hypothesis for testing is 3ns, > > and, finally, the actual inductive testing is 2ns--provides a kind of > > whetstone for categorial thinking about these three. (Yet, even in > > that 1903 passage he remarks that he "will leave the question open.") > > > > Be that as it may, I am beginning to think that you are clearly on to > > something and that that transforming of a predicate into a relation > > which we call hypostatic abstraction certainly ought to be in the > > place of 3ns. Re-reading parts of Jay Zeman's famous and fine article > > on hypostatic abstraction further strengthened that opinion. See: > > http://web.clas.ufl.edu/users/jzeman/peirce_on_abstraction.htm Zeman > > writes: > > > > "It is hypostatic or subjectal abstraction that Peirce is interested > > in; a hint as to why he is interested in it is given in his allusions > > in these passages to mathematical reasoning [. . .] Jaakko Hintikka > > has done us the great service of bringing to our attention and tying > > to contemporary experience one of Peirce's central observations about > > necessary—which is to say mathematical—reasoning: this is that > > nontrivial deductive reasoning, even in areas where explicit > > postulates are employed, always considers something not implied in the > > conceptions so far gained [in the particular course of reasoning in > > question], which neither the definition of the object of research nor > > anything yet known about could of themselves suggest, although they > > give room for it." > > > > As is well known, Peirce calls this kind of reasoning "theorematic" > > (in contrast to "corollarial reasoning) because it introduces "novel > > elements into the reasoning process in the form of icons, which are > > then 'experimented upon in imagination.' " > > > > Zeman quotes Hintikka to the effect that "Peirce himself seems to have > > considered a vindication of the concept of abstraction as the most > > important application of his discovery [of the theorematic/corollarial > > distinction]" and then remarks that "Peirce would indeed have agreed > > that the light shed on necessary reasoning by this distinction helps > > greatly to illuminate the role of abstraction. . ." > > > > See, also: EP2:394 where Peirce comments that it is hypostatic > > abstraction that leads to the generalizality of a predicate and, of > > course, what is general is 3ns. In short, I think you are quite right > > Cathy to have suggested that correction of my categorial assignments. > > As Peirce notes near the end of the "Additament" to the Neglected > > Argument, hypothetic abstraction concerns itself with that which > > necessarily would be *if* certain conditions were established > > (EP2:450). > > > > Best, > > > > Gary > > > > On 2/21/12, Catherine Legg <cl...@waikato.ac.nz> wrote: > >> Gary wrote: > >> > >> > >> For the moment I am seeing these > >> three as forming a genuine tricategorial relationship, which I'd diagram > >> in my trikonic way, thus: > >> > >> Theoretical mathematics: > >> > >> (1ns) mathematical hypothesis formation (creative abduction--that "piece > >> of mathematics") > >> |> (3ns) argumentative proof (of the validity of the mathematics) > >> (2ns) the mathematics itself > >> > >> [...] > >> > >> Wouldn't argumentative proof be the 2ness, and the 3ness would be > >> something like the birth, growth and development of new hypostatic > >> abstractions? > >> > >> Cheers, Cathy > >> > >> > --------------------------------------------------------------------------------- > >> You are receiving this message because you are subscribed to the > PEIRCE-L > >> listserv. To remove yourself from this list, send a message to > >> lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the > body of > >> the message. To post a message to the list, send it to > >> PEIRCE-L@LISTSERV.IUPUI.EDU > >> > > > > > > -- > > Gary Richmond > > Humanities Department > > Philosophy and Critical Thinking > > Communication Studies > > LaGuardia College--City University of New York > > > --------------------------------------------------------------------------------- > You are receiving this message because you are subscribed to the PEIRCE-L > listserv. To remove yourself from this list, send a message to > lists...@listserv.iupui.edu with the line "SIGNOFF PEIRCE-L" in the body > of the message. To post a message to the list, send it to > PEIRCE-L@LISTSERV.IUPUI.EDU > --------------------------------------------------------------------------------- You are receiving this message because you are subscribed to the PEIRCE-L listserv. 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