I *strongly* agree with your analysis, Malgosia. Best,
Gary On 3/11/12, malgosia askanas <m...@panix.com> wrote: > Irving wrote, quoting Peirce MS L75:35-39: > >>"Deduction is only of value in tracing out the consequences of >>hypotheses, which it regards as pure, or unfounded, hypotheses. >>Deduction is divisible into sub-classes in various ways, of which the >>most important is into corollarial and theorematic. Corollarial >>deduction is where it is only necessary to imagine any case in which >>the premisses are true in order to perceive immediately that the >>conclusion holds in that case. Ordinary syllogisms and some deductions >>in the logic of relatives belong to this class. Theorematic deduction >>is deduction in which it is necessary to experiment in the imagination >>upon the image of the premiss in order from the result of such >>experiment to make corollarial deductions to the truth of the >>conclusion. The subdivisions of theorematic deduction are of very high >>theoretical importance. But I cannot go into them in this statement." >> >> >>[...] Peirce's characterization of theorematic and corrolarial >>deduction would seem, on the basis of this quote, to have to do with >>whether the presumption that the premises of a deductive argument or >>proof are true versus whether they require to be established to be >>true [...] > > I would disagree with this reading of the Peirce passage. It seems > to me that the distinction he is making is, rather, between (1) the case > where the conclusion can be seen to follow from the premisses > by virtue of the "logical form" alone, as in "A function which is continuous > on a closed interval is continuous on any subinterval of that interval" > (whose truth is obvious without requiring us to imagine any continuous > function or any interval), and (2) the case where the deduction of the > conclusions from the premisses requires turning one's imagination > upon, and experimenting with, the actual mathematical objects > of which the theorem speaks, as in "A function which is continuous > on a closed interval is bounded on that interval". > > -malgosia > > --------------------------------------------------------------------------------- > 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
