Benjamin Udell wrote: >Yes, the theorematic-vs.-corollarial distinction does not appear in the Peirce >quote to depend on whether the premisses - _up until some lemma_ - already >warrant presumption. > >BUT, but, but, the theorematic deduction does involve the introdution of that >lemma, and the lemma needs to be proven (in terms of some postulate system), >or at least include a definition (in remarkable cases supported by a "proper >postulate") in order to stand as a premiss, and that is what Irving is >referring to.
OK, but how does this connect to the corollarial/theorematic distinction? On the basis purely of the quote from Peirce that Irving was discussing, the theorem, again, could follow from the lemma either corollarially (by virtue purely of "logical form") or theorematically (requiring additional work with the actual mathematical objects of which the theorem speaks). And the lemma, too, could have been obtained either corollarially (a rather needless lemma, in that case) or theorematically. Doesn't this particular distinction, in either case, refer to the nature of the _deduction_ that is required in order to pass from the premisses to the conclusion, rather than referring to the warrant (or lack of it) of presuming the premisses? If the premisses are presumed without warrant, that - it seems to me - does not make the deduction more corollarial or more theorematic; it just makes it uncompleted, and perhaps uncompletable. -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
