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.


You are receiving this message because you are subscribed to the PEIRCE-L 
listserv.  To remove yourself from this list, send a message to 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

Reply via email to