John, List: Thanks for your response.
I phrased my concerns as questions in order to stimulate a through evaluation of conclusions that Ben had drawn. Your response is at least partially true in that the interpretation of any rhetoric statement as a set theoretic symbolization requires that at some parts of the meaning of the rhetoric statement ought to represented in the symbolizations of the translations from one form to another form. However, the simple fact of the matter is that most rhetorical statements do not translate well from the rhetorical form to the strict formal logical form of set theory. The reason for this broad assertion is simple. Most human rhetoric is informal and is not intended, expected nor interpreted as formal statements. Judgments are necessary. Consequently, it appears to me that Ben's assertions about the logic of "round and blue" and the imaginative Peircian graphs of the assertions relating "round and blue" are worth careful study. Ben was, apparently, translating the terms "blue" and "round" from a sentence into a set-theory symbols without weighing the meanings of the terms in a wider context of the objects themselves. Round is a geometric term. Blue is a sensory term. Round and blue are members of two different rhetoric sets or classes. A further question of a similar nature arises from Jon A.'s central hypothesis which he clearly state in his post of February 27, 2015 8:04:32 AM CST > "We take any sign relation L to be subset of a cartesian product O×S×I, where O is the set of objects under consideration in a given discourse, S is the set of signs, and I is the set of interpretant signs involved in the same discourse." Are the rhetorical meaning of the rhetoric terms "objects", "signs" and "interpretant signs" such that these terms can be used as variables for multiplication? In particular, is the set of interpretant signs not a set of signs? Is the meaning of the symbol for a sign change when a rhetorical adjective modifies the noun? What is the meaning of the Cartesian product within the set theory axions in this context? Or, am I missing something is raising this point of identity in relationship to translating from rhetoric form to logical form? These comments are of public concern to CSP scholarship. And these questions are of deep private concern to me as they have arisen frequently in my search for a formal logic of chemistry and the pan-chemical sciences. Cheers jerry On Feb 27, 2015, at 9:00 AM, John Collier wrote: > Wife and husband together would have to be an asymmetric relationship, which > can be put in terms of properties as Mxy & Wx & Hy, M for married, W for > wife, and H for husband. This would imply the order of the relation matters. > For symmetric relations, the order does not matter, such as x and y are > married: Mxy, which says nothing about the gender of those involved. All of > the relations here are ordered pairs, though. In standard notation we can > write the marriage relation as M<x,y>. It would also be true that M<y,x> & > M<x,y>. But if we identify the wife as x, as above, then the order does > matter, and the relation is not symmetric (unless we have two wives married > to each other, of course). > > I see no difference between the rhetorical use and the first order logic use, > and the set-theoretic use above, but I am a logician, and perhaps my rhetoric > is especially tuned to logicalities. Friends have noticed that I wince in one > way or another whenever anything not logical is said in my presence (except > in humour). > > John > > Jerry said: > List, Ben: > > On Feb 24, 2015, at 6:45 PM, Benjamin Udell wrote: > > > Anyway: > "Wxy" ≡ "xy are wife and husband together" (two people uniquely paired in > ordered relation) > > Did you really mean this? > > Or, is a married couple the same couple if they are not an ordered pair in > the sense of set theory? > > That is, are Bill and Mary the same couple as Mary and Bill, independent of > the order of the terms? > > From an earlier thread, another issue is the rhetorical content of a pair of > symbols as the expressions that signify. > > Compare the content of two phrases: > > "husband and wife" > > with > > "round and blue". > > Do these two phrases have the same meaning in rhetoric > as in set theory? > > If so, why? > If not, why not? > > What is the syntactical "difference that makes a difference" that exists in > the two sentences that you assert have the same meaning? > > Cheers > > jerry > > > John Collier, Philosophy, UKZN, Durban 4041 > http://web.ncf.ca/collier > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > 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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