List, Jeff: Jeff's post addresses the fundamentals, not just of CSP's logic but also of his philosophy.
It deserves a careful reading and long reflections on the preciseness of his expressions. It further deserves thoughtful mediations on the seeking the meanings that he may have intended. Even further, it deserves analysis of the relations of habits to usage of number systems as sources of units. Jeff is not fooled by the putative generality of Boolean propositions. Jeff is not fooled by the semantic discord introduced by attempting to communicate with Boolean symbols. Jeff's questions appear to me to be closely associated with a 21th Century form of the CSP's style of questioning. If I may focus on one diagram, it is form of the place where unities reside in the trichotomy as a three by three table (a unity) of self-revealing propositions and self-correcting facts. This expression of the nature of unity as a composition of natural propositions appears to motivate a substantial fraction of CSP's rhetoric. Frankly, IMHO, this post is among the best posts I have have ever read on the Pierce-L. Cheers Jerry On Jun 20, 2015, at 10:16 AM, Jeffrey Brian Downard wrote: > Jon, List, > > The arithmetic example you offer in "Relations & Their Relatives: 9" is > quite clear. Having said that, what should we say about a number system that > only allows positive integers starting with 1? In this number system, the > number 1 can serve in the role of a subtrahend or a difference. It cannot, > however, serve the role of a minuend. What does this show us about the > number 1 in the system of positive integers starting with 1? > > How do things change when we work with a number system allowing only positive > integers and 0? In this case, the number 1 can now serve in any of the three > places. The same follows for the case of 0. But 0 can be the minuend only > where it is also the subtrahend and the difference. What does this show us > about the numbers 0 and 1 in the system of positive integers that include 0? > > Off the top of my head, I would think that the unit has a special place in > all three number systems we are considering (all integers including 0 and > negative, only positive integers starting with 1, and all positive integers > including 0) because the basic operations of addition and subtraction are > both understood in terms of the operation of adding one more or taking one > away. What is more, the number 0 has a very special place in the number > systems that allow such an expression. How might we explain the special role > that 0 and 1 play in such systems? > > --Jeff > > > Jeff Downard > Associate Professor > Department of Philosophy > NAU > (o) 523-8354 > ________________________________________ > From: Jon Awbrey [[email protected]] > Sent: Friday, June 19, 2015 12:40 PM > To: Helmut Raulien > Cc: Peirce List > Subject: [PEIRCE-L] Re: Survey of Relation Theory • 1 > > Helmut, List, > > I wasn't completely sure about the meaning of your question: > > • "Are interpretants an own class?" > > Is "own" a translation of "eigen" maybe? > > At any rate I went with my best guess and took you to be > asking whether interpretants (and the other two classes) > were ontologically distinctive in some way. I rewrote my > last reply as a blog post with this interpretation in mind: > > • Relations & Their Relatives : 9 > ( http://inquiryintoinquiry.com/2015/06/19/relations-their-relatives-9/ ) > > Please let me know if my reading of your sense is right or not. > > Regards, > > Jon > > On 6/18/2015 6:51 PM, Helmut Raulien wrote: >> Supplement: On the other hand, even if interpretants are not an own class >> (or is >> the word "domain"?), their representations in a mind may well be, and >> certainly >> are. So- triadicity is rescued for me, I now think. >> >> Dear Jon, Peircers, >> I am wondering whether, mathematically spoken, there really are 3-adic >> relations >> in semiotics. An interpretant is a 2-adic relation (between representamen and >> object). But are interpretants an own class? Or are they a common class with >> representamens (syntactic domain)- or are some of them so, while others (the >> final interpretants) re-enter into the domain of objects? And: to regard the >> three sets objects, representamens, interpretants, doesnt this regarding >> (action >> of a mind) mean that they are represented? And doesnt representation by a >> mind >> mean, that these representations are all objects, other than the represented? >> So: Is the triadic relation between representamen, object and interpretant >> possibly a relation between three objects? In this case, it is not triadic: >> It >> is a 2-adic relation between the set of objects, and the same set of >> objects- at >> least reducible to this, I suspect. On the other hand one might say: The >> objects >> of a mind are divided into three classes: Representations of representamens, >> objects, and interpretants. Three classes mean 3-adicity. But then there is >> the >> problem again that I have mentioned: Are interpretants an own class? >> Best, >> Helmut > > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > 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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