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
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