Jeff, List,
I have run completely out of time for today, and some of what people
have written I wrote is blurring my memory of what I actually wrote,
so let me just prepare for the morrow's continuance by copying out
the augmented blog edition of my subtraction example and take up
your comments in a context where all the qualifications I made
will be fresh in my and others' minds.
Regards,
Jon
On 6/20/2015 11:16 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 [jawb...@att.net]
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
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