John C., Jeff, lists,
John, You're right, in the sense of 'ordered pair' (e.g., such that, in
set theory, _/relation/_ is defined as ordered pair), it's true that
there's no intuitive sense of 'more' or 'less' or 'earlier' or 'later'
to which the relation appeals as a rule. Every arbitrary sequence is
ordered in a sense; the order for the sequence is given by the sequence
itself and it may or may not follow some pattern of an iterated
operation or the like. I thought that Jeff had an ordering rule in mind
but maybe he didn't.
I too said that we should not think of the object, sign, and
interpretant as 'falling dominoes'. It's because falling dominoes are
dyadic in action, while semiosis is triadic. You also say,
I am not at all clear that there is a unique "order of semiotic
determination"
[End quote]
The process of semiotic determination is what _/defines/_ sign, object,
and interpretant. Some first thing (the sign) is determined by some
second thing (the object) to determine some third thing (the
interpretant) to be related to the second thing (object) as the first
thing (sign) is related to the second thing (object).
The order of semiotic determination directly reflects that. Insofar as
something acts as a _/source/_ of semiotic determination, it is a
semiotic object. A sign is a kind of means or mediator of semiotic
determination, and an interpretant is a kind of end - usually a
secondary end insofar as in its turn it is usually also a sign, a
mediator toward further interpretation. (Peirce somewhere discusses the
'ultimate logical interpretant' which brings semiosis to a close and is
not a sign, at least not a sign in the semiosis that leads to it, but a
disposition to conduct thenceforward.)
Best, Ben
On 1/29/2015 3:52 AM, John Collier wrote:
Ben, List,
I believe that a weaker is required for an ordered triple. Any finite set can be ordered. The Axiom of
Choice, which is controversial, implies that any set including infinite ones can be ordered. The order
need not be anything like 'more' or 'less' in any intuitive sense. For example in a function, like f=ma,
<m,a> is an ordered pair, one from one domain and another from another domain such that their
product is in another domain which is the range of the function. Obviously, under the Newtonian
interpretation m and a are not either more or less than the other in any intuitive (or even
nondegenerate) sense. I think that this is worth remembering when thinking of Peircean triads in
particular. I would go further than saying that we should not think of object, sign and interpretant as
"falling dominos", since I am not at all clear that there is a unique "order of semiotic
determination". This follows from the way I understand irreducible triads as not fully computable,
and hence inherently open-ended.
Best,
John
-----Original Message-----
From: Benjamin Udell [mailto:[email protected]]
Sent: January 28, 2015 7:07 PM
To: [email protected]; 'Peirce-L'
Subject: Re: [PEIRCE-L] Re: Triadic Relations
Jeff, Jon, lists,
I think that all that is required for an ordered triple, or an ordering of any
length, is a rough notion of 'more' or 'less', for example an ordering of
personal preferences, and this is enough for theorems, for example
http://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem.
Exact quantities are not required. In the case of object, sign, interpretant,
insofar as the object determines the sign to determine the interpretant to be
determined by the object as the sign is determined by the object, the order of
semiotic determination is 'object, sign, interpretant', although object, sign,
interpretant are not to be understood as acting like successive falling
dominoes.
Best, Ben
On 1/27/2015 2:08 PM, Jeffrey Brian Downard wrote:
[....]
Here is the starting question: Doesn't the notion of an ordered triple require
that we already have things sorted out in such a way that we are able to
ascribe quantitative values to each subject that is a correlate of the triadic
relation?
[....]
-----------------------------
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 .
