Thank you, Jon! I see it somehow like this: There are action systems and reflection systems. My way of triadizing would be: In an active system the triad is "event (or action), entity (or object), relation (or set of relations, structure)". All these three parts are internalized (represented-as-) entities or objects in a reflecting system, a mind. The triad "event, entity, relation" applies to a reflective system as well, but here the events are that what happens in a mind (representamens??). The relations are the persistent concepts that are present to the mind (like ways of thinking, routines: laws, habits, thirdnesses??), and the entities (immediate objects??) are the concepts or memory contents the mind has access to in a situation (a sign situation). I am not sure of this, it is just a scetch. Maybe it would be better, not to say "entity", but "object". What would an interpretant be? Maybe a new relation...
Best,
Helmut
Gesendet: Freitag, 27. Februar 2015 um 15:04 Uhr
Von: "Jon Awbrey" <[email protected]>
An: "Helmut Raulien" <[email protected]>, "Peirce List" <[email protected]>
Betreff: [PEIRCE-L] Re: Relations & Their Relatives
Von: "Jon Awbrey" <[email protected]>
An: "Helmut Raulien" <[email protected]>, "Peirce List" <[email protected]>
Betreff: [PEIRCE-L] Re: Relations & Their Relatives
Inquiry Blog
• http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-1/
• http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-2/
• http://inquiryintoinquiry.com/2015/02/18/relations-their-relatives-3/
Peirce List
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15704
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15705
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15708
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15716
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15718
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/15719
Helmut, List,
Right, the "divisor of" relation signified by "x|y" is a dyadic relation
on the set of positive integers M, so it can be understood as a subset of
the cartesian product M×M. It is an example of a "partial order", whereas
the "less that or equal to" relation signified by "x ≤ y" is an example of
a total order relation.
And yes, the mathematics of relations can be applied most felicitously
to semiotics, but here we must bump up the adicity or arity to three.
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.
One thing we need to understand here is that the sign relation L ⊆ O×S×I
relevant to a given level of discussion can be rather more abstract than
what we would call a "sign process" proper, that is, a structure extended
through a dimension of time. Many of the most powerful sign relations are
those that generate sign processes through iteration or recursion or other
operations of that sort. When this happens, the most penetrating analysis
of the sign process or semiosis in view will come through grasping the core
sign relation that generates it.
Regards,
Jon
On 2/18/2015 5:51 PM, Helmut Raulien wrote:
> Jon, Jerry, List,
> I think, what you wrote is interesting: That a (mathematical) relation is a
> subset of the set of possible tuples (cartesian product) that are made from the
> elements of two sets, a tuple being a pair of one element from set A and one
> element from set B. Set B can also again be set A, then it is the relation upon
> A. The subset can be chosen arbitrarily, then the reason for the relation is the
> free will of the mathematician at work. Or it may be something like "smaller
> than", then it is the set of tuples in which the first element (from set A) is
> smaller than the second (taken from B). In this case the relation has a natural
> reason, but it still takes a person to see, that one element is smaller than the
> other. And this person also has to define A and B.
> Why am I writing this? I was thinking of how can this mathematics be applied to
> semiotics. Semiotics is metaphysics, that is universal theory of nature. So I
> was thinking: In which way can nature, reality, be separated into two sets? My
> answer is: These two sets are the set of events, and the set of entities. This
> is the most fundamental natural distinction of reality into two sets, that does
> not need an observer concept, because this distinction has existed yet in
> preorganic nature. It is natural.
> Relation now is in the first place a relation between an event and an entity. It
> must be a symmetrical relation, because in preorganic nature there was no
> mathematician to define which is set A and which is set B.
> Now there are two ways to continue: Either compare these considerations with
> Peirce, and ask: Has the triad "Event, entity, relation" something to do with
> "1ness, 2ness, 3ness", or with "representamen, object, interpretant"?
> Or the second way of approach is, to develop a semiotics and a systems theory
> based on the triad "event, entity, relation", not caring about Peirce first, but
> waiting to see later, whether there will be parallelities. I think this is a
> good idea. I want to follow it, but maybe somebody else smarter than me can do
> that faster and more efficient.
> Best,
> Helmut
--
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my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
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-----------------------------
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 .
• http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-1/
• http://inquiryintoinquiry.com/2015/02/17/relations-their-relatives-2/
• http://inquiryintoinquiry.com/2015/02/18/relations-their-relatives-3/
Peirce List
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15704
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15705
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15708
JLRC:http://permalink.gmane.org/gmane.science.philosophy.peirce/15716
JA:http://permalink.gmane.org/gmane.science.philosophy.peirce/15718
HR:http://permalink.gmane.org/gmane.science.philosophy.peirce/15719
Helmut, List,
Right, the "divisor of" relation signified by "x|y" is a dyadic relation
on the set of positive integers M, so it can be understood as a subset of
the cartesian product M×M. It is an example of a "partial order", whereas
the "less that or equal to" relation signified by "x ≤ y" is an example of
a total order relation.
And yes, the mathematics of relations can be applied most felicitously
to semiotics, but here we must bump up the adicity or arity to three.
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.
One thing we need to understand here is that the sign relation L ⊆ O×S×I
relevant to a given level of discussion can be rather more abstract than
what we would call a "sign process" proper, that is, a structure extended
through a dimension of time. Many of the most powerful sign relations are
those that generate sign processes through iteration or recursion or other
operations of that sort. When this happens, the most penetrating analysis
of the sign process or semiosis in view will come through grasping the core
sign relation that generates it.
Regards,
Jon
On 2/18/2015 5:51 PM, Helmut Raulien wrote:
> Jon, Jerry, List,
> I think, what you wrote is interesting: That a (mathematical) relation is a
> subset of the set of possible tuples (cartesian product) that are made from the
> elements of two sets, a tuple being a pair of one element from set A and one
> element from set B. Set B can also again be set A, then it is the relation upon
> A. The subset can be chosen arbitrarily, then the reason for the relation is the
> free will of the mathematician at work. Or it may be something like "smaller
> than", then it is the set of tuples in which the first element (from set A) is
> smaller than the second (taken from B). In this case the relation has a natural
> reason, but it still takes a person to see, that one element is smaller than the
> other. And this person also has to define A and B.
> Why am I writing this? I was thinking of how can this mathematics be applied to
> semiotics. Semiotics is metaphysics, that is universal theory of nature. So I
> was thinking: In which way can nature, reality, be separated into two sets? My
> answer is: These two sets are the set of events, and the set of entities. This
> is the most fundamental natural distinction of reality into two sets, that does
> not need an observer concept, because this distinction has existed yet in
> preorganic nature. It is natural.
> Relation now is in the first place a relation between an event and an entity. It
> must be a symmetrical relation, because in preorganic nature there was no
> mathematician to define which is set A and which is set B.
> Now there are two ways to continue: Either compare these considerations with
> Peirce, and ask: Has the triad "Event, entity, relation" something to do with
> "1ness, 2ness, 3ness", or with "representamen, object, interpretant"?
> Or the second way of approach is, to develop a semiotics and a systems theory
> based on the triad "event, entity, relation", not caring about Peirce first, but
> waiting to see later, whether there will be parallelities. I think this is a
> good idea. I want to follow it, but maybe somebody else smarter than me can do
> that faster and more efficient.
> 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 .
----------------------------- 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 .
