Supplement for Jim: Actually, I dont dislike all -isms. Prisms I like very much, because of the beautiful rainbow colors they make.
Jon, List,
Thank you! I am trying to work it out. Regarding the second link (rel. reduction), I think that I have understood, that the Boolean 0 + 0 = 1 (false plus false is true), like with ordinary numbers -1 * -1 = 1 would be. Now I am trying to dig the meaning of "A", "i", "u", and so on. I will find it, dont help. I have the impression, that in the article the 3-adic sign relation is said to be reducible- that would be astonishing- but again, no need to help me, I try to manage. I think all this is of great help for not stepping into the -ism-trap again. Usualy I dont like -isms either. Just like I dont believe in astrology, but sometimes suspect, that this is so, because I am sagittarius, and sagitariusses are not supersticious.
Best,
Helmut
"Jon Awbrey" <jawb...@att.net> wrote:
Helmut, List,
The facts about relational reducibility are relatively easy
to understand and I included links to relevant discussions
in my initial posting on relation theory:
• Survey of Relation Theory
( http://inquiryintoinquiry.com/2015/05/16/survey-of-relation-theory-%E2%80%A2-1/ )
The following article discusses relational reducibility and
irreducibility in general terms and gives concrete examples
of reducible and irreducible triadic relations of the sort
we find in mathematics and semiotics, illustrating the two
types of reducibility that usually come up in discussions
of the sort that most concern us here:
• Relation Reduction
( http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction )
These examples were introduced in the other articles on
triadic relations and sign relations and I believe that
one could learn a lot from their careful consideration:
• Triadic Relations
( http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation )
• Sign Relations
( http://intersci.ss.uci.edu/wiki/index.php/Sign_relation )
Regards,
Jon
On 6/22/2015 10:24 AM, Helmut Raulien wrote:
> Jon, List,
> yes. And I just think that I must add, that what I have written below is likely
> to be wrong: Somewhere in the internet I have just read, that Peirces reduction
> hypothesis has been proven by mathematics (which proof I dont think that I will
> ever understand). That would mean eg.: A 3-adic relation cannot be reduced to
> 1-adic and/or 2-adic relations. But a 4-adic relation can be reduced to
> relations not higher than 3-adic. So, obviously it has nothing to do
> with naturalism and so on.
> Best,
> Helmut
>
> "Jon Awbrey" <jawb...@att.net> wrote:
> On 6/21/2015 3:31 AM, Helmut Raulien wrote:
> > Supplement:
> > Because I dont want to pass over my below mentioned confusion, or start a
> > tangent, I try to answer my own question: There are concepts, that are a product
> > of reflexion (eg. by having looked at nature), and there are other concepts that
> > come from praeflexion. Mathematics does praeflect, and then prove these
> > concepts, and the Peircean logic of relatives is reflecting nature. Because
> > nature is triadic, the Peircean logic is also. Mathematics is not only
> > reflecting nature, but itself and then preaflecting all that might be possible
> > to justifiedly do with numbers and other abstract (reflected) units, so it is
> > k-adic.
> > Jon, Gary, List,
> > Gary has confirmed, I think, that with ontologism you have meant the FOO, and
> > that this FOO indeed denies the reality of concepts, so also denies triadic
> > relations in nature. Now about the term "nature": Is it so, that in mathematics
> > things are possible, which are not possible in nature? I am refering to the
> > Peircean logic of relations, in which all higher-than-3-adic relations can be
> > reduced to 3-adic relations. Now my question is: In mathematics 4-,5-,6-, and so
> > on-adic relations are unique ones, are they not? Are they not in Peirces logic
> > of relations, because it is a naturalistic thing, and in nature (or in the
> > nature we can percieve), there is only the classes time, space, relation between
> > time and space? Or events, ens (permanent units), 2-adic relations? (of which
> > three the relation is 3-adic). So- is Peircean logic, in contrast to
> > mathematical logic, naturalistic? Naturalism is often not nicely spoken about:
> > "Naturalistic fallacy". But all this I wrote cannot be, because if I say, that
> > concepts are real, then mathematics (which is a concept), is also real, so part
> > of nature. So, higher-than-3-adic relations should be unique (not reducible to
> > 3-adic, as claimed by Peirce). I am confused.
> > Best,
> > Helmut
>
> Well, a state of confusion is one of the provinces that inquiry hails from.
> And relation theory affords a handy atlas of maps to guide the exploration.
>
> Regards,
>
> Jon
--
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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 peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
The facts about relational reducibility are relatively easy
to understand and I included links to relevant discussions
in my initial posting on relation theory:
• Survey of Relation Theory
( http://inquiryintoinquiry.com/2015/05/16/survey-of-relation-theory-%E2%80%A2-1/ )
The following article discusses relational reducibility and
irreducibility in general terms and gives concrete examples
of reducible and irreducible triadic relations of the sort
we find in mathematics and semiotics, illustrating the two
types of reducibility that usually come up in discussions
of the sort that most concern us here:
• Relation Reduction
( http://intersci.ss.uci.edu/wiki/index.php/Relation_reduction )
These examples were introduced in the other articles on
triadic relations and sign relations and I believe that
one could learn a lot from their careful consideration:
• Triadic Relations
( http://intersci.ss.uci.edu/wiki/index.php/Triadic_relation )
• Sign Relations
( http://intersci.ss.uci.edu/wiki/index.php/Sign_relation )
Regards,
Jon
On 6/22/2015 10:24 AM, Helmut Raulien wrote:
> Jon, List,
> yes. And I just think that I must add, that what I have written below is likely
> to be wrong: Somewhere in the internet I have just read, that Peirces reduction
> hypothesis has been proven by mathematics (which proof I dont think that I will
> ever understand). That would mean eg.: A 3-adic relation cannot be reduced to
> 1-adic and/or 2-adic relations. But a 4-adic relation can be reduced to
> relations not higher than 3-adic. So, obviously it has nothing to do
> with naturalism and so on.
> Best,
> Helmut
>
> "Jon Awbrey" <jawb...@att.net> wrote:
> On 6/21/2015 3:31 AM, Helmut Raulien wrote:
> > Supplement:
> > Because I dont want to pass over my below mentioned confusion, or start a
> > tangent, I try to answer my own question: There are concepts, that are a product
> > of reflexion (eg. by having looked at nature), and there are other concepts that
> > come from praeflexion. Mathematics does praeflect, and then prove these
> > concepts, and the Peircean logic of relatives is reflecting nature. Because
> > nature is triadic, the Peircean logic is also. Mathematics is not only
> > reflecting nature, but itself and then preaflecting all that might be possible
> > to justifiedly do with numbers and other abstract (reflected) units, so it is
> > k-adic.
> > Jon, Gary, List,
> > Gary has confirmed, I think, that with ontologism you have meant the FOO, and
> > that this FOO indeed denies the reality of concepts, so also denies triadic
> > relations in nature. Now about the term "nature": Is it so, that in mathematics
> > things are possible, which are not possible in nature? I am refering to the
> > Peircean logic of relations, in which all higher-than-3-adic relations can be
> > reduced to 3-adic relations. Now my question is: In mathematics 4-,5-,6-, and so
> > on-adic relations are unique ones, are they not? Are they not in Peirces logic
> > of relations, because it is a naturalistic thing, and in nature (or in the
> > nature we can percieve), there is only the classes time, space, relation between
> > time and space? Or events, ens (permanent units), 2-adic relations? (of which
> > three the relation is 3-adic). So- is Peircean logic, in contrast to
> > mathematical logic, naturalistic? Naturalism is often not nicely spoken about:
> > "Naturalistic fallacy". But all this I wrote cannot be, because if I say, that
> > concepts are real, then mathematics (which is a concept), is also real, so part
> > of nature. So, higher-than-3-adic relations should be unique (not reducible to
> > 3-adic, as claimed by Peirce). I am confused.
> > Best,
> > Helmut
>
> Well, a state of confusion is one of the provinces that inquiry hails from.
> And relation theory affords a handy atlas of maps to guide the exploration.
>
> Regards,
>
> Jon
--
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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----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
