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" <[email protected]> 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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