Jon, List,
I think too, that S and I are of one class. So, what distinguishes this class from the class of O? I guess it is the classical dualism. S and I are related to events, change, time, and O to the absence of change, permanence, space, or maybe effeteness of change. The classical dualism of mind and matter suits to that: I think that mind relates to change, and matter to permanence (due to effeteness of change / mind). Or is change effete permanence, mind effete matter?? (I dont think so, just a thought experiment).
People do not feel at ease with dualism. We want to know what was first, the hen or the egg, time or space. So we are looking for ways to reduce dualism to monism.
I think, the problem with bringing together Peirce and conventional mathematics is, that Peirces monism is one of time / change, and the conventional mathematical monism is one of space / permanence. With Peirce matter is effete mind. Mathematics is dealing with timeless axioms and time-reversible tautology, so about space problems only. Also the mathematics by Spencer-Brown is only about space: Laws of form. Though "distinction" in fact is an event, his concept of it is the spatial consequence of this event only, the mark which is there (after the event), not the event itself in time. This I have just guessed, as I have not understood the book. What I am uttering, is mostly impressions, I hope I am allowed, or otherwise that you forgive me.
I think it would be ok to postpone the question of dualism reduction to monism by assuming that it is a scale problem: A very slow change is a permanence, on the other hand nothing is permanent forever, everything changes. But in a certain scale, in a certain sign, there are two classes: Change and permanence (Akzidence and substance (Aristotle)?).
What I want to say with this, is: The Peircean theory (my impression) lacks spatial thinking, systems theory, interpreting system, and so on. Mathematics lacks temporal thinking, irreversibility and so on (my impression, I guess I am wrong, just dont know enough about mathematics).
These were just some wild guesses based on impressions and half-knowledges.
Best,
Helmut
27. April 2017 um 22:56 Uhr
Von: "Jon Awbrey" <jawb...@att.net>
Von: "Jon Awbrey" <jawb...@att.net>
Helmut, List ...
Here are links to my blog rehashes of the last few exchanges on this thread:
https://inquiryintoinquiry.com/2017/04/16/icon-index-symbol-%e2%80%a2-7/
https://inquiryintoinquiry.com/2017/04/17/icon-index-symbol-%e2%80%a2-8/
https://inquiryintoinquiry.com/2017/04/24/icon-index-symbol-%e2%80%a2-9/
https://inquiryintoinquiry.com/2017/04/25/icon-index-symbol-%e2%80%a2-10/
https://inquiryintoinquiry.com/2017/04/27/icon-index-symbol-%e2%80%a2-11/
Turning now to your next point:
HR:
> Example: The triadic function “x_1 + x_2 = x_3”, with the
> three sets X_1, X_2, X_3 not being classes of any kind,
> at least not of the special kind (whatever that is),
> that would allow representation, and make it having
> to do with the third category.
Mathematics is rife with examples of triadic relations having all three
relational domains the same. For instance, the binary operation “+”
in “x_1 + x_2 = x_3” is associated with a function fun[+] such that
fun[+] : X × X → X and also with a triadic relation rel[+] such that
rel[+] ⊆ X × X × X.
Semiotics, by contrast, tends to deal with relational domains O, S, I
where the objects in O are distinct in kind from the signs in S and the
interpretant signs in I. As far as S and I go, it is usually convenient
to lump them all into one big set S = I, even if we have to partition that
set into distinct kinds, say, mental concepts and verbal symbols, or signs
from different languages. But even if it's how things tend to work out in
practice, as we currently practice it, there does not seem to be anything
in Peirce's most general definition of a sign relation to prevent all the
relational domains from being the same. So I'll leave that open for now.
Regards,
Jon
On 4/21/2017 4:59 PM, Helmut Raulien wrote:
> Jon, List,
> I am not so sure, if thirdness is about any triadic relation.
> The categories in Peirce's "new list" of them are quality, relation,
> representation. Maybe "representation" is a very special kind of
> triadic relation. A simple triadic or n-adic relation, I think,
> belongs to secondness, and has only two modes, the quality, eg.
> function or caprice (intension), and the resulting set of tuples
> (extension). Example: The triadic function "x_1 + x_2 = x_3",
> with the three sets X_1, X_2, X_3 not being classes of any kind,
> at least not of the special kind (whatever that is), that would
> allow representation, and make it having to do with the third
> category. I guess, that a difference between Peirce's relation
> theory, and his semiotics and category theory, is, that the
> first is about all triadic relations, and the latter only
> about sign relations or representational relations (the
> special kind of triadic relations).
> Best,
> Helmut
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
Here are links to my blog rehashes of the last few exchanges on this thread:
https://inquiryintoinquiry.com/2017/04/16/icon-index-symbol-%e2%80%a2-7/
https://inquiryintoinquiry.com/2017/04/17/icon-index-symbol-%e2%80%a2-8/
https://inquiryintoinquiry.com/2017/04/24/icon-index-symbol-%e2%80%a2-9/
https://inquiryintoinquiry.com/2017/04/25/icon-index-symbol-%e2%80%a2-10/
https://inquiryintoinquiry.com/2017/04/27/icon-index-symbol-%e2%80%a2-11/
Turning now to your next point:
HR:
> Example: The triadic function “x_1 + x_2 = x_3”, with the
> three sets X_1, X_2, X_3 not being classes of any kind,
> at least not of the special kind (whatever that is),
> that would allow representation, and make it having
> to do with the third category.
Mathematics is rife with examples of triadic relations having all three
relational domains the same. For instance, the binary operation “+”
in “x_1 + x_2 = x_3” is associated with a function fun[+] such that
fun[+] : X × X → X and also with a triadic relation rel[+] such that
rel[+] ⊆ X × X × X.
Semiotics, by contrast, tends to deal with relational domains O, S, I
where the objects in O are distinct in kind from the signs in S and the
interpretant signs in I. As far as S and I go, it is usually convenient
to lump them all into one big set S = I, even if we have to partition that
set into distinct kinds, say, mental concepts and verbal symbols, or signs
from different languages. But even if it's how things tend to work out in
practice, as we currently practice it, there does not seem to be anything
in Peirce's most general definition of a sign relation to prevent all the
relational domains from being the same. So I'll leave that open for now.
Regards,
Jon
On 4/21/2017 4:59 PM, Helmut Raulien wrote:
> Jon, List,
> I am not so sure, if thirdness is about any triadic relation.
> The categories in Peirce's "new list" of them are quality, relation,
> representation. Maybe "representation" is a very special kind of
> triadic relation. A simple triadic or n-adic relation, I think,
> belongs to secondness, and has only two modes, the quality, eg.
> function or caprice (intension), and the resulting set of tuples
> (extension). Example: The triadic function "x_1 + x_2 = x_3",
> with the three sets X_1, X_2, X_3 not being classes of any kind,
> at least not of the special kind (whatever that is), that would
> allow representation, and make it having to do with the third
> category. I guess, that a difference between Peirce's relation
> theory, and his semiotics and category theory, is, that the
> first is about all triadic relations, and the latter only
> about sign relations or representational relations (the
> special kind of triadic relations).
> Best,
> Helmut
--
inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache
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