Re: [PEIRCE-L] Re: signs, correlates, and triadic relations - "The union of units unites the unity."

[Jerry LR Chandler]

List:

I heartily disagree with Jon's interpretation of the CSP's writings with 
respect to the concept of a relation.

Jon's basic hypothesis of the concept of expressing mathematics as "tuples" (a 
set of symbols? a set of numbers? a permutation group? a vector? discrete 
semantic objects?) obfuscates the question of what is meant by the term 
"relation" (relative, relate, correlate) and other entailments of the Latin 
root from which these terms originate, e.g., illate. 

Jon's interpretation may also be contradicted by CSP's view of continuity and 
his extra-ordinary definition of it. 

My reading of CSP writings indicate that his philosophy of mathematics and 
logic started with syllogisms and counting and developed over a half century of 
diligently seeking a coherent world view that included the concept of a 
relation in its most general semantic forms. Graphs, medads and triadicity are 
only components of the wider developments of his thinking about the notion of a 
"relation".

Before one can conceptualize a relation, one must first have the notion of an 
identity in mind.
Thus, the metaphysical assertion:

"The union of units unites the unity."

expresses a sentence that infers relations (among units) without making any 
assertion about linear ordering of symbols or the meaning of symbols.

I concur with your remark: 

> But nothing but confusion will reign from propagating the categorical error. 


Cheers

Jerry 




On Nov 27, 2015, at 10:15 AM, Jon Awbrey wrote:

> Gary, all, 
> 
> It is critically important to understand the difference between relations 
> proper and elementary relations, also known as tuples. 
> 
> It is clear from his first work on the logic of relative terms that Peirce 
> understood this difference and its significance. 
> 
> Often in his later work he will speak of classifying relations when he is 
> really classifying types of elementary relations or single tuples.
> 
> The reason for this is fairly easy to understand. Relations proper are a 
> vastly more complex domain to classify than types of tuples so one naturally 
> reverts to the simpler setting as a way of getting a foothold on the 
> complexity of the general case. 
> 
> But nothing but confusion will reign from propagating the categorical error. 
> 
> Regards,
> 
> Jon
> 
> http://inquiryintoinquiry.com
> 
> On Nov 27, 2015, at 10:21 AM,   wrote:
> 
>> List,
>>  
>> Recent discussions have made it clear to me that some readers of Peirce who 
>> focus on the famous diagram of ten sign types (EP2:296) tend to overlook its 
>> context, the “Nomenclature and Divisions of Triadic Relations” (NDTR), and 
>> especially the first page or so, where Peirce is discussing triadic 
>> relations generally before narrowing his focus to semiotic relations. So I 
>> thought it might be worthwhile to present some of it here, in Peirce’s own 
>> words, along with some comments of a corollarial and non-controversial 
>> nature. The text begins on EP2:289, but I’ve used the paragraph numbering in 
>> the CP text here to facilitate reference. From this point on, all words in 
>> this font are directly quoted from Peirce, and my comments are inserted in 
>> [brackets]. I have made bold those parts of Peirce’s text that I wish to 
>> highlight.
>>  
>> Nomenclature and Divisions of Triadic Relations
>>  
>> CP 2.233. The principles and analogies of Phenomenology enable us to 
>> describe, in a distant way, what the divisions of triadic relations must be. 
>> But until we have met with the different kinds a posteriori, and have in 
>> that way been led to recognize their importance, the a priori descriptions 
>> mean little; not nothing at all, but little. Even after we seem to identify 
>> the varieties called for a priori with varieties which the experience of 
>> reflexion leads us to think important, no slight labour is required to make 
>> sure that the divisions we have found a posteriori are precisely those that 
>> have been predicted a priori. In most cases, we find that they are not 
>> precisely identical, owing to the narrowness of our reflexional experience. 
>> It is only after much further arduous analysis that we are able finally to 
>> place in the system the conceptions to which experience has led us. In the 
>> case of triadic relations, no part of this work has, as yet, been 
>> satisfactorily performed, except in some measure for the most important 
>> class of triadic relations, those of signs, or representamens, to their 
>> objects and interpretants.
>> [Most of NDTR will be about this “most important class of triadic 
>> relations,” which Peirce defines here but does not name. I will refer to it 
>> simply as S-O-I, or R-O-I. But before he begins to divide this class into 
>> subclasses, Peirce presents some ‘leading principles’, drawn from 
>> Phenomenology, which will be applied a posteriori to the classification of 
>> signs as familiar phenomena. In my comments, I 

Re: [PEIRCE-L] Re: signs, correlates, and triadic relations - "The union of units unites the unity."

[Sungchul Ji]

Jerry,

I still don't understand what you mean by your mantra

""The union of units unites the unity."

Sung

On Fri, Nov 27, 2015 at 12:58 PM, Jerry LR Chandler <
jerry_lr_chand...@me.com> wrote:

> List:
>
> I heartily disagree with Jon's interpretation of the CSP's writings with
> respect to the concept of a relation.
>
> Jon's basic hypothesis of the concept of expressing mathematics as
> "tuples" (a set of symbols? a set of numbers? a permutation group? a
> vector? discrete semantic objects?) obfuscates the question of what is
> meant by the term "relation" (relative, relate, correlate) and other
> entailments of the Latin root from which these terms originate, e.g.,
> illate.
>
> Jon's interpretation may also be contradicted by CSP's view of continuity
> and his extra-ordinary definition of it.
>
> My reading of CSP writings indicate that his philosophy of mathematics and
> logic started with syllogisms and counting and developed over a half
> century of diligently seeking a coherent world view that included the *concept
> of a relation* in its most general semantic forms. Graphs, medads and
> triadicity are only components of the wider developments of his thinking
> about the notion of a "relation".
>
> Before one can conceptualize a relation, one must first have the notion of
> an identity in mind.
> Thus, the metaphysical assertion:
>
> "The union of units unites the unity."
>
> expresses a sentence that infers relations (among units) without making
> any assertion about linear ordering of symbols or the meaning of symbols.
>
> I concur with your remark:
>
> But nothing but confusion will reign from propagating the categorical
> error.
>
>
> Cheers
>
> Jerry
>
>
>
>
> On Nov 27, 2015, at 10:15 AM, Jon Awbrey wrote:
>
> Gary, all,
>
> It is critically important to understand the difference between relations
> proper and elementary relations, also known as tuples.
>
> It is clear from his first work on the logic of relative terms that Peirce
> understood this difference and its significance.
>
> Often in his later work he will speak of classifying relations when he is
> really classifying types of elementary relations or single tuples.
>
> The reason for this is fairly easy to understand. Relations proper are a
> vastly more complex domain to classify than types of tuples so one
> naturally reverts to the simpler setting as a way of getting a foothold on
> the complexity of the general case.
>
> But nothing but confusion will reign from propagating the categorical
> error.
>
> Regards,
>
> Jon
>
> http://inquiryintoinquiry.com
>
> On Nov 27, 2015, at 10:21 AM,  
> wrote:
>
> List,
>
>
>
> Recent discussions have made it clear to me that some readers of Peirce
> who focus on the famous diagram of ten sign types (EP2:296) tend to
> overlook its context, the “Nomenclature and Divisions of Triadic Relations”
> (NDTR), and especially the first page or so, where Peirce is discussing
> triadic relations *generally* before narrowing his focus to semiotic
> relations. So I thought it might be worthwhile to present some of it here,
> in Peirce’s own words, along with some comments of a corollarial and
> non-controversial nature. The text begins on EP2:289, but I’ve used the
> paragraph numbering in the CP text here to facilitate reference. From this
> point on, all words in this font are directly quoted from Peirce, and my
> comments are inserted in [brackets]. I have made *bold* those parts of
> Peirce’s text that I wish to highlight.
>
>
>
> *Nomenclature and Divisions of Triadic Relations*
>
>
>
> CP 2.233. The principles and analogies of Phenomenology enable us to
> describe, in a distant way, what the divisions of triadic relations must
> be. But until we have met with the different kinds *a posteriori,* and
> have in that way been led to recognize their importance, the *a priori*
> descriptions mean little; not nothing at all, but little. Even after we
> seem to identify the varieties called for *a priori* with varieties which
> the experience of reflexion leads us to think important, no slight labour
> is required to make sure that the divisions we have found *a posteriori*
> are precisely those that have been predicted *a priori.* In most cases,
> we find that they are not precisely identical, owing to the narrowness of
> our reflexional experience. It is only after much further arduous analysis
> that we are able finally to place in the system the conceptions to which
> experience has led us. In the case of triadic relations, no part of this
> work has, as yet, been satisfactorily performed, except in some measure for 
> *the
> most important class of triadic relations, those of signs, or
> representamens, to their objects and interpretants.*
>
> [Most of NDTR will be about this “most important class of triadic
> relations,” which Peirce defines here but does not name. I will refer to it
> simply as S-O-I, or R-O-I. But before he begins to divide this class