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 

Aw: [PEIRCE-L] Re: signs, correlates, and triadic relations

[Helmut Raulien]

Dear All,

Regarding the three types of triadic relations (comparison, performance, thought), I would say, that the thought-type, which is of category three, is the one about semiotical 3adic relations, or signs. The comparison type, I think, is eg. a mathematical elementary 3adic relation, a subset of tuples  of the tuples (3-tuples) in a cartesian product of three sets. These are guesses. Performance i dont have an idea about. I think, there is a lot of confusion about the term "relation", which is not easy to solve. On one hand, relation is secondness, on the other, the semiotic, thirdnessal "triadic relation" is the relation between first-, second- and thirdnessal elements, such as R,O,I,,, primi-, alter-, medisense,,, the three modes of medisense, the three modes of the interpretant, This, very special, semiotical or thirdnessal (think of a better term) 3adicity, Peirce associates with "thought". I think, it also can be associated with "time", because it includes an irreversibility, so a continuity, meaning, there is an evolution of the sign: The result is different from the reason, it is something else or something more. In the comparison type of 3adic relations, reason and result are equal, so there is no continuity, no representation of the past in the future. I also think, that "representation" (to a correlate), i.e. thirdness, is not possible within reversibility, i.e. without the irreversibility of time.

"Relation" is secondness, and to call a thirdnessal 3adicity a "relation" is secondness on the observer level: An observed 3adic sign has three modes of observation: The sign mode (3.1obs), the relation mode (3.2obs), and the interpretation mode (3.3obs). This is only a proposal. in fact, I think, it is very complicated and needs a much closer look at. What is a relation proper?

Best,

Helmut

 

27. November 2015 um 17:15 Uhr
"Jon Awbrey" 
 



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 

[PEIRCE-L] Re: signs, correlates, and triadic relations

[Jon Awbrey]

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 will add some corollaries which follow from 
> these general principles and frame the classification which follows.]
>  
> 234. Provisionally, we may make a rude division of triadic relations, which, 
> we need not doubt, contains important truth, however imperfectly apprehended, 
> into—
> Triadic relations of comparison,
> Triadic relations of performance, and
> Triadic relations of thought.
> 1.Triadic relations of Comparison are those which are of the nature of 
> logical possibilities.
> 2.Triadic relations of Performance are those which are of the nature of 
> actual facts.
> 3.Triadic relations of Thought are those which are of the nature of laws.
> [The numbering I have supplied here suggests how the phenomenological 
> categories (Firstness, Secondness and Thirdness) apply to this “rude division 
> of triadic relations.” Thus we may reword the first to say that logical 
> possibilities are triadic relations in which 1ns predominates; actual facts 
> are triadic relations of Performance, in which 2ns predominates; and laws are 
> triadic relations of Thought, in which 3ns predominates. The ordering of 
> these relations proceeds from simple to complex, as Peirce explains next:]
>  
> 235. We must distinguish between the First, Second, and Third Correlate of 
> any triadic relation.
> The First Correlate is that one of the three which is regarded as of the 
> simplest nature, being a mere possibility if any one of the three is of that 
> nature, and not being a law unless all three are of that nature.
> 236. The Third Correlate is that one of the 

[PEIRCE-L] RE: signs, correlates, and triadic relations

[gnox]

Jon,

 

If it’s critically important to understand the difference between “relations 
proper” and “elementary relations”, can you tell us what that difference is, or 
point us to an explanation? These are not terms that Peirce uses, so how can 
the rest of us tell whether we understand them or not? Being unfamiliar with 
those terms does not indicate lack of understanding of the important concepts 
they signify.

 

Gary f.

 

From: Jon Awbrey [mailto:jawb...@att.net] 
Sent: 27-Nov-15 11:16



 

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






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[PEIRCE-L] Re: signs, correlates, and triadic relations

[Jon Awbrey]

Gary, all,

I used the phrase “relations proper” to emphasize that I was speaking
of relations in the strict sense of the word, not in any looser sense.
I have been reading Peirce for almost 50 years now and I can't always
recall where I read a particular usage.  In the 1970s I spent a couple
of years poring through the microfilm edition of his Nachlass and read
a lot of still unpublished material that is not available to me now.
But there is no doubt from the very concrete notations and examples
that he used in his early notes and papers that he was talking about
the formal objects that are variously called elementary relations,
elements of relations, individual relations, or ordered tuples.

I did, however, more recently discuss a number of selections from Peirce's
1880 Algebra of Logic that dealt with the logic of relatives, so I can say
for a certainly that he was calling these objects or the terms that denote
them by the name of “individual relatives”.

See the excerpts and discussion in the following series of blog posts.

http://inquiryintoinquiry.com/2015/01/30/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-preliminaries/
http://inquiryintoinquiry.com/2015/02/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-1/
http://inquiryintoinquiry.com/2015/02/03/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-2/
http://inquiryintoinquiry.com/2015/02/11/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-3/
http://inquiryintoinquiry.com/2015/02/12/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-4/
http://inquiryintoinquiry.com/2015/02/15/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-5/
http://inquiryintoinquiry.com/2015/02/16/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-6/

And especially the series of comments on Selection 7.

http://inquiryintoinquiry.com/2015/02/28/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-selection-7/
http://inquiryintoinquiry.com/2015/04/13/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-1/
http://inquiryintoinquiry.com/2015/04/19/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-2/
http://inquiryintoinquiry.com/2015/04/23/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-3/
http://inquiryintoinquiry.com/2015/04/24/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-4/
http://inquiryintoinquiry.com/2015/05/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-5/

Regards,

Jon

On 11/27/2015 12:42 PM, g...@gnusystems.ca wrote:

Jon,

If it’s critically important to understand the difference between “relations 
proper” and “elementary relations”, can
you tell us what that difference is, or point us to an explanation? These are 
not terms that Peirce uses, so how can
the rest of us tell whether we understand them or not? Being unfamiliar with 
those terms does not indicate lack of
understanding of the important concepts they signify.

Gary f.

From: Jon Awbrey [mailto:jawb...@att.net] Sent: 27-Nov-15 11:16

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


--

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

[Jerry LR Chandler]

List, Jon:

On Nov 27, 2015, at 11:11 PM, Jon Awbrey wrote:

> I used the phrase “relations proper” to emphasize that I was speaking
> of relations in the strict sense of the word, not in any looser sense.

The meaning of what you are seeking to communicate with this sentence is 
unclear.

Does the phrase:
>  the phrase “relations proper”

refer to biological relations (Mendel's Law)?

refer to chemical relations  (between atoms and molecules)?

refer to social relations (among human being)?

refer international relations (among nations)?

refer to continuous relations (among variables)?

What are the legi-signs (rules, habits) that distinguish "proper relations" 
from its negation, non-proper relations?

Finally, do "proper relations" have unions that unify the units of the tuple?

Cheers

jerry


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RE: [PEIRCE-L] Re: signs, correlates, and triadic relations

[gnox]

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 will add some corollaries which follow from these general 
principles and frame the classification which follows.]

 

234. Provisionally, we may make a rude division of triadic relations, which, we 
need not doubt, contains important truth, however imperfectly apprehended, 
into— 

Triadic relations of comparison,

Triadic relations of performance, and

Triadic relations of thought.

1.Triadic relations of Comparison are those which are of the nature of 
logical possibilities.

2.Triadic relations of Performance are those which are of the nature of 
actual facts. 

3.Triadic relations of Thought are those which are of the nature of laws. 

[The numbering I have supplied here suggests how the phenomenological 
categories (Firstness, Secondness and Thirdness) apply to this “rude division 
of triadic relations.” Thus we may reword the first to say that logical 
possibilities are triadic relations in which 1ns predominates; actual facts are 
triadic relations of Performance, in which 2ns predominates; and laws are 
triadic relations of Thought, in which 3ns predominates. The ordering of these 
relations proceeds from simple to complex, as Peirce explains next:]

 

235. We must distinguish between the First, Second, and Third Correlate of any 
triadic relation. 

The First Correlate is that one of the three which is regarded as of the 
simplest nature, being a mere possibility if any one of the three is of that 
nature, and not being a law unless all three are of that nature. 

236. The Third Correlate is that one of the three which is regarded as of the 
most complex nature, being a law if any one of the three is a law, and not 
being a mere possibility unless all three are of that nature. 

237. The Second Correlate is that one of the three which is regarded as of 
middling complexity, so that if any two are of the same nature, as to being 
either mere possibilities, actual existences, or laws, then the Second 
Correlate is of that same nature, while if the three are all of different 
natures, the Second Correlate is an actual existence. 

[The importance of this general principle can hardly be overestimated. Taken 
together with the text that follows, it explains why the application of three 
trichotomies to S-O-I gives us only ten classes and not 27 (3³), why a 
Qualisign cannot be a Symbol or a Symbol a Qualisign, etc. But this is 
difficult to see until we see how Peirce analyzes the R-O-I relation by its 
correlates, which he does in CP 2.242:]

 

242. A Representamen is the