Robert Marty

Red italic are words of Peirce highlighted by me ; when are underlined it is because this words denote a necessity.

Blue Italic are added by me and point out the classes of signs formalized.

Diagrams repeat the classes of signs mentioned inside every paragraph with the relations proceeding from the lattice of the classes of signs :



254. The three trichotomies of Signs result together in dividing Signs into TEN CLASSES OF SIGNS, of which numerous subdivisions have to be considered. The ten classes are as follows:


            First: A Qualisign   [e.g., a feeling of "red"] is any quality [ 1 ] in so far as it is a sign. Since a quality [ 1 ] is whatever it is positively in itself, a quality can only denote an object by virtue of some common ingredient or similarity; so that a Qualisign is necessarily an Icon. Further, since a quality is a mere logical possibility, it can only be interpreted as a sign of essence, that is, as a Rheme [ 1 ]   . 


            255. Second: An Iconic Sinsign    [e.g., an individual diagram] is any object of experience [ 2 ] in so far as some quality  [ 1 ]  of it makes it determine the idea of an object. Being an Icon, and thus a sign by likeness purely, of whatever it may be like, it can only be interpreted as a sign of essence, or Rheme [ 1 ].


 It will embody a Qualisign .


            256. Third: A Rhematic [ 1 ]  Indexical Sinsign [e.g., a spontaneous cry] is any object of direct experience [ 2 ] so far as it directs attention to an Object [ 2 ]   by which its presence is caused.


It necessarily involves an Iconic Sinsign of a peculiar kind, yet is quite different since it brings the attention of the interpreter to the very Object denoted.



            257. Fourth: A Dicent Sinsign [e.g., a weathercock] is any object of direct experience  [ 2 ] , in so far as it is a sign, and, as such, affords information concerning its Object. This it can only do by being really affected by its Object [ 2 ] ; so that it is necessarily an Index. The only information it can afford is of actual fact [ 2 ].


Such a Sign must involve an Iconic Sinsign to embody the information and a Rhematic Indexical Sinsign    to indicate the Object to which the information refers.



But the mode of combination, or Syntax, of these two must also be significant.


According to me the mode of combination or Syntax evocated by Peirce is represented by the above diagram.


            258. Fifth: An Iconic Legisign [e.g., a diagram, apart from its factual individuality] is any general law or type [ 3 ] , in so far as it requires each instance of it to embody a definite quality [ 1 ]  which renders it fit to call up in the mind the idea of a like object. Being an Icon, it must be a Rheme [ 1 ]  . Being a Legisign, its mode of being is that of governing single Replicas, each of which will be an Iconic Sinsign     of a peculiar kind.



Remember that by 2-255 this Iconic Sinsign embody a Qualisign.


            259. Sixth: A Rhematic [ 1 ] Indexical Legisign  [e.g., a demonstrative pronoun] is any general type or law [ 3 ]  , however established, which requires each instance of it [ 2 ]  to be really affected by its Object in such a manner as merely to draw attention to that Object.


Each Replica of it will be a Rhematic Indexical Sinsign  of a peculiar kind. The Interpretant of a Rhematic Indexical Legisign represents it as an Iconic Legisign   ; and so it is, in a measure--but in a very small measure.



            260. Seventh: A Dicent Indexical[ 2 ]Legisign [e.g., a street cry] is any general type or law [ 3 ]  , however established, which requires each instance of it [ 2 ]   to be really affected by its Object in such a manner as to furnish definite information [ 2 ]  concerning that Object.


It must involve an Iconic Legisign  to signify the information and a Rhematic Indexical Legisign   to denote the subject of that information.


Each Replica of it will be a Dicent Sinsign  of a peculiar kind.



            261. Eighth: A Rhematic Symbol or Symbolic Rheme   [e.g., a common noun] is a sign connected with its Object by an association of general ideas in such a way that its Replica [ 2 ]calls up an image in the mind which image, owing to certain habits or dispositions of that mind, tends to produce a general concept, and the Replica is interpreted as a Sign of an Object that is an instance of that concept  [ 3 ]  . Thus, the Rhematic Symbol either is, or is very like, what the logicians call a General Term. The Rhematic Symbol, like any Symbol, is necessarily itself of the nature of a general type [ 3 ]  , and is thus a Legisign. Its Replica, however, is a Rhematic Indexical Sinsign  of a peculiar kind, in that the image [ 1 ]   it suggests to the mind acts upon a Symbol already in that mind to give rise to a General Concept [ 3 ] . In this it differs from other Rhematic Indexical Sinsigns, including those which are Replicas of Rhematic Indexical Legisign  . Thus, the demonstrative pronoun "that" is a Legisign, being a general type [ 3 ]  ; but it is not a Symbol, since it does not signify a general concept [ 3 ] . Its Replica draws attention to a single Object [ 3 ], and is a Rhematic Indexical Sinsign . A Replica of the word "camel" is likewise a Rhematic Indexical Sinsign , being really affected [ 2 ] , through the knowledge of camels, common to the speaker and auditor, by the real camel [ 2 ]  it denotes, even if this one is not individually known to the auditor; and it is through such real connection [ 2 ] that the word "camel" calls up the idea [ 3 ] of a camel. The same thing is true of the word "phoenix." For although no phoenix really exists, real descriptions [ 2 ]of the phoenix are well known to the speaker and his auditor; and thus the word is really affected[ 2 ]  by the Object denoted. But not only are the Replicas of Rhematic Symbol very different from ordinary Rhematic Indexical Sinsigns  , but so likewise are Replicas of Rhematic Indexical Legisigns  . For the thing denoted by "that" has not affected the replica of the word in any such direct and simple manner as that in which, for example, the ring of a telephone-bell is affected by the person at the other end who wants to make a communication.


The Interpretant of the Rhematic Symbol  often represents it as a Rhematic Indexical Legisign   ; at other times as an Iconic Legisign ; and it does in a small measure partake of the nature of both.



            262. Ninth: A Dicent Symbol  , or ordinary Proposition, is a sign connected with its object by an association of general ideas, and acting like a Rhematic Symbol ,  except    that  its intended  interpretant  represents the  Dicent Symbol  as being, in respect to what it signifies, really affected [ 2 ]  by its Object, so that the existence [ 2 ]   or law [ 3 ]   which it calls to mind must be actually connected with the indicated Object. Thus, the intended Interpretant looks upon the Dicent Symbol  as a Dicent Indexical Legisign ; and if it be true, it does partake of this nature, although this does not represent its whole nature. Like the Rhematic Symbol  , it is necessarily a Legisign. Like the Dicent Sinsign  it is composite inasmuch as it necessarily involves a Rhematic Symbol   (and thus is for its Interpretant an Iconic Legisign to express its information and a Rhematic Indexical Legisign  to indicate the subject of that information. But its Syntax of these is significant. The Replica of the Dicent Symbol is a Dicent Sinsign  of a peculiar kind. This is easily seen to be true when the information the Dicent Symbol conveys is of actual fact. When that information is of a real law, it is not true in the same fullness. For a Dicent Sinsign cannot convey information of law. It is, therefore, true of the Replica of such a Dicent Symbol  only in so far as the law has its being in instances.



            263. Tenth: An Argument   is a sign whose interpretant represents its object as being an ulterior sign [ 3 ] through a law  [ 3 ], namely, the law that the passage from all such premisses to such conclusions tends to the truth. Manifestly, then, its object must be general [ 3 ]  ; that is, the Argument  must be a Symbol. As a Symbol it must, further, be a Legisign. Its Replica is a Dicent Sinsign .



First observation :

If we start with the Argument above and we look back the classes combining every time  the diagram  encounted we rebuild the entire lattice.


Continuing with Peirce's text :


264. The affinities of the ten classes are exhibited by arranging their designations in the triangular table here shown, which has heavy boundaries between adjacent squares that are appropriated to classes alike in only one respect. All other adjacent squares pertain to classes alike in two respects. Squares not adjacent pertain to classes alike in one respect only, except that each of the three squares of the vertices of the triangle pertains to a class differing in all three respects from the classes to which the squares along the opposite side of the triangle are appropriated. The lightly printed designations are superfluous.



Second observation :


Replacing every square designed par Peirce by the corresponding algebraical notation, writing an arrow when the square are adjacents excepted when the relation (affinity) represented by the arrow is the result of a concatenation of two existing relations ( in fact we delete the redundancies )we obtain…the lattice  :





Conclusion :


The extraction of the algebraical lattice of the Peirce's text is realized by means of interpretation of the affinity between the classes of signs in terms of morphisms between the corresponding formalized classes. It seems that it is a progress because the affinities according to Peirce are founded on a  purely formal property without phenomelogical support. In fact the formalization add phenomelogical interpretation of the affinities.