What do you consider the most important topics and/or contributions in the theory of meaning and signs?
John F. Sowa (www.jfsowa.com/pubs/5qsigns.htm, accessed 21 May 2017) answered this question as follows:
The single most important contribution was Peirce’s integration of the theories by the Greeks and Scholastics with modern logic, science, and philosophy. Aristotle laid the foundation in his treatise On Interpretation. His opening paragraph relates language to internal affections (pathêmata), whose existence is not in doubt, but whose nature is unknown:
First we must determine what are noun (onoma)
and verb (rhêma); and after that, what are negation (apophasis), assertion (kataphasis), proposition (apophansis), and sentence (logos). Those in speech (phonê) are symbols (symbola) of affections (pathêmata) in the psyche, and those written (graphomena) are symbols of those in speech. As letters (grammata), so are speech sounds not the same for everyone. But they are signs (sêmeia) primarily of the affections in the psyche, which are the same for everyone, and so are the objects (pragmata) of which they are likenesses (homoiômata). On these matters we speak in the treatise on the psyche, for it is a different subject. (16a1)
In this short passage, Aristotle introduced ideas that have been adopted, ignored, revised, rejected, and dissected over the centuries. By using two different words for sign, he recognized two distinct ways of signifying: sêmeion for a natural sign and symbolon for a conventional sign. With the word sêmeion, which was used for omens and for symptoms of a disease, Aristotle implied that the verbal sign is primarily a natural sign of the mental affection or concept and secondarily a symbol of the object it refers to.
The implication that ‘the verbal sign is primarily a natural sign’ and only ‘secondarily a symbol’ is very suggestive about the nature of what we call ‘natural languages.’ Peirce’s refinements of Aristotle’s semeiotic made such insights more explicit, and sometimes adapted Aristotle’s terms to that end. For instance, Peirce used Aristotle’s ῥῆμα (rhêma) to designate the first in a trichotomy of signs (representamens) which goes back to the logic of the Scholastics:
A representamen is either a rhema, a proposition, or an argument. An argument is a representamen which separately shows what interpretant it is intended to determine. A proposition is a representamen which is not an argument, but which separately indicates what object it is intended to represent. A rhema is a simple representation without such separate part.
Esthetic goodness, or expressiveness, may be possessed, and in some degree must be possessed, by any kind of representamen,— rhema, proposition, or argument.
Moral goodness, or veracity, may be possessed by a proposition or by an argument, but cannot be possessed by a rhema. A mental judgment or inference must possess some degree of veracity.
EP2:204
Peirce’s distinction between esthetic and moral goodness is basic to his account of the ‘normative sciences,’ which include logic as the means of judging the veracity or truth of a proposition. The observation that a rhema can possess ‘expressiveness’ but not ‘veracity’ reflects its Firstness in this trichotomy as ‘a simple representation’ which can only represent a possibility, and not a fact or a reason.
As Peirce put it later in the same year (1903), this trichotomy is a division according to how the sign’s ‘Interpretant represents it as a sign of possibility or as a sign of fact or a sign of reason’ (EP2:291). For this presentation of the trichotomy, Peirce refined the terminology: rhema became rheme (‘a Sign of qualitative Possibility’), and proposition became dicisign (‘a Sign of actual existence’). He kept the term argument for ‘a Sign of law’ (EP2:292).
In his ‘Prolegomena to an Apology for Pragmaticism’ (1906), Peirce departed still further from the traditional trichotomy:
A familiar logical triplet is Term, Proposition, Argument. In order to make this a division of all signs, the first two members have to be much widened.
CP 4.538
For this purpose Peirce coined new terms based on Greek roots, Seme and Pheme. But his explanation of Existential Graphs in that same article employed the term ‘rheme’ to denote a predicate or ‘blank form of proposition,’ where the blanks could be filled by subject-names to compose a complete proposition.
By a rheme, or predicate, will here be meant a blank form of proposition which might have resulted by striking out certain parts of a proposition, and leaving a blank in the place of each, the parts stricken out being such that if each blank were filled with a proper name, a proposition (however nonsensical) would thereby be recomposed.
CP 4.560
Through all these conceptual and terminological changes, there is a kind of continuity with Aristotle’s usage of rhema for a “verb” as distinguished from a “noun” (onoma). Peirce uses rheme for a predicate as opposed to a subject of a proposition. Both predicates and subjects can be called “terms,” but in Existential Graphs that represent propositions, rhemes are primarily signs of qualitative possibility or Firstness while the latter are primarily signs of actual existence or Secondness. The joining or copulation of predicate and subject is the key to the act of meaning performed by the proposition, just as the joining of icon and index is key to the informing power of a symbol, its genuine Thirdness.