Signs and semiosis
Signs can at first glance be seen as a generalization of semantic meaning. Using terms introduced by Ferdinand de Saussure in his study of semiology, we can say that a signifier is a type (exemplified by replicas) associated with a signified. The sign "[cat]", for instance, associates the signifier "cat" (a word-type) to a signified: the idea of a cat. This tool is nimble and was swiftly expanded to visual signs (a stop sign), bio-signs (that elicit behaviour in living beings), and much more. Yet, this approach is still linguistic above all else. Saussure sees signs primarily as nodes in the vast network of language; he assigns to them a relational or structural role rather than freestanding existence. Furthermore, signifier and signified are unequivocally psychological in nature to Saussure.
An alternate view of semiotics by C.S. Peirce took the theory of signs from a linguistic endeavour to a holistic model of metaphysical import, mirroring in pragmatic philosophy what Frege was developing in proto-analytic philosophy. Peirce’s key insight was to describe signs as a triadic entity involving a representamen, an interpretant, and an object. (As an aside, I need to note that I’ll mostly make use of Peirce’s 1903 terminology here — adapting it for my own purposes a needs be. Peirce developed his model over decades, and not only are there several markedly different accounts, his terminological creativity knew no bound, arguably leading to an overabundance of neologisms. Readers should see no harshness here: I empathize with Peirce’s quest for consistent and evocative neologisms).
A representamen would be a type (the utterance of a word, a physical object, a thought) that stands for something else and is in effect the sign’s vehicle. The object is what the representamen stands for. Peirce takes an expansive view of objects, explicitly stating that the object of a sign does not need to exist to fulfil that role; Platonists or Meinongians would find no fault with that idea. Lastly, the interpretant is all that the sign can in itself signify, mean or convey. Peirce steered clear of the term "meaning", perhaps lest his subtle notions be conflated with how others used that term; he also rejected "signification" as too narrow, since too him an interpretant could be an emotion or an action, rather than a verbal expression.
So far we are in familiar territory. Representamen and interpretant seem close enough to, respectively, signifier and signified. Interpretant and object remind us of Frege’s sense and reference. The resulting "semiotic triangle" does not by any means originate with Peirce’s work: it was used in some way, shape or form by Stoics and by medieval scholastics. After Peirce, it became a hallmark with Richards and Ogden’s historically informed book on meaning. But for all the explanatory value of that trichotomy, one may still wonder how signs could make a claim for their own ontological category: can’t they simply be considered as a molecular complex of simpler entities, be they physical, mental or abstract? In the case of the sign for "cat", the triad associates a vehicle, the word "cat", which is determines by an object, the kind "cat", and which determines an interpretant: the meaning of "cat". Can’t the sign simply be an ontological compound made from those semantic atoms? That is where Peirce makes his mark: to him, the relation between a sign’s components is genuinely triadic. That statement rests on his own work in algebraic logic, later referred to as the reduction thesis. Under Peirce’s chosen logical framework, it is possible to prove that the general triadic relation cannot be decomposed into dyadic and monadic ones. At the same time, tetradic, pentadic, and all larger polyadic relations can be decomposed. Therefore monads, dyads and triads appear as the only fundamental relations.
With that idea, we’re reaching the core of what makes this semiotic model special. Peirce doesn’t see triadic relations as a convenient representation of signs only, he identifies the two: any triadic relation is a sort of sign, and is intertwined with the ideas of mediation and of meaning. With that, we’re already traveling beyond the bounds of language interpretation and human communication. Unlike Saussure, Peirce does not see the semiotic process as necessarily involving sentient utterers and interpreters. He attempts to explain his stance through the notion of quasi-mind. That is consistent with his pragmatic approach, which sees human thought as governed by "laws of mind" or habits. The purpose that distinguishes sentient behavior from pure physical consequence is already apparent, to Peirce, in the quasi-purpose of biological evolution, itself a byproduct of physical evolution. Reverting those principles allows to consider structures "expressed" by quasi-utterers (like a crystal, or a beehive) as the sign-vehicles denoting their object (a law or organizing principle of some type). In addition, Peirce vehemently rejects the idea of a single sign existing in a vacuum — the interpretant of a sign can itself be a sign (in some versions of his taxonomy, Peirce calls it the "interpretant sign"), leading to a process of infinite semiosis, which is characteristic of thinking, but obviously broader when applied to quasi-minds. Such a strand of thought can lead to postulating pansemiotic theses, and see the whole universe as a semiotic machine, as some have.
This foundational nature of triadicity/semioticity led Peirce to erect it as a full-blown ontological category he called Thirdness (not his most inspired neologism, but I have nothing better to propose at this time...). As can be expected from our considerations about irreducible relations, his system (which he called cenopythagorean) appeals to three categories.
Firstness is monadic. Its characterization is as a quality or feeling. Modally it indicates possibility. Other terms Peirce associated with it include "complete in itself, freedom, measureless variety, freshness, multiplicity, manifold of sense, peculiar, idiosyncratic"
Secondness is dyadic. Its characterization is as a reaction or resistance. Modally it indicates actuality. Other terms Peirce associated with it include "otherness, comparison, dichotomies, mutual action, will, volition, involuntary attention, shock, sense of change"
Thirdness is triadic. Its characterization is as a representation or habit. Modally it indicates necessity. Other terms Peirce associated with it include "composition, continuity, moderation, comparative, reason, sympathy, intelligence, structure, regularities, representation".
Peirce did not conceive his ontology by appealing to familiar entities like concrete objects and properties. We can only surmise, simplistically, that his firsts (characterized by firstness) could be qualia, that seconds could be denizens of the physical world, and that thirds would cover abstract entities from our third realm, alongside perhaps mental states that are not purely qualitative.
Peirce uses this model to propose his much-discussed classifications of signs. You may note the plural. He was constantly revising his system throughout his life, yielding countless arrangements. I’ll refer to his 10-sign system from 1903 here (in following years, he would develop, albeit not as fully, a 28- and a 66-sign system). The method is based on three trichotomies (Peirce would pleasantly admit he suffered from "triadomania"). The representamen itself could be a first (for instance, an emotion), a second (an uttered word) or a third (the corresponding word-type). The respective names for those are qualisign, sinsign and legisign. The next trichotomy examines the way the object of the sign determines its representamen. If that determination is a first, the representamen is akin to the object in terms of some quality — the relation is said to be iconic (for instance, a stick figure for a person). If it is a second, then the representamen is in an actual connection with the object — an indexical relation (meow sounds indicating a cat is around). If it is a third, the representamen is associated with the object by virtue of a law or habit — that is a symbolic relation (a national flag). The third and last trichotomy is concerned with the way the representamen determines the interpretant. Should that relation be a first, it is called rhematic (for instance, the single name "Joe", the unsaturated predicate "is a man", or a logotype are rhemes: they refer to their object in a symbolic way, but are interpreted as evoking a unitary concept). When that relation is a second, it is called dicent (a proposition or a saturated predicates qualify, since they are interpreted as dyadic relations, or compounds thereof, and associated with an idea of actuality, given their definite truth-value). Lastly, if that relation is a third, the sign is called an argument, and as the name suggests it is exemplified by logical sequences such as a syllogism. Most thoughts are considered by Peirce as arguments.
Careful readers are surely wondering why a system based on a triple trichotomy does not yield 27 kinds of signs, instead of 10. That is because all combinations are not admissible. Peirce showed that the valence of a representamen cannot be exceeded by that of the R-O relationship. Similarly, the valence of an R-O relationship cannot be exceeded by that of the R-I relationship. The 10 resulting types of signs are (1) (rhematic iconic) qualisigns (2) (rhematic) iconic sinsigns (3) rhematic indexical sinsigns (4) dicent (indexical) sinsigns (5) (rhematic) iconic legisigns (6) rhematic indexical legisigns (7) dicent indexical legisigns (8) rhematic symbol(ic legisign) (9) dicent symbol(ic) legisign (10) argument(ative symbolic legisign).
Taking stock of this brief account of Peirce’s semiotics, was I justified in introducing signs as a possibly distinct category alongside meanings, properties, etc.? It seems like a halfway measure: either one adheres to Peirce’s notions of Thirdness and pansemiosis, and then signs are perhaps the only type of abstract entity. Or one doesn’t and then signs can be decomposed and do not constitute a sui generis class of abstracta. But again, what I’m building here is an almost cladistic account of entities that could be the basic bricks of my ontology. I have no qualms over-populating it at the moment.