Peirce’s triadic logic as a meso-logic

By Rodrigo Cáceres.

Mesology (in the sense of von Uexkûll’s Umweltlehre and Watsuji’s fudogaku) has recently attempted to establish a logical foundation for the reality of its subject matter, the milieu. Indeed, mesology’s logical notation for reality, namely S as P for I (an interpreter I takes S as P) goes beyond Aristotelian logic, whose corresponding principles of non-contradiction and excluded middle do not allow for the biaffirmation of both S and P. In other words, reality cannot be S as well as something that is not-S. In order to go beyond Aristotelian logic, mesology has resorted to a logic beyond the West, namely the tetralemma, another logical view present in East at least from the III century A.D in India. The tetralemma, as its name suggests, is a view of four points or corners where beyond the Aristotelian mutually exclusive possibilities of either affirmation or negation (A or not-A) it allows also for binegation (neither A nor not-A) as well as biaffirmation (both A and not-A). 

The significance of resorting to the tetralemma is that by employing it one is able to logically affirm contradictory claims simultaneously. Let us consider the trivial example: “Human nature is rational” and “Human nature is emotional”. Both assertions seem contradictory at first sight, and only one of them can be true within the Aristotelian view. However, what we currently understand from the cognitive sciences is that both statements are true, we are both rational and emotional. More precisely, reason is nested or embedded in emotion, such that we are unable to reason if we are unable to feel (Damasio, 1994). In Humberto Maturana’s terms, whenever we are languaging this is always happening on the basis of a certain emotioning which will predispose our modes of languaging.

Neurobiologist Francisco Varela was also led to such kind of contradictory claim when he asserts his lemma that “the mind neither exists nor does not exist” corresponding to binegation within the tetralemma (neither A nor not-A). He relates this claim to what he calls the “key-point of emergence” from the local to the global, giving the example of neural interactivity at local levels giving rise to a global state or unity “which arises on the basis of local rules and has a different ontological status, because it brings forth with it the creation of an individual or a cognitive unit”. For him, this kind of ontological emergence: 

[R]eveals the importance of conceiving a new mode or type of existence, a new way of characterizing what a thing is. It is a mode of existence from which one cannot say it does not exist (“Francisco does not exist”). I count for something; you are reading what I wrote. At the same time, what is the nature of my existence? We do not assume that there is something substantial or a special quality residing in some part of my brain that makes Francisco be Francisco […] Therefore, it is like saying it is and it is not there”. (Varela, 2000)

One way of solving this apparent contradiction -implicitly suggested by Varela- is through a recognition that reality or ontos (that which is) has different ontological levels, in such a way that at the microscopic level of local neural activity one cannot distinguish such a thing as Francisco (Francisco does not exist). However, at the same time at the macroscopic level of human experience or mediance, Francisco exists through his personality, his image, his writings, etc. (Francisco exists). In this way, just as Varela poses it at the end of his quote, the initial binegation is reframed as a biaffirmation (both A and not-A).

Berque (1996) also discusses another of these contradictions in the context of the ontologies of Heidegger and Watsuji. In his treatment of Dasein, Heidegger ends up establishing that death for Dasein is Dasein’s most proper and unsurpassable possibility, which leads him to conceptualize his notion of being-toward-death (Sein zum Tode). Conversely, Watsuji reframes this notion on the argument that Heidegger’s understanding is an individualistic one. In his own terms, Watsuji poses that: 

man dies, the linkage between men changes, but while dying and changing, men live and the betweenness [aida] of men continues. It is in the fact of ending ceaselessly that this linkage continues ceaselessly. That which, from the point of view of the individual, is being-toward-death [shi e no sonzai], is being-toward-life [sei e no sonzai] from the point of view of society. (cited in Berque, 1996).

Watsuji is able to claim this on the basis of his own ontology, where human existence is mediance, which is composed of two existentially connected ‘halves’, one half being individual and the other collective or social. It is in this sense that while the individual half of being may be finite and oriented towards death, the collective half (composed of institutions, symbols, cultural conventions and agreed meanings, etc.) is able to ceaselessly continue its existence. We have, again, two apparently paradoxical concepts (being-toward-death and being-toward-life) that within Aristotelian logic must be mutually exclusive. However, since Watsuji’s ontology of the milieu is dual or dyadic, comprising both an individual half as well as a collective half, these two may -and they concretely do- be oriented in totally opposite directions at the same time, which amounts to the biaffirmation within the tetralemma (both A and not-A). There is both collective being-toward-life as well as individual being-toward-death.

Another -ontological- example of these paradoxes is Plato’s treatment of chôra in the Timaeus (according to Berque, the ancestor of the concept of milieu), where he describes chôra both as a nurturer or matrix (that which marks) as well as an imprint (that which is marked), contradictory aspects that lead Plato to conclude that chôra is something “hard to believe” (mogis piston), the result of a “bastard reasoning” (logismô tini nothô), renouncing thus to give a definition for it. Berque argues that Plato qualifies chôra in these terms because his logical frame is the one inherited from his predecessor Parmenides, namely the logic of identity of the subject, present in Parmenides’ famous fundamental claim about being: “what is, is” (S is S). It is Aristotle who -as a successor of Plato- makes explicit this logic of identity of the subject and develops it, which is the basis for his syllogism (All men are mortal; Socrates is a man; therefore, Socrates is mortal). Within this logical frame, chôra cannot be at the same time an imprint (S) and its opposite (a matrix: not-S).

According to Lakoff & Johnson (1999), Aristotelian logic is a nothing but a formalization of container logic. Containers in cognitive science are image-schemas that we constantly use in order to make sense of physical objects as well as describing positions and relations in language. The most common container concepts are “in”, “out”, “within”, “inside”, “outside”, “interior”, “exterior”, “enter”, “exit”, which depict the position of a certain entity relative to a container (e.g. “I was in my house; she is in my mind) as well as motion with respect to a container (e.g. I went through the park, I entered the room). The authors argue that Aristotle understands predicates as containers, such that if “Socrates is mortal”, it is understood that Socrates is “within” the category of “mortals”, just like an object inside a container along with many other (mortal) objects inside it (e.g. Socrates, Lakoff, Francisco Varela, etc.). Aristotle’s container logic leads him logically to establish that an entity cannot both have a predicate and not have it (principle of non-contradiction). In metaphorical terms, this means that an entity cannot be at the same time inside and outside a container. Precisely, it can only be true that it is either outside or inside (principle of excluded middle).

Peirce’s logic 

Charles S. Peirce was also quite concerned with logic and especially with the overcoming of nominalism. As one of his main contributions, he developed a triadic system of philosophical categories: Firstness, Secondness and Thirdness, which he derived both logically and phenomenologically. His logical derivation of the categories is the one which will be of interest in this essay, which is based on Peirce’s original logic of relations. His concept of relations is defined in terms of the rhema, a kind of sign.

If parts of a proposition be erased so as to leave blanks in their places, and if these blanks are of such a nature that if each of them be filled by a proper name the result will be a proposition, then the blank form of proposition which was first produced by the erasures is termed a rheme (CP 2.272).

Thus, examples of rhemes are: 

__ is mortal. 

__ is the lover of __.

__ gives __ to __.

Due to his formation as a chemist, Peirce understood rhemes just as atoms having specific valences. Just like the rheme “__ is mortal”, the hydrogen atom has a valence of 1, meaning that it has only one bond available before it is saturated. The concern for Peirce regarding the formalization of his logic of relations, was the number of irreducible relations necessary to account for the formation of complete propositions. Peirce’s answer is three: monadic relations, dyadic relations and triadic relations. In the proposition “Socrates is mortal”, the rheme “__ is mortal” is a monadic predicate insofar as it has only one blank available to be filled. In the proposition “Jean is the lover of Mary”, “lover” functions as a radical that can be linked with two more things before being complete or saturated. In other words, it is a dyadic predicate. Finally, in “Jean gives a book to Mary” and its corresponding rheme “__ gives __ to __”, we are in front of a genuine triadic relation, which means that -according to Peirce- it cannot be understood as a composite of monadic and dyadic relations. If we were to decompose the proposition in “Jean leaves a book” and “Mary picks up a book”, the intention of giving becomes erased, so these two dyadic relations are not equivalent to the triadic relation. It is genuine in that all three elements are indispensable for the proposition to be complete. 

As well as describing the act of giving, triadic relations can also designate the prototype of acts of interpretation. For example, in the proposition “Jean took Mary’s gesture as an offense” we can abstract the following rheme “__took __ as __” which is nothing but the principle of trajective reality: “I takes S as P”. This triadic relation is also genuine in that if we decompose it into dyadic relations “__ as __” (as in ‘a gesture as an offense’, ‘time as money’, ‘future as forward’, ‘S as P’) we would inauthentically abstract the interpretation or mediation of I, the one who takes the logical subject (S) and takes it somewhere else (P).

We could also argue that the principle of creation can also be affirmed through a triadic relation, as in the proposition “Jean made a pot out of clay” whose corresponding rheme is “__ made __ out of __“ having also a valence of three. Indeed, within mesology, reality for a certain living being is more than just an interpretation, it is a creative interpretation, in such a way that the resulting predicate of a particular trajection has a novel ontological status. 

According to Peirce, these three kinds of predicates have an ordinal or hierarchical relation with each other. Monadic relations do not require dyadic relations, but not the other way around, since dyadic relations necessarily involve monadic ones. In turn, dyadic relations can exist without triadic relations, but not the other way around. For Peirce, these three relations constitute universal categories: firstness, secondness and thirdness (or as he prefers to calls them elsewhere: quality, reaction and mediation). 

The ontological status of the sign

One of Peirce’s central concepts, the sign, was defined by him as a third, namely as something “which brings a First into relation to a Second” (CP, 8.332). For Peirce, thirds and thirdness were usually related to processes of mediation, such that at a certain moment looking back on his own earlier work, he notes that: “All my notions are too narrow. Instead of ‘sign’, ought I not to say Medium” (1906: MS 339: 526). 

There is a certain homology that can be noticed between the ‘Umgebung/Umwelten’ distinction  made by the naturalist von Uexküll (that was likely inspired by the noumena/phenomena distinction in Kant) and Peirce’s categories. In a letter to Lady Welby, Peirce defines firstness as “the mode of being of that which is such as it is, positively and without reference to anything else” (CP, 8.328). In other words, firstness is that which is in its self-identity, just like what for Berque takes place with the “universal base [which] does not exist – it does not ek-sist (stand out) from the gangue of its self-identity – if it is not drawn outside by a certain world” (Berque 2019, p.7). 

Starting from the unfolding of this self-identical universe (or universal base) that is concealed, we get to the point where life appears. Life, as Hoffmeyer (1998) argues, establishes a certain asymmetry between the organism and the environment through the production of a membrane which separates the ‘in-side’ from the ‘out-side’. In other words, living organisms are ‘seconds’ in that they overcome the self-identical status of the universe by means of establishing a distinction and, hence, a certain organism-environment dyad or couple. However, this ‘second’ or living organism which distinguishes itself from this self-identical universe cannot directly relate to the latter. This occurs because in order for the organism to interact or react to something that is not itself, the latter has to have some significance which will orient the reaction, and this significance can only be provided by reference to the organism or ‘second’. 

In the literature, this has been approached through several angles. Jakob von Uexküll, for example, claims as a result of his experiments “that an animal may ever enter into relation with an object, this tacit hypothesis [that of behaviourism] is false”. This thesis is meaningful in the background of Uexküll’s distinction between object and sign, the object being the thing in-itself (a first in Peircean notation) and the sign (a third for Peirce, as we shall see) carrying the ‘tone’ of the organism’s ends (object as food, shelter, obstacle, etc.).  

Within biology of cognition, the corresponding notion is the autonomy of the living (Varela, 1979), which founds the idea that living beings are structurally determined systems that define the terms upon which their environment will be assimilated. In this manner, perturbations from the environment cannot be instructive or informative, because it is the very organism who specifies the domain of operational coherences in which he operates.

These perspectives illustrate the logic of this ‘third term’ which completes the triadic relation of a first (objective universe), a second (a self-referential subject) and a third (a sign, i.e. a second that takes a first as a third). Since this is based in Peircean categories, this configuration is ontogenetic or ontochronological (if the reader may cope with this term), meaning that the objective universe happens first, the organism which creates an asymmetry or distinction from this objective basis comes second and finally the sign -the terms upon which the second takes the first- comes in third place.

The sign, as a third, has naturally a paradoxical or ambiguous status. Since we require an object in-itself in order to translate it into a sign, a part of the sign is independent of the interpreter and a part of the sign depends on the interpreter. In other words, the sign (I takes S as P) is both dependent and independent of the interpreter. More precisely, the sign is partly dependent on S (the object in-itself) as well as on I (who translates it into P). 

Following Uexküll, this means that in our personal lives we cannot directly engage with the physical-objective world, instead we can only engage with it through the mediation of the phenomenal (sensation, image, sound, smell, taste, etc.). Only then, it is through the nature of our encounters with the phenomenal that we can abstract the physicality of things, namely through the encounter with things that oppose resistance (sensation), which are heavy (sensation) or tangible (sensation) as opposed to intangible (such as emotions, thoughts, or even air).

In other words, when I takes S as P we shall not infer that the object in-itself (S) is denied through its translation or trajection into P, but only that it is made meaningful in reference to I. However, what is made meaningful on the basis of this ‘universal base’ is only a partial selection, as is the case in that our color vision relies on electromagnetic waves of the relatively small spectrum of 400 to 700 nm. The universal base is not only then made meaningful but also made relevant, since what is taken to be signified is not the totality of the universal base but rather a partial section of it. For Merleau-Ponty, this means that “it is the very organism -according to the nature of its receptors, the threshold of its nervous centers and the movement of its organs- which chooses the stimuli of the physical world upon which it will react.”

It should be noted that this process of signification or trajection (S as P) presupposes what Berque calls subjecthood, namely “the fact of being a subject, not an object, and being capable thus of trajecting the environment (S) according to its own predicates (P).”. However, this subjecthood which discloses a world of color images, sounds, sensations, etc. is not our own subjecthood (in the subjective, more restricted sense). One way of seeing this is that we -as living persons- are confronted to an already constituted milieu of signs which we understand and interact with, such that we do not participate in the bringing forth of the reality (S as P) of the signs that we experience. Our own subjecthood, in a more restricted sense, is nested in the sense of “me”, in our capacity to make decisions, to evaluate, to create, move freely, think consciously, etc. In other words, our own subjecthood seems to be embedded in a more encompassing subjecthood, the latter being responsible for the bringing forth of our experiential milieu.

Another way of seeing this is through Heidegger’s idea that “a human being is the entity which in its being has this very being as an issue”. In other words, for Heidegger it is Dasein who is concerned with ontological questions about his own being. And, as we know from evolution, Dasein is at the frontier of cosmogenesis and complexity: it is the creature who can make use of language, reason and freedom of thought, devices that are indispensable requirements to be able to pose ontological/metaphysical questions and be concerned by them in the first place. However, when Dasein opens his eyes, finds himself surrounded by a world and then asks ontological questions concerning this ‘being’, he has no clue that this world was brought forth by an active process of creative interpretation of a concealed ‘universal base’, mediated by a more encompassing form of subjecthood that his very organism enables. 

For Lakoff & Johnson (1999), the collection of all these interpretations that are effortlessly made and do not require our participation (Dasein’s participation) lead them to conceptualize a “cognitive unconscious”, that is, cognitive activity that happens below the conscious level or even too fast for us to notice that it happened. Later in the book, these authors speak of a ‘hidden hand’ of this cognitive unconscious, implying intentionality and choice on its part, although these aspects are hidden from our consciousness since we operate with the already selected contents made available by this cognitive unconscious (whether it is frames, prototypes, metaphorical inferences, etc.). 

This amounts to notice that through mesology we need to acknowledge the existence of the unconscious as a central part of our being. However, it is not the unconscious in a psychoanalytic sense, but more precisely whatever occurs without our participation and at the same time presupposes a certain subjecthood. This subjecthood is the one that chooses the kinds of interpretations that are effectively made, even those which found our very experiential reality (S as P).

Brock (1949) brings up an example which can illustrate this conscious/unconscious relation:

human beings consciously perceive only a small fraction of all biological processes. If, for example, we put a drop of acetic acid of a particular concentration on our tongue, we will perceive the taste of something sour; and if we put a drop with the same concentration on the sphincter of the stomach it will contract, but there is no sensation of taste. Looked at from a biological point of view, the tongue as well as the pylorus "perceive" something, but only in the first case do we experience the perceptual cue consciously. 

Within the frame presented by Brock, we need to abandon the idea of considering consciousness as a faculty or attribute, like we do with faculties like memory and language. Framing consciousness as something one ‘has/has not’ immediately puts us within the Aristotelian frame of attributes and their mutual exclusivity: one cannot at the same time have consciousness and not have it. Yet this is precisely what is put forth in the example: there is a multitude of biological processes, some of which enter our conscious awareness and some do not. Once more, we get to a biaffirmation: we are both aware and not aware of our bodily operations.

References

Berque, A. (1996). The Question of Space: From Heidegger to Watsuji. Ecumene, 3(4), 373–383. doi:10.1177/147447409600300401 

Berque, A. (2019). An enquiry into the ontological and logical foundations of sustainability: Toward a conceptual integration of the interface ‘Nature/Humanity’. Global Sustainability, 2.

Damasio, A. R. (1994). Descartes’ error: Emotion, rationality and the human brain.

Lakoff, G., & Johnson, M. (1999). Philosophy in the flesh: The embodied mind and its challenge to western thought (Vol. 640). New York: Basic books.

McNabb, D. (2019). Hombre, signo y cosmos: La filosofía de Charles S. Peirce. Fondo de Cultura Economica.

Hoffmeyer, Jesper. (1998). Surfaces inside surfaces: On the origin of agency and life. Cybernetics & Human Knowing. 5. 33-42.

Varela, F. (2000). El fenómeno de la vida. Dolmen. Santiago.

Von Uexküll, T. (1987). The Sign Theory of Jakob von Uexküll. Classics of Semiotics, 147–179. doi:10.1007/978-1-4757-9700-8_7