C.W.Spinks
Peirce and Triadomania
A Walk in the Semiotic Wilderness

Mouton de Gruyter 1991


17 Triadomania explored
Categorical thinking
The categories are, of course, one of philosophy‘s perennial problems going back to Aristotle's conversion of a legal term into a logical one that describes the extension of a predicate, that is, the
category“ is concerned with distributive classification and how one knows what to include under the rubric of a term. The "category" thus has become a logical problem of classification and extension preparatory to determining how terms may interact in logical assertions, propositions, and syllogisms; the category in one way or another assigns distribution to terms, memberships within sets, and boundaries to the sets.

Of course, although logicians may grimace at my treatment of logical terminology, much of the philosophical interest in the categorical problem is a concern for the grammar of terms as subject and predicates and how those grammatical items include or exclude other terms, for
the effects of grammatical categories lie at the core of the issues of Realism and Nominalism in Logic, since the role of subject, predicate and copula are the architectonics of Indo-European logic.

18 Such concerns for the grammar of terms are a major impetus in the historical development of semiotics, but historically where those logico-grammatical categories seem to make a major shift in philosophy is Kant‘s turning of the semi-grammatical operation of Aristotle into an epistemological and ethical one of judgements, perception, and knowledge.

That adaption moves logic from being basically a grammatical calculus into being a theory of knowing or epistemology, and it is here that Peirce finds his entry, for through the categories he finds both the logic of discovery in the Semeiotic and a grammar of discovery in the Logic of Relatives. That is, one can adequately describe both the process and the structure of knowing, for the tri-relative influence operates in both the Semeiotic and Logic.

Peirce's interest in the categories goes back to his early interest in Kant. His "Short List" of three categories, which frames the whole development of Peirce's thinking, stems from his early Kantian and Hegelian critiques on the dialectic of knowing, the tension of the Ideal and the Real., and the categorical relation between Being and Substance. Peirce saw the need for a vast reconstruction of the philosophic tradition to answer „the riddle of the sphinx“ which Peirce conceived in terms of the
processes of naming, signing and classification.
By following Kant, he was able to keep philosophy within „the prescribed limits…of the world of appearances“, and by following Hegel, he was able to be confident of the „influence of Reason“ upon the philosopher‘s activities.
Peirce was dissatisfied with both procedures as he found them. Against Kant he would argue that it was bona fide stance to think of the unthinkable transcendental object; and against Hegel he would argue that the dialectic of Reason in Nature could not be postulated with a basis of precise and detailed logical and scientific investigation.

These two poles are the anchoring points of Peirce's Scholastic Realism:
an epistemological logic which recognises the power of the sign and yet expects that there is some immediate and dynamic relation between the world of objects and the world of signs. Thus, it is from these critiques and from the development of categories that Peirce is able to create his sign theory of cognition, the general theory of scientific explanation, and a general critique of epistemology.

The process of critique is a lifelong one for Peirce…The foundation for the categories is to be found in Peirce’s study of Schiller’s Aesthetische Briefe. From Schiller he develops the first vestige of the three categories as the I, It, and Thou to establish „harmony between the analytic and the synthetic methods of Kant and Schiller“. Later Peirce tries to join Kant’s four main categories of Quantity, Quality, Relation, and Modality to Schiller’s three pronominal categories in order to produce something which Esposito presents as a four-layered trichotomy, in which there are three stages: the first being an absolute indifference, the second an undeveloped differentiation; and the third a further combination of the two.
Thus, „One can hardly fail to notice the three fundamental conceptions at work…The I emerges as a nakedness, the It is externality, and the Thou as the combination of these in the dyadic relation of truth“. And Esposito argues that from this first statement of the three relations, „Peirce‘s task, then, became that of explicating how the real (platonic and idealistic) and actual (physical and sensory) were related on how one merged into the other“. So from the first the categorical impetus seeks some unity, semiotic or logic, in both the philosophy and science.

2.2 Prescission and precision
The process by which Peirce describes and generates his categories is
prescission, a term which despite its centrality to Peircean thinking is not very clearly understood. Still he goes out of his way several times to make a distinction between prescission and precision. For example, in „Issues of Pragmaticism“ in 1905, he discusses vague and definite signs as a way of explaining the characteristics of pragmaticism, the fourth of which is concerned with the vagueness of the „acritically indubitable“.

He first makes a distinction between the determinate and the definite by saying that determination has to do with a characteristic which „inheres“ in a subject or is predicated for it; this determination being exactly the general nature of signs which make them signs. He, then, makes a distinction between definite, or determined signs and vague signs on the basis of prescision, and from that distinction he launches into a longish etymological lesson on the terms of
precision and prescission.

If we desire to rescue the good ship Philosophy for the service of Science from the hands of lawless rovers of the sea of literature, we shall do well to keep prescind, presciss, prescission, and prescissive on the one hand, to refer to dissection in hypotheses, while precide, precise, precision, and precisive are used so as to refer exclusively to an expression of determination which is made either full or free for the interpreter.
We shall thus do much to relieve the stem „abstract“ from staggering under the double burden of conveying
the idea of prescission as well as the unrelated and very important idea of the creation of ens rationis out of epos pteroen – to filch the phrase to furnish a name for an expression of non-substantive thought - an operation that has been treated as a subject of ridicule - this hypostatic abstraction - but which gives mathematics half its power“ (CP 5.449).

Thus, it is important to look at how prescission works. First, Peirce defines the term as „mental separation…which arises from attention to one element and neglect of the other“. It is a term derived from Scotus’s praecisio, the act of supposing, but Peirce turns it into
a subset of abstraction and the process of classification by which to deal with the categorical limitations of terms.
More importantly, he makes it the major process by which the categories are discovered and the very mark of distinction of the categories themselves -
the different functions of the human mind and its interaction with the physical world.

Boe: to prescind - to separate or single out in thought; abstract.; prescission - dissection in hypothesis; an expression of non-substantive thought; mental separation; a subset of abstraction; the categorical limitations of terms; Duns Scotus: praescisio - an act of supposing.
prae-scindere - scindere - to divide; vor-unterscheiden
to prescind - to detach for purposes of thought : Für Zwecke des Denkens lösen

Peirce divides abstraction into two types, prescissive and hypostatic. Prescissive abstraction is „ that operation of the mind by which we pay attention to one feature of a percept to the disregard of others“ (4.235); it is apparently an active perception, or an active imagination, that is invested with very little grammaticality in categorical operations of classification, for it produces statements like „it is light“. It is a vague sign.

However, I do not think Peirce here is simply talking about existential import, or as he puts it, „the expression of nonsubstantive thought“even though „empty categories“are suggested by „non-substantive thought“.
Rather hypostatic abstraction is primarily a grammatical transformation of categorical operations for purposes of classification; it is a matter of distribution of terms as the classical logicians termed it.

To Peirce hypostatizing „ consists in taking a feature of a percept or percepts (after they have already been prescinded from other elements of the percept), so as to take propositional form in the judgement (4.235) Then after the prescission, hypostatizing functions „in concealing this fact to consist in the relation between the subject of the judgement and another subject, which has a mode of being that merely consists in the truth of propositions of which the corresponding term is the predicate“ (4.235)

Thus, the statement „it is light“ is transformed into „there is light here“. Such grammatical operations for Peirce are, of course, quasi-fictions, and although they happen to be very useful for cognition, mathematical, and/or signed thinking, Peirce’s real emphasis is that such operations are
generalisations, the essential Thirdness of sign activity.

Of course, one may ask how can Thirdness be „quasi-fiction“ since it eventually leads to the Ultimate Interpretant, and the answer lies in the process of approximation that is necessary for
semiosis growing from prescission toward abstractions (as substantive thoughts) and finally to a hypostatic abstractions which assert the relations as real and external to the sign. What is at issue here, I think, is the gradations and divisions of abstraction as a generalising process and a transformation from pure Firstness to semeiotic Thirdness.

Boe: the gradations and divisions of abstraction as a generalising process and a transformation from pure Firstness to semeiotic Thirdness.

This may sound, initially to the non-logician’s ear, like the twisting, serpentine spoor of a Scholastic thinker, and so it may be, but it is also more than just Thomistic word play. This is not a matter of assumed angels sitting on the metaphorical heads of possible brains, but
the distinctive differences between prescission and precision are at the very forefront of how human perception of the actual world and human cognition of the real world are interconnected. Like the geometrical abstractions of trigonometric ratios, prescission is an act of imaginative perception utilising the potential of the mind to perceive this stuff phenomena, but unlike the Platonic geometers, it makes no assumptions about the other elements from which it is prescinded.
Prescission is activity boundary between the analog and digital. It is the Peircean equivalent to No Mind, or Mu as ther Zen philosophers call it: the ability to sense/perceive without the imposition of digital categories. It is, I suspect, the heart of semiosis, the factoring out of characteristics, which are used without regard to some governing conceptual map.

Prescission is only partially a sign process; it is, as Peirce argues about Firstness, a sign in its purest potential functioning as a totally generative metaphoric structure that does not need the crossing of semantic markers. It is a marker of the abductive energy, the process of imagination, and sign generation and is all the Firstness of sign, fault of actual predication or perceptual judgement. It is, I believe, the last (or first depending on the direction of your analysis) frontier of the sign system where there is the edge between the knowing and knowable world.

Much like Julia Kristeva’s
chora and Eco’s „implicature“, it is an edge where of the ambivalence of sign function has freest play. (I call this edge the Trickster point; it is the locale of systemic ambivalences), it is the area of musement, to use Peirce’s term: wonderment, awe, speculation, imagination, discovery etc. At least this kind of semiotic boundary seems to be hypothetically true for Peirce, for prescission is the ability to separate out mentally without assertive prejudice as to the existence, relation, or distribution of terms, and Peirce utilises it consistently to separate out the categories from Kant’s Substance and Being.

Boe: chora - Trickster-point - musement

Prescission traces back the stages of perceptual judgement to before the percipuum. It traces to the very edges of its beginning before any kind of resistance is demanded by secondness; that is, beyond the need for assertion and before the dyadic resistance of the percipuum.

Prescission is a difficult concept, but it is one of the most powerful developed by Peirce and also one of the few which he keeps throughout his life work.


It is a free energy producer headed towards full Firstness and total potentiality, and
it seems to be as close to non-signed stuff as the human mind can come. It is the only possible margin of human knowing, for on the other side, that is only unsigned chaos, unknowing and unknowable - a world without mind and devoid of understanding or beyond Mind without need for understanding.

Zeroness – Firstness – Secondness – Thirdness

Zeroness
23 In Peirce’s „Short List of Categories (1867), he actually lists five different categories: the „accidents“ of Firstness, Secondness and Thirdness framed by the two Kantian categories of Being and Substance. However, these three accidents are consistently reduced (or expanded) by Peirce into the Three categories, and since the whole full list of categories is argued on the basis of prescission, I think it is worthwhile to look at Peorce‘s process of excluding Being and Substance from his Short List of fortuitous „accidents“.

Esposito argues that Peirce wanted to reduce the separation between the real and the actual in order to underscore that the untouchable transcendence, in either the Platonic Real or the Kantian object, can be abandoned in favour of a transcendental ego that will later become the sign user, without any assertion or association of mentalism characteristic of either Kant's idealism or Plato’s rationalism.

The non-mimetic quality of the Real forms and the transcendence of the object have a subtle way of prioritizing the ego that connects the shadow with substance and validates being over becoming. So Peirce essentially performs an un-separation of the Ideal from the Actual by prescission, arguing that the categories are prescinded from the process of passing from being to substance:

The conception of being arises upon the formation of a proposition.
A proposition always has to express the quality…
Quality, therefore is the first conception in order in passing from being to substance.
Reference to a ground (of a quality) cannot be prescinded from being, but being can be prescinded from it… Reference to a correlate cannot be prescinded from reference to a ground, but reference to a ground can be prescinded from reference to a correlate…And finally a reference to an interpretant cannot be prescinded from reference to correlate, but the latter can be prescinded from the former" (1.551-553).

However, Peirce is really insisting that semiotic Firstness is the last functional level of prescission. There may be Being, but there is no Pure Being as a ground of reference, there is no nothingness, for „the ground (of being) is the self (of pure being) abstracted from the concreteness which implies the possibility of another“(1.557)

Thus, it is - as Wilden argues - that
there is no zero in nature; the continuum is analog; and the digital sign system, based on the concept of zero, is an overlay, a sign overlay, or „reference to“, Peirce would say. There is, at base because of the limitations and possibilities of prescission, only a singleness of stuff, a continuum of being which, if pure and categorical, would be transcendental and unknowable.
Being, in its Kantian sense, cannot be prescinded because it is a hypostatic abstraction, a hypostatic Self as it were, for it grammatically categorises and distributes the classifications by its very transcendental untouchability.

Being comes from propositional thinking and is not at all of Firstness in the sense of „red“ or „redness“, it is no predicate other than as „existence“, and „being“ must function as a copula. To reify „being“ is to reify the copula and to walk down the forked path of either the transcendental object or transcendental ego - all substance or all being, the situation Peirce‘s critique is designed to avoid. So in the Peircean critique,

Pure Being is just a hypostatic abstraction, but
the inventive logical power lies in the precission of being from stuff and substance as a „verb-ing“ (3.459), a monadic quality of feeling which says absolutely nothing about other parts. „It just is-ing“, to create a non-English sentence, a thusness no more and no less than the potential to Be.

The arguments of Peirce, like those of Kant and others who deal with metaphysical being, are difficult and sophisticated arguments, and I am not sure I fully understand them. Better minds than mine and will have to explain the difference between Kant and Peirce. Still, although my explanation may be wrongheaded philosophically unsophisticated, the problem on
the Transcendental Real is as old as a mythologizing humankind.

Plato’s Real and Kant’s transcendental object are basically cosmogonies that explain the origin of things in terms of the beginnings of objects. They narratize a world order, which as Peirce‘s secondness argues, is something we already know in the marrow of our experience.

Of course, we can (by prescission) conceive of a state before the order, old chaos as the Greeks put it, or pre-firmament for those of the Hebraic influence, or Mandelbrotian sets for those of non-linear fascination, but if we hypostatically abstract that pre-order, we are simply creating a cosmogony to explain the beginnings of things.

As Lacan‘s mirror stage, we look into the metaphysical darkness and see the self as Other hypostatically staring back at us. This Other in the cosmos apparently becomes a fundamental problem for our species, whether it be the Great Turtle and the Big Bang, Raven and the Red Shift, or Lilith and entropy,
because as Peirce argued we are a sign using intelligence.

Boe: we are a sign using intelligence.

The prescision of reference can establish only a sign probability of interpretants layered between the absolutes of being and substance (1.337).
The before-the-known-order is out of our perceptive reach because it is a hypostatic abstraction, ens rationis, and there is no analog thing for the digital no-thing.

As Peirce says, „were our experience of them (qualities) not so fragmentary, there would be no abrupt demarcation between them at all“(1.418)
Thus, as Peirce puts it in his Issues of Pragmaticism, „The Kantist has only to abjure from the bottom of his heart the proposition that a thing-in-itself can, however indirectly, be conceived; and then correct the details of Kant‘s doctrine accordingly, and he will find himself to have become a Critical Common-sensist“ (5.452)

Peirce in all logical (and spiritual) honesty without being lost in the hypostatic dream of Cartesian doubt, uses prescission to create a cosmology which is semeiotic: „The origin of things, considered not as leading to anything, but in itself, contains the idea of First“ (6.32). As he puts it in The Logic of Continuity (1898), „
The very first and most fundamental element that we have to assume is a Freedom, or Chance, or Spontaneity, by virtue of which the general vague nothing-in-particular-ness that preceded the chaos took on a thousand definite qualities“(6.200).

26 A prescissive understanding of sign relation will avoid the hypo-static creation of a cosmogony because prescission does not allow the assertive, distributive classification of hypostatic abstraction that makes the secondness of cognition useless, rather it makes secondness and thirdness absolutely necessary.

The semiotic qualities, in the face of pure zero, „in the general vague nothing-in-particular-ness that preceded the chaos“(6.200) will always be quasi-fictions. Being, substance, and all the semiotic host of geometrical abstraction will always be abstractions, and a transcendental relationship will be the basis of our knowing.

I am, of course, arguing here that Firstness is essentially a singleness apart from any zeroness, for that idea seems to be reflected in Peirce‘s arguments about prescission and precision. As he says discussing logical quantity, „the distribution of the first subject, is either singular (that is, determinate, which renders it substantially negligible in formal logic), or universal (that is, general) or particular (as the mediaeval logicians say, that is vague or indefinite). It is a curious fact that in the logic of relatives it is the first and the last quantifiers of a proposition that are of chief importance (5.450)

Of course, one can object that I am distorting logical terms for metaphysical ones, but that is intentional, for Peirce‘s arguments here (as always) are about perception and the expression of perception, and Peirce often links logic and metaphysics. There is little in Peirce that is mysticism of the categories, but rather logical distinctions between prescission and precision are at the heart of his categorical critique, not only in a logical sense, but the metaphysical one.

It is, I think part of the epistemology that Peirce developed in the Logic of Relatives, pragmaticism, and semeiotic as devices for showing the merging of the ideal real and the actual. Or, to put it more directly, it is his considered position that the semeiotic is the proper method of critique in both logic and metaphysics. As he wrote in the Objective Logic (1898),

We start, then, with nothing, pure zero. But this is not the nothing of negation. For not means other than, and another is merely a synonym of the ordinal numeral second. As such it implies a first, while the present pure zero is prior to every first. The nothing of negation is the nothing of death, which comes second to, or after everything. But this pure zero is the nothing of not having been born. There is no individual thing, no compulsion, outward or inward, no law. It is the germinal nothing, in which the whole universe is involved or foreshadowed. As such, it is absolutely undefined and unlimited possibility - boundless possibility. There is no compulsion and no law. It is boundless freedom. (6.217)

Boe: "germinal nothing" : quote in "Wisdom of Insecurity"

27
Firstness
Let us turn to look more directly at this „germinal nothing“and see how Peirce treats Firstness as a category per se. The first thing to note about his category of Firstness is that it is monadic; that is, „an element which, except that it is thought as applying to some subject, has no other characters than those which are complete in it without any reference to anything else“(1.292)

The primacy of the number one in number theory would suggest that the monadic idea of
a potentiated one that by combination with itself or two or three can produce the series of whole numbers that we count with. In the Logic of Relatives (1896), Peirce represents Firstness as a monadic proposition signified by a single blank to be potentially filled (3.465), and both the predicate and the Rheme are seen as having the monadic blank (4.543). Thus, the one consistent operation for Peirce‘s monadic structure is the idea of a single slot to be potentially filled by some other relations, and that slotedness or blankness, implies a division and distribution within the pre-established continuum. The monad is the quintessential singleness available.

I suppose the two of the more well-known definitions of Firstness are his lecture note that „Category the First is the idea of that which is such as it is a regardless of anything else. That is to say it is a Quality of Feeling“ (5.66), and this definition to Lady Welby that „Firstness is the mode of being of that which is such as it is, positively and without reference to anything else“(8.328).

But in the first definition Peirce is plainly more concerned with the psychological aspects of perception, and he works very hard to argue that quality is not dependent on the senses (1.422). Rather he identifies Firstness with „possibility“ (1.25), for „It is impossible to hold consistently that the quality only exists when it actually inheres in a body. If that were so, nothing but individual facts would be true“ (1.422). Therefore
quality is independent of both body and mind (6.327), and Peirce calls „ its form Firstness, Orience, or originality. It would be something which is what it is without reference to anything else within and without it, regardless of all force or reason“(2.85). So Firstness is both the feeling of quality and possibility of quality , but for perceptual minds it is also the possibility of feeling a quality.

However, in the definition for Lady Welby, Peirce seems to take a slightly different orientation toward being and positiveness. I suspect this is because
the origin of feelings is particularly, for Peirce, both a logical and psychological problem, one which he uses to draw a boundary between idealism and realism, logic and metaphysics, and his own pragmaticism and William James pragmatism. As he stresses in another letter to James, „If we imagine that feeling retains its positive character, but absolutely loses all relation (and thereby all vividness, which is only the sense of shock), it no longer is exactly what we call feeling. It is a mere sense of quality“ (8.267). Rather, Peirce argues, „I do not see how that (sense of quality) can be described except as something such as it is, positively, of itself“ (8.267). So it is important to understand why Peirce wishes to stress the positive qualities so much.

In Guess at a Riddle (1890), Peirce built a string of adjectives that describes Firstness as „ first, present, immediate, fresh, new, initiative, original, spontaneous, free, vivid, conscious, and evanescent“ (1.357), although these adjectives pretty well express the range (except for positiveness) that he gave to Firstness throughout his life, Firstness is here not called „positive“. Nevertheless, as he does in the third and fifth „Lectures on Pragmatism“ (1903), he identifies this quality with „aesthetic feeling“ (5.110), as spontaneous freshness, or as the object of phenomenology (5.122),, and such a usage is somewhat like Peirce‘s sense of „positive“. Thus, not only is Firstness „mere possibility“ (2.235) for object-ness, it is also a „Perfect simplicity“ (6.376) of being for subjects „essentially indifferent to continuity“, and it „lends itself readily to generalisation but is not itself general“ (6.205). Essentially Peirce realises that Firstness must be seen in terms of „positive suchness“ (7.630) as a contrast with the ambivalent „thisness“ of dyadism (1.497).

The first absolute boundary
29 Since Firstness entails a kind of immediacy that is total, or at least is capable of Absoluteness, Peirce separates sensation and perception, as seconds, from sense-quality and the percept, as firsts, in order to avoid the pitfalls of psychologism. The Quality of Feeling is intimately bound up with consciousness, but is of a peculiar kind in that „It is a mere tone of consciousness“ (6.530), which as such a tone of „consciousness in its first state might be called primisense“ (6.551).

Holding to the principle of prescission, Peirce argues that „in the percept, these elements of Firstness are perceived to be connected in definite ways“ (7.625), for the sense-quality is „a feeling“ which „emerges from the indefinite potentiality only by its own vital Firstness and spontaneity“ (6.198); that is, with positiveness that is distinct from the zero state of „nothingness-in-particular“. So, it is equally clear that, for Peirce, the other primary notion of Firstness is that of the potentiality as a positive, not as a reactive. He often refers to Firstness in terms of potentiality as signs dealing with the secondary characteristics of objects, but this potentiality is also part and parcel of the pragmatic view of perception.

Firstness is he „general vague nothing-in-particular-ness that preceded chaos“ (6.200), for it is from this nothing-in-particularness that we are able to generate perception in all the vividness that Peirce identifies with sensory secondness. In fact, despite Peirce‘s not recognising any forms of degeneracy in Firstness, he does stipulate degrees of vividness in the quality of feeling. However, such apparent variation is not a contradiction as much as it is an attempt to prescind percept from perception and feeling from sensation. Thus, just as Peirce tries to define a percipuum as immediately interpreted by perceptual judgement, he also maintains, that although sense qualities have different degrees of intensity, the greatest intensity will „not belong to the Firstness quality, but to the Secondness or insistency of the particular application of that quality“ (7.496). He then ends the argument of the most interesting contention:
„ I have endeavoured to ascertain whether there is in any ordinary state of consciousness a definite minimum degree of vividness, as there is certainly a maximum degree. But all my experiments upon careful mathematical discussion point to the presence of ideas so very dim, or wanting in vividness, that I am strongly inclined to say, as a first approximation at any rate, that the
vividness ranges all the way down to zero, and that every cell that ever can be sentient is in some degree sentient as long as it is alive at all“ (7.497).

By recognising the ranges of vividness from a definite maximum to a zero minimum, Peirce is able to prescind feeling from sensation and percept from perception (at the point of the percpuum). He is able to keep quality of feeling from being just a human psychological construct because he makes it a matter of sign activity based on the potential for a Firstness to be moved along the path of intensity to secondness. Yet when this is placed in the context of The Logic of Continuity, Peirce has quite clearly maintained the integrity of his categories, for he says, „we must not assume the qualities arose separate and came into relation afterwards. It was just the reverse. The general indefinite potentiality became limited and heterogenous“ (6.199). And later he continues, „Firstness is essentially indifferent to continuity. It leads readily to generalisation, but is not itself general. The limit between is essentially discontinuous, or anti-general. It is insistently this here. Thus, the original potentiality is essentially continuous, or general“ (6.205)

Firstness is the quality of feeling that is potentiated for sign use, but what remains to be seen is how that potential is realised in relation to the categories of Secondness and Thirdness.


31
Secondness
Peirce‘s second category is, of course, dualistic and dyadic, that is, „an elementary idea of something that would possess such characters as it does possess relatively to something else but regardless of any third object of any category“ (1.292).

Like the term monadic,“dyadic“ is a term also derived from Peirce‘s expertise in chemistry, mathematics, and logic. And he generally uses those derived patterns in the same manner as the monads, based on chemical bonding, mathematical structure, and logical relations. Rather than one slot to be filled, the dyad has two slots.

It is a binary which Peirce identifies with the yoking subjects and predicates in propositions and mathematical arguments
. But the dyad is much more productive for Peirce than Firstness, for it is the most obvious of the categories. It is in many ways the clearest and most graspable of the categories because it is the most common, the most insistent, and the most readily available of
the three universes of experience.

Boe: categories - universes of experience

The dyad is clearly a relation of „two subjects brought into oneness“, but the dyad is not just „the subject; it has the subjects as one element of it“ (1.326). It is the source of a unity with „no generality in it“ (1. 328). It is the source a unity of individuality that „involves a distinct reference to the possibility, not of duality merely, as positive unity does, but of plurality (in the sense of more than two)“ (6.376).

As Peirce puts it, „When we come to the dyad, we have the unit, which is, in itself, entirely without determination, and whose existence lies in the possibility of an identical opposite, or of being indeterminately over against itself alone“ (1.447).

The unity of the dyad is „the peculiar kind“of unity at having to do with its distribution and its opposites. It is reproductive, but dyads can combine, with monads, other dyads, or possible dyads to produce ever new dyadic structures…
The dyadic structure is the Pythagorean inverse ratio, which has been the driver of so much of Western scientific thinking (6.211),

32
Peirce identifies four other characteristics with the dyad that complicates even this notion of dichotomous fertility.

The first complication is, of course, implied by the nature of a unified relation; that is, the dyad is a set and it has a structure (1.445).

The second complication may be the most crucial one, for Peirce identifies the dyad with otherness and opposition (1.447), and he utilises it as the essential marker of perception, action, reality, and secondness:
We are continually bumping up against hard fact. We expected one thing, or passively took it for granted, and have the image of it in our minds, but
experience forces the idea into the background, and compels us to think quite differently. It is a double consciousness. We become aware of ourselves in becoming aware of the not-self. The waking state is a consciousness of reaction; and as the consciousness itself is two-side; so the idea of other, of not, becomes a very pivot of thought. To this element I give the name of Secondness“ (1.324).

Boe: Selbstreferenz - Fremdreferenz

The third complication is the sense of „force“ as expressed in the notion of resistance, struggle, and a dynamic hic et nunc, for those are what detail our experience of actuality as experience.

And the fourth complication, growing from the third, it his notion that
actuality in fact duality, or reality and logicality, are basically dyadic relations, from which we finally be able to use the thirdness of sign relation to merge the real and the actual.

Peirce is strikingly a structural thinker as his logic, semeiotic and phenomenology suggests, but it is with the concept of dyadic secondness that he is able to begin to trace the pattern of structure in both the actual world and the sign world.

One must not think that Peirce is simply and strangely enamoured of numbers. He is not a later day numerologist, rather he senses
the fundamental patterning of humans sentience and tries to operate with it in a systematic way. Peirce's concept of valency from chemistry and dyadic relations from logic are perfect generators for the kind of sense which he gave to structure in science, metaphysics, law, etc, for as he points out „natural classification takes place by dichotomies“(1.438).

Boe: the actual world and the sign world - patterning of human sentience

Moreover, his general familiarity with binary numbers and his own concept of dyadic structure demonstrate the power of its structure, and if one pauses just a moment to reflect on how important binary structures are the contemporary life (whether genetically, semiotically, or electronically), then one has some sense of the potential of even such a minimal concept of structure.

However, Peirce does not conceive of dyadic structures as minimal even if he takes secondness to be an idea that „must be reckoned as an easy one to comprehend“(1.358).

Secondness is easy to comprehend because its sense of Otherness is essential and continual to human thinking.
The power of our „two-sided consciousness“is that it generates the world as Other, as the Not-itself of the perceiving consciousness. In fact, this sense of Otherness is the most easily comprehended marker of secondness:

In the idea of reality, secondness is predominant; for the real is that which insists upon forcing its way to recognition as something other than the mind's creation“(1.325).

This otherness comes from both sense and will because „In sense and will, there are reactions of secondness between the ego and the non-ego (which non-ego may be an object of direct consciousness). In will, the events leading up to the act are internal, and we say we are agents more than patients. In sense, the antecedent events are not within us; and besides, the object of which we form a perception remains unaffected. Consequently, we say that we are patients, not agents“(1.325).

However, Peirce is equally careful not to allow this concept of otherness and opposition to reduce itself to dualism, for the pragmatic of his phenomenology, of his „Synechism, even in its less stalwart forms, can never abide dualism“ (7.570). He knows that an unrestrained dualism will leave any analysis as „unrelated chunks of being“and insists that „the synechist will not admit that physical and psychical phenomena are entirely distinct, but will insist that all phenomena are of one character“(7.570).

Secondness as Other is the essence of fact, contingent or unconditional, for it is „force without all reason, brute force“(1.427). The Other is always resistant, but Peirce's sense of „bruteness“ is not some Hobbesian reading of the term, for he is using „brute“ more in a logical vein than a cynical one, and more in the playful tone than a despairing one. In fact, he tends to emphasise the surprising qualities of the struggle with secondness and think of experience more as a teacher who uses practical jokes than some cruel, uncaring torture of poor, helpless humans (5.51).

The dyadic structure of fact exists by the occurrences or recurrencies of individuality and actuality which eventually become concepts by Thirdness, for „Whenever we come to know fact, it is by its resisting us“(1.430). Moreover, the essence of that resistance is Duns Scotus’s phrase hic et nunc, for it is there here and now of secondness that produces the insistent thisness of experience, be it the resistance of doors, the struggle with ladders, or the compounds in of perception and sensation. (I should point out that while secondness produces "thisness", Firstness produces "thusness" - the first term suggesting "thingness"and the second term suggesting "becoming". Both are "vivid" and "insistent", but "thisness" is archetypically other.)

Therefore, Peirce's bruteness is no more than resistance, and any hardness of facts „lies in the insistent see over percept, it's entirely irrational insistency“ (7.659). „A brute force is only a complication of binarities. The bruteness will consist in the absence of any reason, regularity, or rule, which should take part in the action as a third on mediating element. Binarity is one of my categories“(2.84). The brute forces just the „thisness“ of the dyadic structure, the binary compulsion, and the absence of reason and ruled that compels us to know the universe as other.

35 Still, from Thirdness, one can begin to see this pattern of brute resistance as „written“ into the universe as the „laws“ of time and space, because their „feeling of quality“ make up the determinate insistence of the hic et nunc. There are regularities of repetition, and if one seeks to be a realist, then one has to try to explain the laws of nature and the regularities of secondness. Peirce puts the problem this way: „the explanation of the laws of nature must be of such a nature that it shall explain why these should have the particular values they have. But these particular values have nothing rational about them. They are mere arbitrary Secondnesses“ (7.511), which are „the experience of effort, prescinded from the idea of a purpose“ (8.330). Thus, Peirce returns here to his prime generator of prescission, for the prescission of an arbitrary secondness „from the idea of a purpose“goes to the heart of the structural conception of secondness. Despite all the characteristics listed for secondness, it still is, even as brute force, resistance, or insistence, mostly a prescissive abstraction that must come to terms with the fabric of time and space.

Boe: telos - purpose - volition

The role of degeneracy
Therefore, all Peirce's pragmatic discussions of the laws of nature show him dealing with two particularly factitious aspects: the first is the recurrences and regularities of individual facts which produce the „absolutely determinate, fixed fait accompli“ of past fact; and the second is the capacity of human sign systems to produce, by predication and prediction, other future facts of a universe whose elements of Brute Force are both arbitrary and individual, and yet original and capable of generalisation.

This may seem paradoxical, for it is paradoxical, at least from a perspective of hypostatic abstraction. The dyadic structure must yield the self and the not-self, the individual and the general, the recurrent and the unique to
a two-sided consciousness, for it is by its very nature ambi-valent, pulling in both directions of the dyad. If hypostatically abstracted, it will produce contradictions of paradox, but if prescinded, it will produce the contraries of paradox - the epistemological ghosts of degeneracy and genuineness.

36 It is an essential function of the logic of relatives to do this kind of prescission: genuine categories prescinded from Substance and Being or degrees of degeneracy prescinded from genuine portrayal, just as much as it does any other kind of abstraction. After all, the system being developed is simultaneously a logic and semiotic; the roots of secondness in the dyadic structures of chemistry and mathematics and in the confrontation of subject with predicate in a proposition are matters of both classification and predication. The construction of the arbitrary otherness of brute, individual fact into the regularities of predication and prediction is a problem of the relations which exist between the three categories themselves.

38 The generality that seems to be implicit in the ensigned discussion of secondness is a result of
the thirdness of representation.

38 Thirdness
The process of approximation and solution of the ambivalences of secondness is thirdness, and Thirdness is of course, triadic; that is, „an elementary idea of something which should be such as it were relatively to two others in different ways, but regardless of any fourth“(1.292).
Like Peirce‘s other numerical terms, „triadic“ is a term derived from his expertise as a chemist, mathematician, and logician. However, this structure is really the final one, for although there are other such structures as „polyads“, these will be reducible to either monads, dyads, or triads, and as Peirce says „it can be proved that no element can have a higher valency than three“. This third valancy is, of course, the three structural slots to be filled, and the importance that Peirce gives to it is the source of all his joking concern about triadomany.

But Thirdness is also the source of much of his genius in developing the semeiotic. In a letter to Lady Welby Peirce writes of the mistaken fascination that some have had for dyadic relations, for „Secondness cannot compass Thirdness. Even in the most degenerate form of Thirdness, and Thirdness has two grades of degeneracy, something may be detected which is not mere secondness. If you take any ordinary triadic relation, you will always find a mental element in it. Brute action is secondness, and mentality involves Thirdness“(8.331).

Thus,
it is mentality of the triadic relation that Peirce pursues with the triadic structure of Thirdness, and it is the triadic relation of semiosis that allow him to move between the Scylla and Charybdis of positivistic materialism and vacuous nominalism or between the epistemological millstones of an absolutely deterministic Secondness as totally other and an absolutely undetermined Firstness as no-thing.

Boe: mental - mentality; the triadic relation of semiosis

The triad is logically a predicate joined with the monadic „verb-ing“ of Firstness and the dyadic subject of secondness, and Peirce is insistent that triadic structure is the final logical structure and the full expression of thought or reason.

But here's not being doctrinaire with this argument. First, just as Esposito argues, Peirce sees the categories as an evolutionary model in which, although one may present Firstness as a first of potentially or present secondness as a second of actuality,
the real joining, or perhaps one should say „originary“ point, will be through the third of thought and sign.

What has happened is that one has followed a trail of prescissive reasoning on which „it turns out that the study of each conception in all its features brings a clear conception that precisely a given conception is called for“(1.490). And even though the trail head is a triangular benchmark, Peirce still seeks to demonstrate experimentally through the graphs, and his analysis that there is a „triadic clause of the laws logic that recognises three elements in truth, the idea, or predicate, the fact or subject, and the thought which originally put them together and recognises they are together“(1.485).

Thus, one must start from the position of Thirdness, and although the strands of the weave may be prescinded from one another, ultimately the fabric of thought is whole cloth. Throughout the logical critique in the Algebra of Logic and the Logic of Relatives,
the triadic structure of relation is being explored even when he's seems to be most concerned with dyadic relations, for what is of interest to him is that all structures above triadic can be explained in terms of triads and that, by prescission, monads and dyads also can be explained in terms of triads.
The triple relative is the seed of logic, for „Every dual relative may be regarded as equivalent to a triple relative, just as every absolute term as equivalent to a dual relative“(3.317).

Evolutionary Cosmology
The triadic categories forman
evolutionary cosmology“ (6.102), and from the tensions between the absolute first of tychism, or pure chance, and the absolute last of anancasm, Peirce is able to reach his synechism by arguing that „a triadic relationship cannot be built up from dyadic relationships. Whoever thinks it can be so composed has overlooked the fact that composition is itself a triadic relationship, between two (or more) components and the composite whole“ (6.321.

Anancasm:(Wicki) Peirce held the view, which he called objective idealism, that "matter is effete mind, inveterate habits becoming physical laws".[120] Peirce asserted the reality of
(1) chance (his tychist view),
(2) mechanical necessity (anancist view), and
(3) that which he called the law of love (agapist view), echoing his categories Firstness, Secondness, and Thirdness, respectively.
He held that fortuitous variation (which he also called "sporting"), mechanical necessity, and creative love are the three modes of evolution (modes called "tychasm", "anancasm", and "agapasm") of the cosmos and its parts. He found his conception of agapasm embodied in Lamarckian evolution; the overall idea in any case is that of evolution tending toward an end or goal, and it could also be the evolution of a mind or a society; it is the kind of evolution which manifests workings of mind in some general sense. He said that overall he was a synechist, holding with reality of continuity,[122] especially of space, time, and law.[123]

Anancasm, Anancastic Evolution
(see also Anancasticism, Anancism, Tychasm, Agapasm ) "Three modes of evolution have thus been brought before us: evolution by fortuitous variation, evolution by mechanical necessity, and evolution by creative love. We may term them tychastic evolution, or tychasm, anancastic evolution, or anancasm, and agapastic evolution, or agapasm. The doctrines which represent these as severally of principal importance we may term tychasticism, anancasticism, and agapasticism. On the other hand the mere propositions that absolute chance, mechanical necessity, and the law of love are severally operative in the cosmos may receive the names of tychism, anancism, and agapism. All three modes of evolution are composed of the same general elements. Agapasm exhibits them the most clearly. [---] Just so, tychasm and anancasm are degenerate forms of agapasm." ('Evolutionary Love', CP 6.302-303, 1893)

Thus, the emblem of evolutionary love (6.287) is the triad, the ----< , the forked stick, really is „an emblem of fertility in comparison with which the holy phallus of religion’s youth is a poor stick indeed“(4.310), and the categories really do form a whole cloth even if we „see that it is impossible to deal with a triad without being forced to recognise the triad of which one member is positive but ineffective, another is the opponent of that, and a third intermediate between these two, is all potent. The ideas of our three categories could not be better stated in so few words“ (4.317).

If Peirce's arguments are correct, and I think they are, then „Reality is an affair of Thirdness as Thirdness, that is, in its mediation between Secondness and Firstness“(5.121). It is the medium or connecting bond between the absolute first and last.

Peirce
Beobachtung dritter Ordnung

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