Why tetrastic?

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...to 1st level ...regard...↑ 2nd level with...↑

...w.r.t. 1. Decision- makings, power. Appropriation, adoption, assumption:

...w.r.t. 2. Abilities, means. Production, processing, adaptation:

...w.r.t. 3. Affectivity, ends. Consumption, expression, conversion:

...w.r.t. 4. Cognition, checks. Assimilation, rumination, integration:

≣ ↓ Each row: a research ‘family.’ → |||| Each column: a research ‘coterie of friendly cousins.’

1. Mapping, pathfinding (objectification-like processes):

2. Counting, measure, apportionment (representation-like processes):

3. Calculation, coding, appraisal (interpretation-like processes):

4. Inference, reason (& reason’s crackups) (inferential & (dis-) confirmatory processes):

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1. Decision- makings, power...↑ Contendings:

Affairs of power (polit., milit., etc.).

Business, trade, economic affairs.

Show, sports & games, fashion, etc.

Case-building, debate, dialogue, etc.

1. Pure Mathematics: Typical conclusions: via equivalences Subject in scope: universals that aren't universes

Many-to-many (graph theory, topology, simult. eqs., extremi­zation, etc.).

One-to-many (enumeration, measure, integration, etc.).

Many-to-one (algebra & groups, deriva­tives, etc.).

One-to-one (math-induction applica­bility conditions, structures of order, limits, etc.).

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2. Abilities, means...↑ Practices (cooperation, tolerance, etc.):

Management, compliance, etc.

Work, labor, skill-plying, etc.

Recreations, hobbies, entertaining, etc.

Study, communication, etc.

2. Applied yet mathematically deep mathematics: Typical conclusions: forward-only deduction (except in historical overlaps with pure maths) Subject in scope: totalities, universes

Deductive maths of optimization.

Deductive maths of probability.

Deductive maths of information.

Deductive maths of logic.

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3. Affectivity, ends...↑ Valuings (communion, joining, etc.):

Ruling / governing valuings (relig., morals, etc.).

“Care-how,” valuings re: work, production, competence, etc.

Affective and gratificational valuings.

Cognitive valuings, curio­sity, love of knowledge, rigorism, etc.

3. Abstract yet positive- phenomenally deep sciences/studies: Typical conclusions: ampliative induction Subject in scope: non-universal generals

Inverse optimization problems [Google on them ].

Statistical theory.

Descriptive & inductive information theory.

Philosophy.

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4. Cognition, checks...↑ Disciplines (supports, checks, & balances):

Ruling / governing arts. Object(ive) in scope: (multi-) singulars among more singulars

“Know-how,” practical / productive arts/scis. Object(ive) in scope: non-universal generals

Affective arts (music, literature, visual, dramatic, etc.). Object(ive) in scope: totalities, universes

Sciences, maths, & disciplines intermediate between them. Object(ive) in scope: universals that aren't universes

4. Concrete empirical (“special”) sciences/studies: Typical conclusions: surmise Subject in scope: (multi-)singulars among more singulars

Forces.

Matter.

Life.

Intelligent life.

Tetrastic structures several but similar.

The 4 turns of becoming:	4 rough tags:	The 4 phases of code-bound communic.	4 phases of intelligent communication (code-unbound enough to try out & evolve codes):	The 4 stages of creative process (Helmholtz & Poincaré). ~ The 4 stages of aesthetic apprehension (revised Joyce). ~~ The 4 aesthetic properties (Aristotle plus Aquinas). :	4 categories:	4 sets of kinetic & associated mechanical conceptions:	The 4 Causes’ revised principles , & the 4 Causes a little revised:	4 kinds of complex systems:	4 levels of concrete pheno­mena:	The human forms of revised prin­ci­ples of the 4 Causes:
Starts (at t) (isn’t till t, is since t).	Main cause, driving cause.	Source.	Semiotic object (Peirce: “the agent”).	Saturation. ~ Arrest. ~~ Due directive magnitude, due force	Object(s)- to- object(s) relator.	System’s external momenta or forces.	Agens, beginning, effector (Aristotle: "initiating source of change or rest").	Sensitive dependence on initial conditions (await inverse-optimizational treatment?).	Forces.	Will, conation, character.
Continues (at t) (is till t, is since t).	Further cause, intermediate cause.	Encoding.	Sign (Peirce: “the patient”).	Incubation. ~ Fascination. ~~ Due proportion, due rhythm, harmony, etc.	Whetherhood (Y/N, pro­bability, infor­mative­ness, logical condi­tioning, etc.).	System’s internal energy or power (down thru the elementary particles) (rest energy :: rest mass)	Sustinens (patiens), middle, means, matter/process (rest mass :: rest energy)	Fluctuation-smoothing depen­dence on intermediate-stage conditions (stochastic processes).	Matter.	Ability, competence.
Stops (at t) (is till t, isn’t since t).	Main effect, culminant effect.	Decoding.	Interpretant (interpretation) (Peirce: “the act”).	Illumination. ~ Takenness, enrapturement. ~~ Radiance, vibrance.	Attribute	System’s external energy or power.	Actum, end, culmination.	Corrective (feedback) depen­dence on output conditions (cybernetic processes).	Life.	Affectivity, sensibility.
Continues-Not-To (at t) (isn’t till t, isn’t since t).	Further effect, “side”/ “after”- effect.	Destination.	Recognizant (recognition, verification, etc.).	Verification. ~ Attachment. ~~ Wholeness, (structural) integrity.	Substance (this man, this horse) (or hyposta­tization).	System’s internal momenta or forces (including down thru the elementary particles) (statically or otherwise balanced relative to an observer at rest).	Sustentum, check, form, structure, evidence, etc.	Fortificative dependence on sign-&-evidence conditions (intelligent processes).	Intelligent life.	Cognition, intelligence, knowledge.

The four conjunctive compounds of simple term-quantities including a seemingly near-blind window. Universal Special G e n e r a l “H” as universal -cum -general : Given Hx, as to OTHERS THAN x there are both nothing non-H (“H” as universal) & something H (“H” as general). “H” as special -cum -general : Given Hx, as to OTHERS THAN x there are both something non-H (“H” as special) & something H (“H” as general). S i n g u l a r “H” as universal -cum -singular *: Given Hx, as to OTHERS THAN x there are both nothing non-H (“H” as universal) & nothing H (“H” as singular). “H” as special -cum -singular : Given Hx, as to OTHERS THAN x there are both something non-H (“H” as special) & nothing H (“H” as singular). * The universal-cum -singular is not restricted to a one-object universe when one allows a polyadic “singular” (i.e., polyad of singulars) just as one allows the polyadic general and universal, though maybe it should be called something other than “singular.” For a discussion click here. . Research families and typical modes of conclusions Reversible deduction (neither adds nor removes info). —— Pure mathe­matics (abt. the object(s)-to- object(s) relators adduced thru the imagination or its extensions by both removing & adding info). Non-reversible deduction (only removes info). —— Applied yet mathe­mati­cally deep maths (abt. “whetherhoods,”, universes, etc., info-increasingly imputed through the intellect or its extensions. Amplia­tive induc­tion (only adds info). —— Abstract yet positive- phenomenally deep sciences/ studies (abt. attributes info-decreasingly abstracted thru the sensory & intuitive faculties or their extensions. Surmise, abductive inference (both adds & removes info). —— Concrete empirical sciences/ studies (abt. the concreta accessed thru commonsense perception or its extensions without info-changing abstraction, at least in intention). . Inference modes & SYSTEMATIC ECHOES Ampliative inference: Adds info, doesn’t preserve truth. Deduction: Adds no info, preserves truth. Precisive inference: Removes info, doesn’t preserve falsity. Surmise, abductive inference: Adds info, removes info; preserves neither truth nor falsity. Conclusion tends to be to causes, reasons, entities, laws, “puzzle pieces,” on principles of SIMPLICITY, NATURALNESS, EFFICIENCY. Compare versus OPTIMALITY w.r.t. MANY-TO-MANY relationships. Non-reversible deduction: Adds no info, removes info; preserves truth but not falsity. Conclusion tends to be to a not actually recognized though already formally implied thing sifted out on principles of NOVELTY OF ASPECT. Compare versus INFORMATION w.r.t. MANY-TO-ONE relationships. “Retentive” inference: Removes no info, preserves falsity. Compare versus PROBABILITY w.r.t. ONE-TO-MANY relationships. Conclusion tends to be to tendencies, trends, extensions of a quality, etc., on principles of LIKENESS of sufficiently representative portions or samples to a whole. Adds info, removes no info; preserves falsity but not truth: Ampliative induction. Compare versus TRUTH w.r.t. ONE-TO-ONE relationships (all true propositions are materially equivalent-cum -subcontrary). Conclusion tends to be to something formally equivalent to the premisses but in different form, on principles of DEPTH. (In mathematical induction, the conjunction of minimal case with heredity is equivalent to the conclusion.) Adds no info, removes no info; preserves both truth & falsity: Reversible deduction.

Tetrastic structures seem to have been neglected by philosophy, at least in comparison to dyads and dichotomies and even to triads and trichotomies. Yet they seem to work rather well to bring a little more system to some traditional philosophical structures, and it’s useful to cultivate an intuition for them. In deductive logic, there are the logical connectives, the quantificational forms, etc., and a logician gets to know those structures inside and out. I would argue that philosophy is the field which deals with the inverse problem to that of deductive theory of logic (or as it’s sometimes called nowadays, just plain “logic”), rises to concerns of a general kind with complex processes of the intelligent mind and heart, and of society, and tends to draw ampliatively inductive conclusions.[2]

[2] Of course, if philosophers do not so conceive of it, then in an important sense philosophy is not the field which deals with the inverse problem to that of (deductive theory of) logic, rises to concerns of a general kind with complex processes of the intelligent mind and heart, and of society, and tends to draw ampliatively inductive conclusions. But what other secure place will persist for philosophy as primarily a research discipline, and a major one at that? Philosophy — cast by some in philosophy’s linguistic analysis school as the analysis of arguments, in contradistinction to logic as the theory of arguments (by which I take them to mean deductive theory of arguments themselves deductive, inductive, What is philosophy? Which are its sibs and which its close cousins? or whatever) — philosophy would be reduced, if people took this seriously, to a subdiscipline (explicit arguments encountered in the world) within applied deductive theory of logic, itself an interdisciplinary subdiscipline, and a fine one it is (if it indeed exists as a discipline), serving as liaison between the world and ‘pure’ deductive theory of logic, a fine role but not the kind of thing to merit a separate department, much less a separate building, at every liberal arts college or university in civilization. The phenomenologists and existentialists seem uninterested in connecting philosophy with research in general (rather than with human & social studies only) — even Merleau-Ponty seemed to find something distinctly sinister in science, sinister, that is, in some way that philosophy seemed not to be for him. The analytic linguistic turn and the phenomenological epoché alike, either one taken as philosophy’s basis, seem to estrange philosophical schools from each other (who cares, right?) and to estrange philosophy from other research (there, philosophers should care), leaving philosophy taken mostly unseriously by non-philosophers. Meanwhile it proves more quixotic or cynical, than fruitful, to make a virtue of seeming necessity and define philosophy as some sort of perplexity research, sheer intelligent conversation, literary expression of theoretical problems, or other such half-intentional jests. Philosophers seldom, since the system-builders’ time, have tried to take the obvious course of investigating philosophy’s connections, resemblances, interdependencies, etc., with other fields, in order to help conclude where philosophy belongs. As for Rorty, who actually proposed redefining philosophy as some sort of literary field (as if literature didn’t already have enough problems), he seems some sort of self-deprecating, ingratiating philosophy-is-empty-so-don’t-be-intimidated-by-it type destined for salons if he is not already a fixture there, even as he seeks gingerly to replace truth with the glass gem of warranted assertion and with the politically loaded mantling of the democratic exchange of views as a supreme value over (and inevitably superseding) that of the value formerly known as “truth.” C.S. Peirce seems to have been the last philosopher to make real headway in the classifications of research and philosophy's place and role. Meanwhile, the “children” — really, the sibs and cousins — have grown up and the mansion has become a city where philosophy retains a place for the time being. Amateur and professional alike in philosophy delight in complex reasoning processes, and philosophy’s reflexivity ever tempts them to go at it with might and main. But, again, no real place, no secure and capacious place, remains for philosophy in modern research, except in the family of fields drawing inductive generalizations as conclusions, researching phenomena in general (e.g., statistical theory), where philosophy would fit reasonably well as the ampliatively-inductive inverse of deductive theory of logic, likewise as statistical theory is the inverse of probability theory. Recognition of this as philosophy’s locus means attributing to philosophy a distinctive and affirmative core which broadly, deeply, brightly, and firmly anchors and relates philosophy to research in general. (In that place, philosophy remains capable of producing essentially domain-independent deductive formalisms based on “contingent” or phenomenologically developed assumptions.) It might be a good idea to work out a reasonable elementary level of philosophy, just as there are elementary levels of communication theory, cybernetics, statistical theory, etc. E.g., in a sense, philosophy studies reason : philosophers treat, as subject matter, things (or stuff or whatever), and signs and evidences of them, and interpretations thereof, and recognitions / (dis)confirmations thereof. And, in a sense, philosophy studies experience and phenomena in general : Philosophers do not, qua philosophers, make cogent surmises to entities and laws subject to special tests; nor qua philosophers do they draw deductive and mathematical conclusions, tried though some have so to base philosophy. So, if philosophical conclusions are by ampliative induction (as distinguished from surmise and from any kind of deduction), then — philosophy’s sibs are its fellow areas of research into phenomena in general, and the family consists of: (1) the young field of inverse optimization problems; (2) statistical theory; (3) the descriptive and ampliatively-inductive areas of information theory; and (4) philosophy itself — and philosophy’s inter-family band of friendly cousins includes its fellow areas of research into reason and reason’s crackups, and consists of: (1) order and mathematical-induction applicability conditions; (2) deductive mathematics of logic; (3) philosophy itself; and (4) areas much pitied and envied — for their conclusions, as cogent as they can make them, are by that power of surmise which is a wonder at their subject matter’s heart as well —: the social and human studies. Philosophy, as one of the studies or sciences of reason, is an especially reflexive discipline, so by all means the Socratic Apology and related dialogues should remain in introductory courses.

This is to say that philosophy stands to formal and mathematical logics, as statistical theory stands to probability theory. (A nice thing about tetrastics is that they lead one to trace out patterns of so-called inverse relationships.) Tetrastic structures do recurrently peek out or emerge in philosophy but go undiscussed as a theme, appear recurrently with sometimes less transparency than has been brought to those in deductive logic. So, it’s good for the philosophically minded person to become familiar with some of the more obviously structured ones (not to mention with at least some elementary deductive-logical structures!).

Semiotics

The semiotic tetrads which I have pursued echo the tetrachotomies. Also, no element of such a tetrad can be reduced to any of its fellows; nor can such a tetrad discard one of its four elements without losing its integral semiotic or, if you prefer, integral semiotic-cum -observationalistic, character. I do not aspire to frame a Peirce-style reduction thesis about an irreducibility and sufficiency of tetrads generally. But the semiotic tetrads do align with the tetrachotomies, and more than one such tetrachotomy is conceived in terms of a given pair of closely related independent two-value parameters generating exactly four possible options of the given kind. That sort of sufficiency and irreducibility may prove extendible to the semiotic tetrads themselves. So tetrastics are not entirely the potential mere uncontroversial workaday philosophical tool that I was starting to make them seem, and they’ve led me into some arguments (usually amicable!) with Peirceans.

Charles Sanders Peirce’s triads and trichotomies seem to me to be better when reworked as tetrasms, either by addition of a fourth element or by “dis-conflation” of one element into two, or by deeper reworking. But Peirce’s “triastic” structures are not generally such that I would say that there is in every case some same element missing which you could just pop back into place. Still, insofar as his categorial conceptions of reaction, quality, and representation are involved, and insofar as the category of representation is the category of meaning (in a broad sense), I hold that what’s missing as a separate category is that of legitimacy and of one thing’s counting as another legitimately — particularly for evidentiary and interactional purposes. However, I see this extra category as the logical or semiotic category; so what do I do with Peirce’s Thirdness as Representation? Insofar as it characterizes a “communication” system but not a verificatory system, I think of it as value or importance, perhaps in a kind of information-theoretic sense. Now, to emphasize ideas like those of value or importance is, I think, to emphasize the third communication stage, decoding (1st, source; 2nd, encoding; 3rd, decoding; 4th, destination), or the third semiotic stage, the interpretant (I see a fourth stage in semiosis: collaterally based recognition). Such is the kind of threeness or thirdlike-ness that I find there.

Now, Peirce’s own writing shows a constant awareness that knowledge and reasonable belief are reached through adequately explored experience and indeed research. This awareness is the outer essence of his Pragmaticism (the inner essence being his recommendation that, in clarifying one’s conceptions, one best does so in terms of conceivable experience that would conceivably have practical relevance).

But I think that Peirce’s Pragmaticist view is not adequately built into Peirce’s basic semiotic structure which is object-sign-interpretant (sign = not necessarily a linguistic symbol, but anyway something interpretable as saying something about something; interpretant = interpretation in the sense of product, rather than activity, of interpreting; there’s an old word “interpretament ” from Medieval Latin interpretamentum (see Charles Short’s definition via Perseus Tufts) which means an interpretation as a product; Peirce probably knew the word well but perhaps thought it too lengthy).

Peircean triad, augmented to a tetrad by incorporating a semiotically determined, object-observant subject.

Absent, from the object-sign-interpretant triad, is the semiotically determined relationship whereby the sign and its interpretant (which is a mere construal) are brought to the experiential test against the object which they merely represent. Pragmaticism itself agrees that there is no way but the passing of such a test for sign and interpretant to merit recognition as legitimate and truthful. A sign is “almost” its (the sign’s) object and conveys information about the object, but is not the object, so familiarity with the sign is not familiarity with the object. The interpretant is the sign’s meaning clarified, such that the interpretant itself is a sign (a) of the object and also (b) of interpretant’s “predecessor” as a sign of the object. Peirce, unlike so many before and since, saw that there’s much more to signs as a general phenomenon (general like statisticality and information) than “signifier” and “signified.” Not only does a sign require and address itself to interpretation, but the interpretant itself is a sign, a night’s womb to a further interpretant dawn, just as a translation is into something itself further translatable, a ramification has ramifications, and meaning means, means ceaselessly and sometimes to our chagrin (Merleau-Ponty said “we are condemned to meaning”) — and so the interpretant is a sign, promoting and provoking further interpretation. But the interpretant, though it’s a sign, is not an object’s “mere” sign which one would never guess is also a sign about a previous thing-as-sign about the same object, instead the interpretant is a sign having reference to an interpreted sign as well as to the object, and in fact practically all signs are like this in the interpreter’s perspective, links in chains stretching both fore and aft, just not always with clarity (so usually it’s a relative question, a role question — “is it the sign or the interpretant?” — just like the question of which codings are encodings and which are decodings), and Peirce unswervingly conceived the interpretive chain as operative all the way down to the level of the infinitesimal and the truly continuous which he ultimately regarded as beyond all multitudes or Cantor’s alephs. Actually so continuous or not, perpetual interpretation is sometimes to our chagrin, yet it also, for instance, lets us see around the bends of planets and hearts. But the caveat, the string attached, is this, that, the mere fact that you interpret, understand, take some appearances, some events, some words, as signs about some object, doesn’t mean that you really know or really reasonably believe or learn anything about that object, i.e., and, as Peirce states, sign and interpretant contain none of the needed familiarity-dependent understanding of the object, and such familiarity and experience must be had collaterally. Therefore, (a) the collateral experience is no mere sign or interpretant in the sense and in those relations in which it is the collateral experience, and (b) only through changes of semiotic frame of reference can such experience be analyzed into signs and interpretants. Likewise (and only likewise) can interpretants be analyzed into pre-interpretant signs, and signs into objects — every supposed reduction of such experience to signs and interpretants marches onward all too powerfully, to reduce away the classic semiotic triad itself. To say that we can shift frames and regard the recognition as a sign or interpretant of some other object (as it likely is) is to say that we can simply bar our eyes from the question of what is the semiotic status or role of the collaterally object-observant recognition of the interpretant and sign as corresponding to the object already in question. We could likewise ignore, as some do, the questions of what is the interpretant, even what is the sign. The sign’s object is not per se the recognition, for then signs and interpretants would never be needed. Nor is the verificative recognition some representational, qualitative, or reactive aspect or relation of interpretant or sign or sign’s object; if that were so, then one or more, among object, sign, and interpretant, could somehow, or in some combination or relation, contain conveyable familiarity with the sign’s object. In sum, it is completely ruled out, that the recognition is interpretant or sign or object or any representational, qualitative, or reactive aspect of any of them or relation among them. Could the recognition still be some kind of relationship among object, sign, and interpretant? Yes, if and only if that relationship contains familiarity with the object. Object-observation-based recognition of the sign and interpretant as corresponding to the object ipso facto contains familarity with the object and conveys such familiarity across the memory and experience of whatever mind (or “commind” or “quasimind”) which it inhabits. There are chains not only of interpretation but also of recognition and verification which are not mere interpretation, mere construal.

Left to its “own devices,” semiosis could not learn the difference between sense and nonsense; it could still, as it does, lead to hopeful monsters, like they say of biological evolution, but hopeful monsters which go untested, unchecked.

Instead there is to philosophically acknowledge as a semiotic phase or element the observational / experiential recognition formed as collateral to sign and interpretant in respect of the object and to explore it as a further complex of semiotically determined relationships. It might be a recognition of a hat being worn as one expected, or a recognition of one’s hopes as unexpectedly fulfilled; or a recognition of a given interpretant as resting soundly enough upon recalled experience. Beyond the category of value, import, meaning, etc., is the category of consistency, truth, validity, soundness, and not just in the sense of the shallow or trivial but even and especially in the sense of the challenging deep. Beyond the end or culmination or actum as actualization, comes the check or checking, the sustentum, alitum, or altum as borneness, sustention, a system’s agencies’ balancement and stabilization. “Beyond” in some logical sense. The check doesn’t shed the end or leave it behind.

Edward Dahlberg & Charles Olson
Conn. U's Charles Olson Research Collection

1. Objectification. Conception, percept, image, etc. Correlated with: graph theory & maths of many-to-many relationships, deductive theory of optimization, the (young) field of inverse optimization problems, and sciences of motion & forces.	3. Interpretation. Inference to a conception, percept, image, etc. Correlated with: algebra & maths of many-to-one relationships, deductive theory of information, ampliatively-inductive information theory & cybernetics, and biological sciences.
2. Representation. Judgment. Correlated with: enumerative combinatorics & maths of one-to-many relationships (measure & integration, etc.), probability theory, statistical theory, and the material sciences.	4. Recognition. Inference to a judgment. Correlated with: maths of order and one-to-one relationships, deductive theory of logic, philosophy, and the sciences/studies of intelligent life.

1st is the BEGINNING: forceful, leading, ice-breaking, vying, trying, exploring, deliberating, decision-making, conceiving, designing, optimizing, adoptive, appropriative, sensitive, magnifying, exaggerative, creative, “so be it?” • 2nd is the MIDDLE OR MEANS: resource, fostering, patient, nourishing, tempering, mediating, harmonizing, normalizing, finessing, executing, cooperating, adaptive, processing, “so be it.” • 3rd is the END: converting, rewarding, motivating, consuming, affection, communing, expressing, interpreting, precising, picky, adjusting, enlivening, perfecting, sharpening, culminating, “is it?” • 4th is the CHECK OR CHECKING, solidifying, establishing, ruminating, assimilating, confirming, integrating, cognizing, grounding, staunch, structured, supports, checks, and balances, building, renovating, evolving, “it is.”