What of these other fours?
 Post appears BELOW Table of Contents.
 This blog focuses on similarities between others' four-folds, tetrads, tetrachotomies, and mine, and includes links to online information on others’ fours in their own terms. It results from overgrowth of an old post at The Tetrast "What of these other fours?".
Table of Contents

Fours that I've
adopted or adapted:
Fours with a striking
likeness to mine:
Fours involving some
likeness to mine:
More-or-less different fours:
Unless otherwise stated within the post, first posted on Friday, December 5, 2008. Post times here are just a device to control the order of appearance. Most of the posts are based on entries in an older post "What of These Other Fours?" at The Tetrast.
Walter Watson's archic profiles

(First posted April 26, 2014)

The pluralist philosopher Walter Watson in his book The Architectonics of Meaning: Foundations of the New Pluralism (SUNY, 1985) argues that four 'archic' variables are necessary and sufficient to account for the plural views in philosophy. The publisher's description:

The Architectonics of Meaning is a lucid demonstration of the purposes, methods, and implications of philosophical semantics that both supports and builds on Richard McKeon's and other noted pluralists' convictions that multiple philosophical approaches are viable. Watson ingeniously explores ways to systematize these approaches, and the result is a well-structured instrument for understanding texts. This book exemplifies both general and particular aspects of systematic pluralism, reorienting our understanding of the realms of knowing, doing, and making.

I don't have the book but have perused passages via Google Books and have read the review by George B. Pepper. Watson was brought to my attention in messages from a Tetrast reader. Watson is a pluralist, and holds with the "reciprocal priority" of various archic choices, although he also holds that there is a progression of archic profiles. There are 256 possible combinations of the values of the archic variables, and 256 squared, equaling 65,536, possible combinations of such values as characterizing the given text and such values as characterizing the given interpreter. Some values have affinities with one another and these form archic profiles, in particular Sophistic, Democritean, Platonic, and Aristotelian.

Walter Watson's 4×4 archic matrix

Archic variables
archic profile
archic profile
archic profile
archic profile
(inexhaustible world, practical effects).
(revelatory, oracular).
(as signified by the text):
(under the surface).
(generic traits).
METHOD:Agonistic. Logistic. Dialectic. Problematic
(generic/specific or essential/accidental features).
(purpose that makes the text function):
(universal rational order).
(noetic self-completion).

Watson correlates the four archic profiles with Aristotle's four causes, as shown in the table below. Next, there is some likeness between, on one hand, the archic profiles and, on the other hand, Aristotle's four causes as correlated to some fours of mine that I most recently discussed at "Telos, entelechy, Aristotle's Four Causes, pleasure, happiness" at The Tetrast. The likeness involving my versions of the four causes is poorest, though not quite absent, in the case of the Platonic archic profile.

Archic profile according to Watson: 1. Sophistic:
2. Democritean:
3. Platonic:
4. Aristotelian:
Correlation with Aristotle's four causes,
according to Watson (e.g., on Page 159):
1. Efficient cause. 2. Matter. 3. Form. 4. End, final cause.
MORE-OR-LESS correlated
Aristotelian cause &
related ideas... (as I see them):
1. Efficient cause,

—Motion, forces.
—Decision processes.
2. Matter,

—Matter, (internal) resources.
—Stochastic processes.
3. End, final cause, telos, as

—Energy, life.
—Communication processes.
4. Form as structure &
as entelechy.

—Structure, mind.
—Inference processes.
...and power of the psyche:1. Will, conation. 2. Ability, competence. 3. Affectivity. 4. Cognition.
...and side of the psyche's life:1. Strivings, dedications.2. Practices, skills.3. Valuings, devotions.4. Recognizings, knowledges.
...and psyche's interbehavior:1. Conflict, competition,
rivalry, dispute.
2. Cooperation, tolerance, etc. 3. Communing,
valuational community.
4. Checks & balances.
...and (with distinctions similar yet ortho-
gonal to those among the interbehaviors)

the psyche's behavior as aiming for
change brought to or drawn from objects:
1. Potition, appropriation,
adoption, taking charge.
2. Production, processing,
3. Consumption, expression. 4. Rumination, digestion,

Watson correlates not the final cause, but the formal cause, with the Platonic archic profile; and not the formal cause, but the final cause, with the Aristotelian archic profile. Indeed Plato is the philosopher of the Ideas, a.k.a. the Forms — form as idea, eidos, species, which words originally meant look, appearance, view, and have never strongly connoted form in the sense of structure.

Unless otherwise stated within the post, first posted on Friday, December 5, 2008. Post times here are just a device to control the order of appearance. Most of the posts are based on entries in an older post "What of These Other Fours?" at The Tetrast.
Graham Harman's Quadruple Object

First posted April 17, 2014. Recentest significant edit: October 14, 2016. Since this is the first new post in years, I'll let it sit on the home page for a while.

Harman in his book The Quadruple Object says that an object has four poles — real object (inexhaustible object in itself, unknowable), sensual object, real quality, sensual quality.

Harman characterizes four pairings of those poles as involving 'tensions':

  1. Time is the tension between sensual object and sensual quality.
  2. Space is the tension between real object and sensual quality.
  3. Husserlian eidos is the tension between sensual object and real quality.
  4. Essence is the tension between real object and real quality.

I have read quotes from The Quadruple Object in reviews and perused passages from it via Google Books. Harman's quadruple object seems unlike my fourfolds, since I hold that object and quality (or characteristic) form a fourfold with modality (in a broad sense, including feasibility, probability, information, and givenness) and mathematical relation. His fourfold of tensions seems unlike my fourfolds.

The following material on page 79 is of a kind probably more interesting to me than to many:

The number one is the password of monism. Despite its comforting promise of holistic unity, it tends to be too sanguine in its implicit assertion that difference and strife are less real than a primal harmony in things. The number two seems to announce a conflict of two opposed principles. But such dualism turns out to be paradoxically monotonous, since usually nothing occurs but a constant struggle back and forth across the divide. The number three seems more sophisticated [...].

Then we come to a passage at which cognoscenti of Charles Sanders Peirce may wince or scoff:

The number three seems more sophisticated, with its claim to unify two opposed principles in a dynamic third term that both preserves and transcends the crucial features of the two opposite terms; it is essentially dualism with the introduction of a mediator, as in Hegel's dialectic and Heidegger's own repetitive threes. But the frequent danger of threefold structures is that of false happy endings that neuter the tragic force of opposition, uniting all opposites in a place too easily accessible to human resolution.

Harman goes on to mention famous fourfolds in philosophy, notes that they tend to result from the crossing of two given axes, and offers two criteria for a good fourfold — its axes must be "well-chosen," not merely incidental to each other, and it must offer a "useful account" of how the fourfold's members interrelate, an account in which the four parts don't just sit "in static co-existence".

To one like me who hasn't read widely enough in philosophy to have a good sense of how the various-numbered philosophical divisions have worked out, it will somewhat seem cloud-talk, not that I myself don't try to talk it occasionally. As they say, here goes. My sense of it is that, when a duality involves positive conflict, the conflict is between two vying to be the one, the first — first, not in Peirce's sense of the fresh, novel, etc., but in the sense of the determinative, the beginning qua leader, arché, not beginner qua neophyte (to originate is not exactly the same as to be originated). Yet, when two meet and harmonize to some end-as-a-third, then to the extent that, of the first two, one leads and the other follows, the follower (secundum) is the mediator, the harmonizer. In other words, instead of thesis-antithesis-synthesis, we have:

The only picture at all like this of which I know in past philosophy is that of Aristotle's four causes — efficient, material, final (as telos), and formal (as entelechy, having in completeness, being at an end, as Joe Sachs put it). This works better when one conceives of form as structure — rather than of form as appearance or look (original meaning of Greek eidos and Latin species).

So, (third-phase) false happy endings, of which Harman warns, and unhappy endings more generally, are often to some extent avoided or corrected by consideration, anticipation, recognition, etc., of (fourth-phase) completenesses, end states, entelechies — consideration of aptness of means, unintended consequences, clashes of values, and so on.

I add a third criterion for a good fourfold: meaningful pattern via verticals, horizontals, and diagonals:

1. Beginning, impetus.
Dynamism, instability.
2. Middle, means.
Consistency, endurance.


3. Culmination, end, telos.
Differentiation, vigor, vibrancy.
4. Settled state, entelechy, standing-finished.
Stability, structural integrity.

Both 1 & 2 (along the left vertical) involve the earlier.
Both 3 & 4 (along the right vertical) involve the later.

Both 1 & 3 (along the top horizontal) involve change and suggest external relations.
Both 2 & 4 (along the bottom horizontal) involve non-change and suggest internal relations.

Both 1 & 4 (along the downward-sloping diagonal) are more space-like in that sense in which they are directional opposings (those in dynamism and those in structural integrity).
Both 2 & 3 (along the upward-sloping diagonal) are more time-like in that sense in which they are not directional opposings (either in endurance or in vigor).

(Those are three sets of pairs, where is the fourth, if any? Insofar as those sets reflect potential inversions or 'flips' of the square, there is a fourth flip-related operation, the one which leaves the square the same as before, equivalent to doing any of the other flippings twice. One could think of it as involving the square's each quadrant's pairing with itself.)

I vote for a fourth criterion awarding extra points if a four-fold's four items are also ordered. And a fifth criterion awarding more extra points if the ordering can recur nicely enough in a loop.

Unless otherwise stated within the post, first posted on Friday, December 5, 2008. Post times here are just a device to control the order of appearance. Most of the posts are based on entries in an older post "What of These Other Fours?" at The Tetrast.
Mining Aristotle's Four Causes for order & balance
Recentest significant change: October 29, 2013.
Udate July 28 & Sept. 5, 2013:

I recently overcame a kind of brain glitch about the impetus-means-end-check four-fold. I had long thought of my fourth stage (entelechy, "check") as involving verification that one has, so to speak, hit a target. So the prospect of verifiability could influence one's choice of targets. That was just not a strong enough conception of entelechy's part in the four-fold, and it kept nagging me though at length I drifted to other concerns. Then something that Dewey said finally set me on a better path . It's not just a matter of verifying one's "hits," but of whether the goals were good ideas in the first place. The prospective entelechy helps us consider unintended consequences, develop general values, and deal with conflicts among values. Thus entelechy guides ends (not to mention means and beginnings). Hedonism focuses only on end, telos, culmination, etc., and ignores entelechy. That's it in a nutshell. See "Telos, entelechy, Aristotle's Four Causes, pleasure, & happiness" at The Tetrast. End of update.

The Four Causes (aítia) or reasons that make a thing what it is —
the efficient cause
(a.k.a. the agent cause),
the matter,the end, the form or shape
— and their three Principles —
— of Aristotle and the Scholastics — are part of what got me interested in four-folds, tetrachotomies, tetrads. I never thought that they were "just a list" as some 20th-Century philosophers have believed. The Four Causes do, however, seem to need to have some further symmetry and order brought to light. (I've a taste for symmetry and order which I seem somehow to have inhaled from the intellectual air many years ago, though obviously not from the philosophical air of the time.) I, I, I — promise that my self-references will diminish as the post progresses. Anyway, connoisseurs and aficionados of the Four Causes, please do at least inspect the long table which concludes this post.

I discuss the Four Causes quite a bit, especially in these posts:
Tetrastic version of the Four Causes & their Principles.
1. Beginning, impetus.
Agent cause, mechanism, etc.
Agency, operation.
Mover, affector, agent.
Source of change or rest.

Compare versus net momentum,
impulse, force.
2. Middle, means, development.
Material, composition.
Bearing, coping.
Bearer, endurer.
Mediation of change or rest.

Compare versus rest mass,
rest energy, internal work & power.
3. End, telos, culmination.
Actualization, differentiation, etc.
Act, action, activity.
Moved, affected, acted-on.
Culmination of change or rest.

Compare versus (non-rest) energy,
work, power.
4. Check, entelechy, establishment.
Borneness, balancement.
Borne, endured.
Settlement/resolution of change or rest.

Compare versus internally balanced
momenta (potential & kinetic), impulses, forces.

Note: Momentum, force, etc., do not "cause" energy, work, power, as "effects."
Instead the quantities were originally conceived of in the attempt to quantify "causativeness" and effect.

- "Compare to Aristotle, Aquinas, & Peirce"
- "The Four Causes, their principles, special relativity, Thomistic beauty,

and I touch on them elsewhere, especially in "Why tetrastic?".

Basically, I think that Aristotle and the Scholastics missed the potential symmetry in the causal principles (agent, patient, act). Aquinas subdivided act into action and form, so that he had something like four causal principles for four causes, but it still isn't regular enough. The principles must be re-conceived, somewhat, as the agent, the bearer, the act, and, furthermore, the borne — which seems too neat and simple to be true, surely philosophers thought of it and, apparently, dismissed it for whatever reason — but for my part (I'm no expert on the ancients or the Scholastics) I don't know of any ancient or Scholastic philosopher's considering it (and dismissing it or otherwise), and it works. The borne (or "borneness"), as a cause, is the more-or-less stable balancement of forces, the form or structure, the standing finished, the settlement, establishment, entelechy.

• Of course,
(1) the Ancient Greek paschein, "to bear," more exclusively meant "to suffer" than "to bear up under," making it a bit harder to think of the borne as the supported, the founded; Aristotle and the Scholastics thought not of a borneness but of a passion, a suffering (which in turn was not considered a causal principle); and
(2) the corresponding Latin pati (which could mean "to endure" in the sense of "to bear up under") was a deponent, conjugated mostly in the passive voice with active sense, thus making a bit harder a distinct conception of the passive-sense "borne" correlated to the bearer (patiens).
• Yet, both (1) and (2) seem small hurdles. But it seems that nobody suspected that there was a prize to seek beyond them. Heck, maybe I'm alone in suspecting or believing it today.

1. To bear or allow and to do or drive (or make something do something) are opposed like possibility and necessity, so right there one should wonder whether active-voice and passive-voice versions of both to bear and to drive might be involved in some interesting and unusual square of opposition.
2, The patient or bearer indeed has endurance and patience, except to the extent that an agent drives it into a kind of ("passionate") impatience which is act. Likewise a (mechanical) agent potentially (while under restraint) or actually moves (changes position), and, in driving a patient into act, the agent drives it except to the extent that the agent is borne, supported, balanced into a kind of inagency which is borneness, balancement. This is the sort of thing that "borneness" means at a rudimentary level.
3. The two opposed ideas of patience and act are time ideas (like rest mass versus (non-rest) energy respectively and like proper time versus time dilation respectively). Likewise the two opposed ideas of agency and borneness, are distance ideas, like unbalanced momentum (or impulse or force) versus balanced momentum (or impulse or force) respectively, and like velocity versus slowness allied with a direction (slowness rather than rest since the possession of some balanced momenta does not mean that a system has no net momentum), involving magnitudes with directions and directional opposability.

Form in the sense of the formal cause needs to be conceived (or re-conceived, if necessary) as structure rather than as figure, aspect, appearance, etc.  One can think of the four causes at various levels, but at a given level, for instance the physical level, one should practice consistency of conception. If one sees, at the physical level, a forceful or impellent agent cause, a material cause, and a final cause which amounts to action, work done, for mechanical conservation and thermodynamic decay at the least, then it is rather difficult to see, at such a physical level, what role is held by figure, aspect, or appearance in making a thing what it is. On the other hand, consider a more-or-less stable balance of forces, a structure, which, despite or partly thanks to its mobility, flexibility, or lack thereof, etc., makes a thing what it is. That makes more sense as a fellow "why" within the family of such "why"s as matter and force — and it much better correlates to the idea of an entelechy, a final settled, stabilized form, than figure, aspect, or appearance do.

Underlying equivalences
along the diagonals.


Objection: There is a kind of equivalence and redundancy between balanced forces (the structure) and unbalanced forces (agencies), since they're all force or impulse or whatever in some sense.
Response: That's not a bug but a feature, indeed a solution, since it is likewise as there is an equivalence between mass and energy (for instance work done). If there's to be an equivalence between the patient matter and the actional end, then we should wonder why there were not also an equivalence between an efficient agent and a form. The differences between the external and the internal, and between the unbalanced and the balanced, and between the stable and the unstable, mean that mere redundancies are not involved, but instead complementary versions of a mode. It goes even further than the mass-energy equivalence and the underlying equivalence between balanced and unbalanced momenta. Time and space have a deep unity and are expressible in the same units; likewise mass, energy, and momentum have a deep unity and are expressible in the same units.

Objection: Form or structure does not belong with the other causes at least at the mechanical level. The other causes are about push, pull, action, endurance, etc. Form involves spatial arrangement and pattern.
Response: The basic structural issues of balance and stability are certainly relevant issues in mechanics. Generally the idea of structure meshes with other ideas in mechanics. The agentlike quantities momentum, impulse, and force all include spatial direction in their formulas. The strong association of direction with agency is not confined to modern mechanics, insofar as forceful agents have long been considered as opposable from opposite directions. The importance of spatial direction is shared by (A) net force, impulse, momentum, and (B) a structure or arrangement of balanced forces or momenta. In fact spatial direction is a significant factor even for time quantities such as mass and energy but in ways depending on the distance quantities.

Objection: A thing's form is not its establishment but instead is its definition.
Response: A thing's form in that sense is not necessarily its structure or even its outward shape but instead its genus conjoined with its species' difference from its genus.

Objection: Form should be regarded as figure, aspect, or appearance, in order to provide a place or at least a doorway for the idea of information among the causes (see the syllable "form" sometimes written in upper case in the word "inFORMation").
Response: (A) Figure, aspect, appearance, bloom, variegation, and indeed information itself, as kinds of differentiation, are (in terms of the four causes and their principles) energy and activity ideas, rather than structure and stability ideas; and (B) energy and information seem akin also because of the connection between Shannon's information entropy and Boltzmann entropy.

Sidebox: Systematic exhaustion of possible combinations of the change ideas underpinning beginning, middle, end, check.
Beginning, similar to starting up (e.g., at time t)
— X occurs? no (for some period) till t, yes (for some period) since t.
Middle, similar to continuing (e.g., at time t)
— X occurs? yes (for some period) till t, yes (for some period) since t.
End, culmination, similar to stopping (e.g., at time t)
— X occurs? yes (for some period) till t, no (for some period) since t.
Check, entelechy, similar to refraining, holding (e.g., at time t)
— X occurs? no (for some period) till t, no (for some period) since t.
Be that as it may, generally there are "layers" of the four causes which need to be teased apart rather than being represented by only this or that cause in a patchwork. It's a question of consistency of conceptions. For instance, if we have the end as a cause, then what of a beginning and a middle or means? And as beginning and middle are distinguished as beginning versus continuation (like a staying begun), what of end as ending, culmination versus end as settlement, entelechy, a standing finished?

For further arguments or likenesses thereof, see my links above. For examples, see the large table below.

If, in human affairs, the end is generally happiness, then (stop and ask yourself) what, in human affairs, is the corresponding beginning? A question seldom asked. And the middle or means? And the standing finished, settlement, the entelechy? Of course the feeling of happiness involves an appreciation of luck, since luck plays some role in success; but luck favors those who try. Aristotle held that virtue (excellence of character) leads to happiness; but virtues and happiness are at different levels of generality: by virtues one attempts, seeks, takes, and sticks with one's values, like Ayn Rand kept saying. So, where happiness is the value, what is the corresponding virtue? I think that Lincoln comes close: "A man is about as happy as he makes up his mind to be." Anyway, maybe you've thought of some answers to all these questions. For my attempted answers, see the large table's bottom row below.

The Four Causes & Related Principles
externalefficient cause  
end, final cause 
internalpatientform, formal cause
matter, material cause
middle, means
end, telos
check, entelechy

Tetrastic (elaborated)
Existence (consistently extreme version).Efficient cause.Sustainer.Consumer, exhauster.Assimilator / suppressor.
Causes as turns of becoming.Beginning.Middle, means.End, telos.Check, entelechy, standing finished.
Causes as rational characters.The strong has the rational character of a beginning (an impetus or the source of an impetus).The apt has the rational character of a middle or means.The good has the rational character of an end.The true, sound, (fallibistically) wise has the rational character of a check, entelechy.
Causes as stages.Impetus.Development, process.Culmination.Settlement, establishment.
Human causal principles.Will, conation.
Character. Virtues, vices, etc.
Ability, dealing.
Competence. Métiers, etc.
Sensibility. Values, etc.
Intelligence. Knowledgeability, etc.
Static or quasi-static causes.Essential tensions, pressures (of a thing especially as in its environment but also internally).Composition, material (of a thing but also of its external relations, environment, media, etc.).Differentiation, diversification (of a thing especially as a system among others in its environment, but also as among its parts, organs).Unitary structure (of a thing especially but also of its external relations, environment, etc.).
 Correlatives, examples, etc.
Correlated research foci.Regimes (systems of plurally instanced universals).Domains (universes of discourse or total populations & their parameters).Kinds, varieties; species. (At once general & special, i.e., neither universal nor individual.)Individuals (connected, ordered, etc.) in a larger world.
Correlated concrete phenomena.Motion & forces.Matter.Life.Mind.
Kinetic / mechanical correlatives.Net momentum, impulse, force.Rest mass, rest energy, internal work & power.(Non-rest) energy, work, power.Internal, balanced momenta (potential & kinetic), impulses, forces.
Basic subsistence.Catching or gathering the food.Cooking or otherwise preparing the food.Presenting, consuming, enjoying the food.Digesting & reflecting on the food.
Bahavioral phases / foci.Adoption, appropriation, assumption, control.Processing, adaptation, production.Consumption, expression, conversion.Rumination, assimilation, learnings.
Inter-behaviors.Vying — conflict, competition, rivalry, contention.Cooperation, tolerance, minding one's (own) business.Community, distinctive unitings.Checks & balances.
Vying's prizes.Power, influence.Wealth, means, wherewithal.Glory, wattage, 'action.'Honor, validation, standing.
(Human causal-principle) applications—& excellences.(Volition, conation):
Struggle / striving.
—Determination / dedication.
(Abiity, dealing):
—Skill / technical art.
—(Fallibilistic) knowledge.
Methods of learning.Struggle: Trial & error
(including variation).
Practice & repetition.Appreciation & emulation (better known as identification & imitation).Reflection & testing
(the reasoning process).
Temporal zones of communication and cause & effect.The almost-now, events along swiftest paths fanning outward from oneself.The later future.The just-now, barely-now, events along swiftest paths incoming to oneself.The earlier past.
Modes of attribution of characters.Optima & feasibles.Probabilities.Information, "newsiness."Bases, facts, data.
General processes.Decision processes.Stochastic processes.Info / communication processes.Inference processes, logic.
General processes, human aspect.Plotting, demarcating, objectification.Correlating, measurement, apportionment, counting, forming a representation.Drawing a (weak or strong) implication, e.g., calculation.Drawing a lesson, inference to a judgment.
Some classes of signs (a Peirce trichotomy of signs, augmented).Index.Semblance, likeness.Symbol, and (in a perhaps more general sense) functional surrogate.Proxy, model that which counts as its represented object under transformations and, so to speak, makes the same "decisions" as its object would make, by following the same rules. I don't mean "proxy" in the sense of tree rings as proxy for thermometers.
Modes of inference:Surmise. Automatically preserves neither truth nor falsity.Strictly ampliative induction.Forward-only deduction.Equivalential deduction.
Ironic aspectual criteria of above-correlated inference modes' conclusions.Naturalness, facility, efficiency.Likeliness (I don't mean in a Bayesian sense to its extent of incorporating subjective estimates of probability into the reasoning itself).Novelty.Nontriviality.
Scientific inquiry into concrete phenomena:Explanatory hypothesis (to an entity, law, etc.)Characterizing the phenomenon in light of the hypothesis, inducing to likely scenarios.
Aw heck, I'm unsure here.
Noting a distinctive consequence (prediction).Reproducing (not merely repeating) the test/prediction in various equivalent forms.
Tetradic semiosic stages (augmented Peirce).Objectification.Representation.Interpretation.Establishment.
Communication stages.Source.Encoding.Decoding.Destination (verification is generally a destination's task.)
Creative process (Helmholtz & Poincaré).Saturation (getting handles on a problem).Incubation.Illumination (e.g., as in "eureka!").Verification.
Requisites for beauty (augmented Aquinas).Due magnitude & direction.Harmony, due proportion, due rhythm.Radiance, vibrance.(Structural) wholeness, integrity.
Aesthetic stages (augmented Joyce).Arrest.Fascination.Enchantment.Attachment, devotion.
Art's four poles.Subject matter (mastering it from an artistic standpoint).Artist (materials, technique, sensibility).Art work (the point, the artistic effect; publishing it, performing it).Audience (target audience, reception, etc. The audience isn't always right but then what is?)
Artistic genres
(Some Joyce plus Gerald L. Bruns plus what):
Foci: volition & audience.
Critical, contentional, persuasional, seductive, proselytic, etc.
Cf. vyings.
Foci: ability & artwork.
'Formalist', 'hermetic', etc.
Cf. cooperation, tolerance, minding one's (own) business. Workaholic Hephaistos's focus on work to exclusion of world.
Foci: affectivity & artist.
Cf. community, distinctive unitings.
Foci: cognition & subject matter.
Cf. checks & balances.
Causes in human life's affairs.The beginning:
Endeavor (one's life's dynamics as strong & freely undertaken).
The middle, means:
Self-application, industry (one's life's processes as dependable & cultivated).
The end, telos, culmination:
Happiness (one's life's activities as vibrant & pleasurable).
The entelechy, the standing finished:
Assurance (one's life's balancements as sure & known).

Special relativity's light cone & the mind's temporal perspectives
Light cone. Special relativity's four zones of communication and cause & effect (the light cone) — the future light cone's surface, the future light cone's interior, the past light cone's surface, the past light cone's interior. I incorporate a generalization of that ubiquitous structure into my tetrastics, particularly in terms of modes of the psyche.

Quick review (which I just now added, then mostly deleted, from Wikipedia):
Any event E has a light cone comprised of four zones of possible communication and cause and effect:
1. Events on event E's future light cone can be reached by a light pulse from event E. E can appear to them.
2. Events in event E's future light cone can be reached by a slower-than-light (material) particle from E.
3. Events on event E's past light cone can send a light pulse to E. They can appear to E.
4. Events in event E's past light cone can send a material particle to E.

Generalizable spacetime stucture of communication and cause & effect. Light cone times: Almost now (feasibles & optimals). Later (probabilities). Barely Now (news, information). Earlier (bases, facts, data, for logical conclusions). (Outside those four zones is a strictly incommunicado zone, the (absolute) elsewhere of E. Events there never can affect or be affected by E.)

Of course, as one continues through time, one's light cone continues with one or, to put it another way, one has a more-or-less continuous succession of light cones. That event which is elsewhere and incommunicado at a given time is so for only a while for one enduring through time and, if the event be nearby, it's a very short while.

From the outer limits to the inner mind
The times “almost now,” “later,” “barely now, just now,” and “earlier”, mentioned in the above table, point to a generalization from the ubiquitous physical case of relativity’s light cone. Now, we say, generally speaking, that one’s past affects one’s future but not vice versa. Should we likewise distinguish the present which one affects and the present which affects one? Aren’t they pretty much the same zone with respect to the somewhat prolonged present which a mind actually experiences? Yet they turn out to be worth our distinguishing as times oftener than we do so.
Tetrastic 4x4 of modes of the psyche.Will, conation:Dealing, ability:Affectivity:Cognition:
(Like future light cone's surface.) For almost now:Trying.Testing, devising.Desire.Fancy, "impression."
(Like future light cone's inside.) For later:Seeking.Preparing, approach.Hope, confid.Expectation, anticip.
(Like past light cone's surface.) For just now:Taking, picking.Achieving.Pleasure, satisf.Noticing, discernment.
(Like past light cone's inside) For earlier:Adherence, habit.Maintaining, skill.Attachment.Memory.

For instance, we can distinguish four modes of will - trying, seeking, taking and adhering -, all four, in terms of four possible time orientations in a single system. And we can see, in parallel, (a) a seeking as a unity arising across successive tryings, and (b) an adhering as a unity arising across successive takings/pickings. And we can see the difference between outspreading signals (on the future light cone) and incoming signals (on the past light cone) as similar to the difference between efferent (as for example with efferent nerves carrying signals out from the brain to the muscles) and afferent (as for example with afferent nerves carrying signals to the brain from sensory receptors).  And the efferent/afferent difference also resembles the difference between the "active" faculties (will & ability) and the "receptive" faculties (affectivity & cognition), and especially that between will and affectivity.
Admittedly simplistic comparisonTimeHuman causal principle
efferent (like force)The almost now.Will, conation.
(like finesse)The later.Ability, dealing.
afferent (like excitedness)The just now.Affectivity.
(like supportedness)The earlier.Cognition.
If the will is itself "efferent," then how can it have modes correlated to all four times?  It can, because the will's objects can pertain to all four times. For instance, when one wills something as something which one has willed before, in the past, then that's adhering to the thing. Habit (in the English word's everyday sense) is steady such adherence, and is past-oriented will (pace the Scholastics) just as memory is past-oriented cognition.

It seems that some sort of generalization of the ubiquitous light cone structure (a generalization not involving a very high, exact, constant speed limit) is more illuminating in many cases than the standard past-present-future trichotomy, though I certainly don't think that the light cone idea would rightly supplant the past-present-future trichotomy in all cases.

So much also for the idea that theoretical physics should be ignored in phenomenology. Physics won't settle general phenomenological questions but it can embody some general phenomenal structures which we have simply failed to notice in doing a phenomenology.

The initial point is:
• to recognize the philosophical generality of the idea of a finite general upper speed limit and the general import, for any system of communication and cause/effect, of finite general practical upper limits on the speed of signal propagation, though the given medium’s effective speed limit be less high and exact than some ultimate physical limit like lightspeed, and
• to recognize that mutually causal relationships involved with co-present objects don’t absolutely unite outgoing potency and incoming information, don’t render them indistinguishable in a wash of instantaneity -- don’t actually so unite them any more than they phenomenologically so unite them (the phenomenological aspect is more easily noticed from the viewpoints of the objects involved; compare with Merleau-Ponty’s idea of the never completed circuit between touching and being touched and even between touching oneself and being touched by oneself). Instead, two “presents” differ like future and past, differ as the respective edges, surfaces, of future and past. The difference runs deep -
The difference runs deep
the present (the almost present)
toward which one acts and addresses oneself
the present (the just-now present)
which acts upon one and is addressed to one
that to which one is (almost now) present that which is (just barely now) present to one
that for which one improvises (at least somewhat) that which appears to one
outgoing best shots of not-yet-measured direct feasibilityincoming actual hits of not-yet-verified information
Then we can see, in parallel, (a) the future as an entrainment, or as a continuous unification, of successive almost-nows, and (b) the past as an entrainment, or as a continuous unification, of successive just-nows. This can be seen systematically reflected throughout the tetrastic 4x4 table (above) of time-orientational modes of the psyche, in the columns under will, dealing, affectivity, and cognition. Again for instance, we can see (a) a seeking as a unity arising across successive tryings, and (b) an adhering as a unity arising across successive takings/pickings. Of course, also, the future holds future pasts, and the past holds past futures, invading that which is elsewhere and incommunicado at the moment, in the thickening cross-hatching of spacetime.

Source, encoding, decoding, destination
Communication theory
1. Source.
2. Encoding. 
2½. Channel.
3. Decoding. 
4. Destination.
Tetrastic semiotic
1. Object.
2. Sign. 
3. Interpretant. 
4. Recognizant, veri­ficant, establishment.
Made badly needed corrections April 7, 2012.

Claude Shannon's communication-theoretic scenario, when cast as four stages, involves source, encoding (sender), decoding (receiver), and destination . (However, the communication channel is often included as a stage, on a par with the others and between encoding and decoding. Solutions to the challenge of the channel and its noise shape a lot of communication theory; but the challenge is to minimize the noise and avoid information loss; the generation or modification of signals is desirable only in the other stages.) My augmentation of C.S. Peirce's semiotic process (a.k.a. semiosis) to include a fourth and (dis)verificatory/(dis)confirmatory stage brings semiosis into alignment and correlation with the fourfold version of Shannon's scenario. The field of experience in or against which a decoding (and ultimately the encoding and source as well) is tested is, first of all, that of the destination. Note: semiosis differs in that it is not code-bound like info-theoretic communication; the continual renovation and occasional redesign of a communication system is a kind of "evolution" (pace biologists!) whereby semiosis is arguably definable, and which, I argue, comes about through such testing. As for channels and noise, I'm unsure of precisely what the semiotic analogs to them would be.

Helmholtz, Poincaré, & the creative process

In The Quark and the Jaguar, theoretical physicist Murray Gell-Mann discusses the creative process in terms of Helmholz's three stages of saturation, incubation, and illumination, and the verification stage added thereto by Poincaré. This accords quite well with “my” foursome of beginning, middle, end, check. On pp. 264-265, Gell-Mann says that he and some physicists, biologists, painters, and poets compared experiences of discovery, & that their accounts were remarkably similar. The entire passage from which I've drawn excerpts is available through Google books http://www.google.com/search?q=%22each+found+a+contradiction%22+Gell-Mann. All ellipses below are mine.

[...]. We had each found a contradiction between the established way of doing things and something we needed to accomplish: in art, the statement of a feeling, a thought, an insight; theoretical science, the explanation of some experimental facts in the face of an accepted “paradigm” that did not permit such an explanation.
  First, we had worked, for days or weeks or months, filling our minds with the difficulties of the problem in question and trying to overcome them. Second, there had come a time when further conscious thought was useless, even though we continued to carry the problem around with us. Third, suddenly, while we were cycling or shaving or cooking [...], the crucial idea had come. We had shaken loose from the rut we were in.
  We were all impressed with the congruence of our stories. Later on I learned that the insight about this act of creation was in fact rather old. Hermann Von Helmholtz [...] described the three stages of conceiving an idea as saturation, incubation, and illumination, in perfect agreement with what the members of our group [...] had discussed a century later.
  In 1908, Henri Poincaré added a fourth stage, important though rather obvious -- verification. He described his own experience in developing a theory of a certain kind of mathematical function. He worked on the problem steadily for two weeks without success. One night, sleepless, it seemed to him that “ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination.” Still, he did not have the solution. But, a day or so later, he was boarding a bus [...]. “The idea came to me, without anything in my thoughts seeming to have paved the way for it, that the transformations I had used to define these functions were identical with those of non-Euclidean geometry. [...] I felt a perfect certainty. On my return to Caen, for conscience’s sake, I verified the result.”
  The psychologist Graham Wallas formally described the process in 1926, and it has been standard ever since in the relevant branch of psychology, though I think none of us at the [...] meeting had ever heard of it. I first came across it in a popular book by Morton Hunt entitled The Universe Within, from which the above translated quotations are drawn.

(1) In saturation, one is taking hold of the problem, taking it on. That’s the beginning.
(2) If this does not lead soon either to illumination or to dropping the problem, then there is incubation, in which, though the problem remains unsolved, one has gotten its elements sufficiently under control to process the problem without having to consciously think about it (though of course one still can so think). It may consist, as Gell-Mann points out in the passage's fuller version, in little more than unconscious stewing over established assumptions till one or another of them softens in the mind. Anyway, that’s the middle.
(3) Illumination is the eureka, the ending, the climax.
(4) Verification/falsification is the checking.
I'd say that it's a very good match.

Penelope Merritt's account of traditional four-symbolism
Red drop-shape, storm-blue lips-shape, vivid-gold solid triangle, at jazzy tilts, and hard-green solid square, all against a black infinity sign against a white pentagon against a black hexagaon, etc., i.e. a background of higher polygons crowding up behind one another, alternating black & white.Penelope Merritt’s account of traditional four-symbolism “A Few Thoughts On the Number Four” at samuel-beckett.net is one of the very few which I’ve read which reminds me at all of my fours. Incidentally thereto (at least I think it's a coincidence), it’s one of the few accounts of number symbolism which don’t make me sleepy. Most such accounts that I’ve seen, even the brief ones, soon amble into vague numerological mazes. But this Penelope weaves plain and clear. (She is with the Community Center for the Performing Arts, Eugene, Oregon.)

Now, I’m interested rather more in recurrent logical patterns, than in number symbolism and elaborate games of artificially synesthetic apprehensions of small positive integers (and I don’t believe in synchronicity or believe that numbers have magic powers). But logic and reason involve fourfolds which do get reflected in common ideas, whence traditional number symbolism draws.

After Penelope’s initial discussion, she goes on to discuss the number five, which represents things like expansion, destabilization, catalysis. This is like a new beginning, a new first stage, that works upon the stabilization which is the fourth stage.

Then Penelope discusses the four Gospels, the four elements, the four humors, and there the correlations with my tetrastic structures seem weak, so I will focus on her initial discussion.

“One represents the male principle, the ‘yang’. It is raw energy, positive, original and creative. In the creative process it is the original spark of an idea.”

Here, at a beginning, I think of forces, movements, directional and opposable, roving and wandering, more than I think of energy.

“Two is the feminine principle, the ‘yin’. It is the gestational period in which things begin to form, the earth into which the seed of one’s idea is planted. In the creative process there is almost always a similar period when an original impulse ‘cooks’ for a time, even if only in sleep or distraction.

Here, at a middle, I similarly think of gestation, processing, producing, adaptation. Here I also think particularly of rhythm, regularity, constancy, homeostasis, patience, endurance, dependability, perseverance, etc.
“Three is the synthesis of one and two. It is ideation and self-expression, the creation itself, the finished idea.

Here, at an end or culmination, I think of those things and of vibrancy, claritas or radiance, energy, vigor, and also selectiveness, perfectiveness, etc.

“Four is the material manifestation of three, the actual physical realisation, order and systematisation of the idea. It is the making real of the dream represented by three.

Here, at a check or checking, similarly I think of stability, firmness, solidification, confirmation, entelechy.
Penelope goes on to say, “Four has come to be considered the number of labour and stability” I don’t associate stage four (my “check” or “checking”) with labor except (as often happens) insofar as labor bears out and verifies, or disconfirms, that which is discovered in stage three (my “end” or “culmination”). Instead I would associate, most of all, stage two (my “middle,” “means,” “mediation”) with processing, production, labor, adaptation, etc. Penelope elsewhere in her essay says that four is associated with both dependability and stability; I think, for "four," less about dependability across time and more about balance and stability across space, structuring and stabilization (of opposed forces and movements), etc., rumination, digestion, assimilation, integration, concrete embodiment. Staunchness and solidity.
In terms of various kinds of strength, one might do it this way:
1 {beginnings}. Might, dynamism.
2 {middles}. Endurance, patience.
3 {ends}. Vigor, vibrance.
4 {checks}. Firmness, solidity.

I have long been somewhat aware of yin-yang ideas, seed and soil, etc., but I know little of any further number symbolism. Yet I didn’t pick my four out of a hat. Above, note the diagonal oppositions between 1. might, dynamism, & 4. firmness, solidity, (will travel vs. won’t travel) whereof the familiar fantastic extremes are the irresistable force and the immovable object, and between 2. endurance, patience, & 3. vigor, vibrance, (will be patient vs. won’t be patient), whereof the respective fantastic extremes are the unflappable and the undampable. These are ideas in abstract balance. And they are anything but an arbitrary pairing of dyads. Note that 1. might, dynamism, & 4. firmness, solidity, (will travel vs. won’t travel) are space or distance ideas, while 2. endurance, patience, & 3. vigor, vibrance, (will be patient vs. won’t be patient), are time ideas. They have distinguishable physical meanings reflected in a system’s
1. Momentum, impulse, force.
2. Rest mass, rest energy, internal work & power
3. Energy, work, power.
4. Internally balanced momenta (kinetic & potential), impulses, forces.

Physics quantities. Momentum, mass, energy, etc.They also correlate pretty well with Aristotle’s Four Causes:
1. {might} efficient,
2. {endurance} material,
3. {vigor} final,
4. {firmness} formal.
Worthy of note is the correlation of Aristotle’s four causes with the systematically interrelated kinetic & mechanical conceptions above (remembering that kinetic and related mechanical conceptions arose from attempts to quantify cause and effect, but are not conceptions of causes and effects per se, much less conceptions of things related to each other as cause and effect, e.g., momentum and force are not considered to “cause” energy, work, or power as “effects”).
— In comparing with Aristotle’s causes, one may wish to think not just of momentum and energy but also of impulse and work, and of force and power. Force, for instance, involves change (or rigidity, opposition to change) of a system’s motion, shape, state, or condition. And thinking of internal force and power makes us think of a material system rather than, say, merely a cloud of variously traveling photons (which as a whole travels slower than light and so has the kinetic values which some given material system might have).
— “Power” here means rate of work done or energy transported, such that “wattage” would be the least bad word for it in everyday metaphors, because the quantity called “power” in physics is decidedly unlike political-style power, which is instead forcelike, directional and opposable, winner of a contest among those who would lead and be first; wattage-style power is comparatively more suggestive of a different prize, that of being that which wins the contest among ends and perfections: “vibes,” charisma, radiance, popularity, glamour, show, etc., though one should think of horsepower, vigor, whatever kind of vitality, and not only of candlepower. To be sure, I don’t think for a moment that social and poetic forces determine theoretical physics; however I like some kinds of common metaphors and I think that it’s interesting to see how far they can be taken and to see whether underlying logical similarities between systematic sets (especially foursomes) of conceptions can be brought to light).

The volitional or conational characterizations which I made —
1. wandering,
2. perseverance,
3. selectiveness,
4. staunchness, unbudgingness.
— are based on considerations about variability and constancy in light of the structure of logical quantity. As I said in “Why tetrastic?,” some fourfolds echo each other in ways for which I have not yet managed, at least to my satisfaction, to uncover the reasons, even when the fourfolds separately from each other have seemed clear enough. Turn a sign this way, then that, align it with others, the world seems to crack open, and the chase may be on. I disbelieve in a collective unconscious (Jungian, panpsychic, or otherwise) and I really have no precise idea why, for instance, there would be a correlation or analogy stretching from mechanical and kinetic concepts such as force, energy, mass, etc. (and related concepts of time and distance), to logical modes of constancy and variability, and even to, of all things, aspects of traditional number symbolism. I can only assume that it reflects some similarity in their respective logical structures, and guess, as I usually do, that broad conceptual structures elaborated so as to exhaust the logical possibilities in their respective realms sometimes end up with a family resemblance which sometimes spurs philosophical qualitative inductive generalizations but is seldom subjected to thematization and careful treatment and which may just as often spur a writer or artist as a philosopher. Penelope also, as shown, characterizes the numbers in terms of the creative process, which brings us to the post, "Helmholtz, Poincaré, & the creative process."

John Boyd's OODA loop
Correlations, not flat equations.
1. Observation (data intake).
2. Orientation.
3. Decision.
4. Action.
Tetrastic modes
of the psyche:
3. Affectivity.
4. Cognition.
1. Will, conation.
2. Dealing, ability.
Tetrastic stages in
a generalized loop.
1. Adopt.
2. Apply.
3. Take in.
4. Digest.
John Boyd's OODA loop — Observation, orientation, decision, action. There seems not too bad a correlation, except for a few things. In my non-reordered, "default" version the loop would begin with decision -- DAOO. There my short answer is that a reordering can be perfectly "okay, philosophically" as long as it is regular, relationship-preservative. The biggest difference seems instead to be that in my version, "observation" (the intake of data) would have, at its core, affective evaluation -- i.e., one is confronted by good or by bad or by an irresistable challenge -- etc. In battle, of course, it's important to keep cool under fire, and meanwhile Boyd emphasizes the intake of data via the senses. Next, Boyd portrays orientation as a cognitively digestive stage, yet "orientation" remains the right word for that which he's discussing, cognition with pertinence to one's immediate situation.

But why would I want to order even the generalized loop differently? If I think that Boyd's ordering is just fine, then why don't I make it the standard for more general orderings? Where the action is a kind of means, the decision to it is a beginning, an undertaking. From one's ensuing action springs a result, an effect or lack thereof, which one observes (or tries to observe, anyway) and evaluates, especially for its likeness or unlikeness to one's intent, and one considers it carefully, checking it against various things including one's experience and expectations. Beginning -- middle/means -- end -- check. Thence one may loop back to the decision stage again, as indeed one may have already done in getting into the current go-round. (Discussion of beginnings, means, ends, and checks.)

Ken Wilber's Four Quadrants & four moral development stages
Ken Wilber's Four Quadrants — Interior-Individual, Exterior-Individual, Interior-Collective, Exterior-Collective.
Ken Wilber's Four Quadrants
(Source: Wikipedia
Quadrant (UL)


e.g. Freud
Quadrant (UR)


e.g. Skinner
Quadrant (LL)


e.g. Gadamer
Quadrant (LR)


e.g. Marx [sic]
As far as I can tell, his foursome of quadrants doesn't correlate with any of my fours. It's interesting, though, and it consists of four combinations of values of paired two-valued parameters. Maybe I'll find a way to adapt it, though I'd be likelier to include Smith or Hayek than Marx as an example.

On the other hand, the way in which Wilber divides stages of moral development does seem to correlate, somewhat, with the way that I treat logical quantity, which involves conjoined quantifications, four conjunctions of answers to two twinned but mutually independent quantity questions (see my post "E.J. Lowe's four-category ontology" or the longer "Logical quantity & the problem of universals").

Correlations, not equations
Wilber's moral development stages
(source: Wikipedia http://en.wikipedia.org/wiki/AQAL)
Tetrastic logical quantities
(Also see my "Logical quantity & the problem of universals."
Note: Wilber apparently assigns meanings to colors. My use of colors unrelated to his. Note, however, that the hues of color which I use (habitually) for the logical quantities are systematically opposite in feeling to the correlated Wilberian moral development stage.
Egocentric (similar to
Carol Gilligan's 'Selfish' stage).
Singular, or singulars taken as in a polyad, in a larger world.A. B-C. D. E. F. G. …
Ethnocentric or Sociocentric
(Gilligan's 'Care' stage).
Special-cum-general, i.e.,
neither universal (e.g., mathematical) nor singular (like you & me)
# # # # # …
* * * * *
# # # # # …
(Gilligan's 'Universal Care' stage).
(total population & its parameters, universe of discourse, gamut).
Pie chart. Photobucket
(Gilligan's 'Integrated' stage)
Universal but not a universe, i.e.,
there's more than one instantiation of it in its universe

••  ••
••  ••     ••  ••

The most questionable correlation is that between Wilber's "Being-centric" stage and the repeatedly instantiated universal. Wilber associates the "Being-centric" stage with a final and mystical stage of moral development. The immediate problem isn't the mysticism since, on my side of the correlation, there are merely logical quantities. The immediate question is whether by "Being" he means something that correlates with the repeatedly (indeed sometimes endlessly repeatably) instantiated universal. Of course, since being is that which everything has (though never in the same way twice), he probably does mean something similar to the universal that is not the universe or world.

Jacques Lacan's Four Discourses
Jacques Lacan's Four Discourses — Master, University, Hysteric, and Analyst. I wouldn't go along with a presumptive attitude of authority = bad, resistance = good. Yet, I do discern a certain weak but unmistakable echo of some of my fourfolds. In order to resist verbosity, maybe I can get away with bit of connect-the-dots.
Lacan (Source: Veryard Projects at http://www.users.globalnet.co.uk/~rxv/books/lacan.htmSlavoj Zizek's example
from the opera Don Giovanni
(Source: Veryard Projects at
Tetrastic echoes, not equivalents (mine). Imagine the items in this column as if they had been qualified or altered a little in order to apply in particular to academic knowledge and discourse. Note: I don't share Lacan's & Zizek's antipathy toward non-socialist power and wealth. Update: I've learned that Zizek is quite the enfant terrible, profitably praising Hitler & Stalin (snifter clink to David Thompson).
Discourse of the MasterStruggle for mastery / domination / penetration. Based on Hegel's Master/Slave paradox.Don Ottavio inauthentic,
Power. Ruling/governing arts.
Discourse of the UniversityProvision and worship of "objective" knowledge - usually in the unacknowledged service of some external master discourse.Leporelloinauthentic,
Wealth, means. Productive arts.
Discourse of the HystericSymptoms embodying and revealing resistance to the prevailing master discourse.Donna Elviraauthentic,
Splendor, glamour, "wattage," etc. The affective, expressive, "consumptual" arts.
Discourse of the AnalystDeliberate subversion of the prevailing master discourse.Donna Annaauthentic,
Honor, standing, legitimacy. The "ruminative arts" -- maths & sciences.

William Vallicella's Mighty Tetrad
(Actual first date of this post: December 28, 2008. Recentest significant change: October 23, 2010.)

Vallicella discusses his Mighty Tetrad in three posts linked at http://web.archive.org/web/20070811194657/http://maverickphilosopher.powerblogs.com/posts/chain_1115071783.shtml:
• "Money, Sex, Power, and Fame" (May 2, 2005 at 3:09pm)
• "Radix Omnium Malorum" (May 2, 2005, 3:33pm)
• "Radix Omnium Malorum Update" (May 3, 2005, 9:24am)
and in
• "The Mighty Tetrad: Money, Power, Sex, and Recognition," versions Jan 15, 2008, 9:33am, Jan 22, 2008, 3:06 am, but gone from the Internet, and Feb 8, 2008, 3:01 am, also gone from the Internet.
Update (10/23/2010): "Beguilement," September 21, 2010. (Pause of update.)

Power, wealth, glory, honor, 4 rewards of conflict. Photobucket. There's definitely a correlation with one of my tetrachotomies - that of
1. power, 2. wealth, 3. glory, and 4. honor.
I tried to post a comment about his Mighty Tetrad at his blog some years ago, but it took a month or two before I received posting privileges there, and I pretty much forgot about it.

Normally I wouldn't forget about a correlation but his jocular label "Mighty Tetrad" suggested that he didn't mean to plant his flag on his Mighty Tetrad as consisting in mots justes for exactly four philosophically systematic chief motivators of behavior; he was more interested in arguing that neither money nor power nor sex nor fame (nor any other motivation of their kind) is evil or the root of all evil, and that each of the four is a good liable to perversion. I agree with him about all of that. Update of October 23, 2010, resumed: In his September 21, 2010 post "Beguilement," he says:
The Russian prelest means 'beguilement.' It is indeed a beguiling world. The four chief beguilers: sex, money, power, fame. In their grip a man finds this empty and ephemeral world a veritable plenum of reality.
And that's the whole post. (Pause of update.)

Meanwhile, on the other hand, I was of course interested in getting four such ideas, getting them just right, and relating them to other fourfolds. I had continually sifted through common phrases such as "fame and fortune," "power and wealth," etc. I had long been playing with ideas of four disparaged motivators, four modes of that which anthropologists call "mana," etc. It was one of many paths that I took to developing my fours. I was relating them back to Aristotle's Four Causes. At one point I regarded the motivators as
1. power,
2. money,
3. sex, and
4. too narrowly, a kind status awarded for being smart or knowledgeable, which would also lead to the awardee's learning things, since people try to trade info for info.

By the time that I read Vallicella's posts, I was thinking:
1. power,
2. wealth,
3. glamour/wattage/glory (including vitality, horsepower, sex and sexuality, "action" as they say, etc.), and,
4. still all too narrowly, some sort of "guruship" in a loose sense.

Much later, in considering the idea of legitimacy, I saw that honor and standing are the attribution of legitimacy to a person or thing in some respect (legitimacy and, sometimes, authority in the sense of authoritativeness), just as glory, glamour, etc., are the attribution of intrinsic value or importance to a person or thing in some respect. The value/legitimacy difference parallels the affectivity/cognition difference and the goodness/truth difference (and seems related to the role/status difference). As you may or may not have noticed, I was conceiving my "mana tetrad" according to ideas of
1. will,
2. ability,
3. affectivity, and
4. cognition,
as well as the Four Causes.

By 2008, Vallicella had replaced the idea of fame with the idea of recognition. In a 2008 post on the Mighty Tetrad, Vallicella says, "One might wonder about recognition especially as it shades off into fame, and beyond that, into empty celebrity. Is it really good?" I'd say that as recognition shades off into fame, it is becoming glamour or glory rather than honor and standing but it not in itself a bad thing for all that, if you like occasional applause, sexuality, "good vibrations," and so forth; it is, so to speak, another incarnation of Aquinas's third requisite for beauty, claritas, "radiance" or "brilliancy" as of coloration; beauty itself has often enough been called the splendor of truth.

Update of October 23, 2010, resumed. Now Vallicella characterizes his mighty tetrad as "the four chief beguilers." To beguile means to charm, captivate, delight, but also to lure, to mislead by causing desire or pleasure. Beguilement itself is related to the idea of glamour. But what of deception, is it part of some foursome? Here's my current best guess:
1. coercion,
2. pay-to-play extortion,
3. manipulation, incitement, sycophancy, etc.,
4. deception, fraud.
(End of update.)

Correlations, parallelisms, etc.
Inter-behaviors:Vying — confict, competition, rivalry, contention, arenas.Cooperation, tolerance, occupational spheres.Distinctive unitings, communities by value.Checks & balances, supports, disciplines.
Vying's prizes:Power, influence.Wealth, means, resources.Glory, wattage, 'action'.Honor, validation, standing.
Vying's arenas:Decision processes about decision-making, beginnings, archai, leaderships. Deciding who or what gets to decide.

Political & martial affairs; also vis-à-vis nature (hunting, firefighting).
Decision processes about means.

Economics (business, commerce, finance).
Decision processes about values, ends, perfections.

Popular culture (sports, fashion, ostent, entertainment, etc.).
Decision processes about establishments, legitimacies.

Society (teachings, statuses, traditions, debates, etc.)
Aristotle's 4 causes:Efficient cause, agent cause.Matter.End (should be revised to ending, teleiosis).Form (should be revised to structure), entelechy.
Mechanics analogs:Net momentum, impulse, force (directional & opposable).Rest mass, rest energy, internal work & power.(Non-rest) energy, work, power.Internal, balanced momenta (potential & kinetic), impulses, forces.
Human causal principles:Agency, impetus:
Will & conation. Character.
Patience, mediation:
Ability, dealing. Competence.
Actualization, culmination:
Affectivity. Sensibility & values.
Borneness, establishment:
Cognition. Intelligence.
Basic subsistence:Hunting or gathering the food.Cooking or otherwise preparing the food.Presenting, consuming, enjoying the food.Digesting & reflecting on the food.
Sectors:Assumption, adoption, control.Processing, production, adaptation.Consumption, expression, conversion.Rumination, digestion, assimilation.
Greek gods:Zeus, Ares, Athena, Diana.Gaia, Demeter, Pluto, Vesta, Hephaistos.Aphrodite, Persephone, Pan, Dionysos.Apollo, Athena (again).
In tracing correlations among four-folds, it becomes evident that the four motivators are four prizes of vying, prizes of conflict, competition, rivalry, contention.

Now, power, wealth, glory, and honor, are in a sense beginning, means, end(ing), and establishment or entelechy, such that each of them is seen as an end. Means as end: wealth as goal. Entelechy, establishment, as end: how many times, in practical matters, have you heard one person ask another, "What are you trying to prove?" People don't act to prove things only in inquiry. In daily life, people sometimes act to prove themselves as being legitimately this or that, deserving of some sort of recognition or honor or accorded status (or in order to avoid a status) or to prove that some people do or don't deserve some status. Ours is an honor culture, but we have rather different ideas about honor than, say, a culture which hinges a family's honor murderously on the chastity of its unmarried daughters. Honor is about legitimacy and reality (which we recognize and acknowledge, and therein is the connection which I had been seeking with the idea of cognition and knowledge); to honor something is, as by a contract made in the imagination, to treat it as having the force of the actual even if it doesn't have the prompt and direct effect of the actual; and so we honor mathematical postulates, our contracts, and our fallen warriors in one way or another.
In the mind there is a continual play of obscure images which coming between the eyes and their prey seem pictures on the screen at the movies. Somewhere there appears to be a mal-adjustment. The wish would be to see not floating visions of unknown purport but the imaginative qualities of the actual things being perceived accompany their gross vision in a slow dance, interpreting as they go. But inasmuch as this will not always be the case one must dance nevertheless as he can. — William Carlos Williams, Kora in Hell.
"Interpreting"? Calculating, translating, decoding, converting? Make it marking bounds and objectifying; measuring and representing; converting and interpreting; and entraining and verifying (or overturning).