Mining Aristotle's Four Causes for order & balance
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 —
agent,	patient,	act

— 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(ing), teleiosis, 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. Structure. & 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.

Balance:
Underlying equivalences
along the diagonals.

agent bearer

X

act borne

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.

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.

Aristotle

external	efficient cause		end, final cause
	agent
			act
internal	patient		form, formal cause
	matter, material cause

Tetrastic

beginning agent bearer middle, means

end(ing), teleiosis act borneness check, entelechy

Tetrastic (elaborated)

	1. AGENT.	2. BEARER.	3. ACT.	4. BORNENESS.
Existence (consistently extreme version).	Efficient cause.	Sustainer.	Consumer, exhauster.	Assimilator / suppressor.
Causes as turns of becoming.	Beginning.	Middle, means.	End (-ing), teleiosis.	Check, entelechy, standing finished.
Causes as rational characters.	The strong has the rational character of a beginning (a deciding).	The apt has the rational character of a middle or means.	The good has the rational character of an end.	The true, real, genuine 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.	Affectivity. Sensibility. Values, etc.	Cognition. 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.	Laws, universal constraints, regime (plurally instanced universals).	Elements, media & materials, domain (universe of discourse or total population & its 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.
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.
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.
General processes.	Decision processes.	Stochastic processes.	Info / communication processes.	Inference processes.
Some classes of signs (a Peirce trichotomy of signs, augmented).	Index.	Semblance, likeness.	Symbol, and (in a perhaps more general sense) functional surrogate.	Proxy, that which counts as its signified object under transformations and, so to speak, makes the same "decisions" as its object would make, by following the same rules.
Modes of inference:	Surmise. Automatically preserves neither truth nor falsity.	Strictly ampliative induction.	Forward-only deduction.	Equivalential deduction.
Scientific inquiry into concrete phenomena:	Explanatory hypothesis (to an entity, law, etc.)	Disambiguation, ancillary hypotheses, adjustments.	Prediction.	Framing of experiences or tests that, individually or collectively, would (if possible) crucially test the prediction. Note: crucially test the prediction, not the hypothesis, and do so in terms of truth and falsity or some more "nuanced" range of truth statuses designated for preservation across equivalences.
Tetradic semiosic stages (augmented Peirce).	Objectification.	Representation.	Interpretation.	Establishment.
Communication stages.	Source.	Encoding.	Decoding.	Recipient (verification is generally a recipient'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. Lyric. Cf. community, distinctive unitings.	Foci: cognition & subject matter. Dramatic. 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: Happiness (one's life's activities as vibrant & pleasurable).	The entelechy: Assurance (one's life's balancements as sure & known).

- posted by The Tetrast @ 10:31 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Special relativity's light cone & the mind's temporal perspectives
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:

(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 comparison	Time	Human 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 -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. - posted by The Tetrast @ 10:28 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Claude Shannon's source, encoding, decoding, recipient

Communication theory
1. Source. 2. Encoding.  2½. Channel.	3. Decoding.  4. Recipient.
Tetrastic semiotic
1. Object. 2. Sign.	3. Interpretant.  4. Recognizant, veri­ficant, establishment.

Claude Shannon's communication-theoretic scenario, when cast as four stages, involves source, encoding, decoding, and recipient (a.k.a. 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 recipient. 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. - posted by The Tetrast @ 10:26 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

E.J. Lowe's four-category ontology
E.J. Lowe, also known as Jonathan Lowe, proposes a quantificationally arbitrary square of ontological categories — Kinds, attributes, objects, and modes (property-particulars, a.k.a. tropes, e.g., this redness). There's a kind of double half-way correlation to my fours.

Basically, Lowe considers, as comprising his first categorial dichotomy, the particular (the singular or individual) and the universal (by which he means that which has more than one instance, and which I instead call the general). Logically there are four such quantities, not just two, arising simply and naturally. But Lowe is eclectic and doesn't consider as categorial divisions (1) the sweepingly universal in the sense of that which is true monadically or polyadically of everything ("one," "two," etc.) and is therefore extremely formalizable, or (2) the special in the sense of that which lacks such extremely formalizable universality ("blue," "elastic," "Jack," etc.).

Perhaps the biggest impediment in taking inventory of logical quantities has been that we don't usually consider both the monadic singular and the polyadic singular (or polyad of singulars) as being, both of them, singular, just as we consider both the monadic general and the polyadic general as being general. Another impediment has been a common initial veering into regarding the sweepingly universal only as a highest genus, strictly monadic, trivial for most purposes, and confined to a narrowly gabled attic, so to speak, of the house of logical quantities, an attic with room for just one such universal, logically equivalent to every such universal. Perhaps a third impediment has been some sort of neglect about defining logical quantity for terms through some same question or questions asked in all cases.

Given a term "H" true of something (call it "x"), the question of its logical quantity then depends on quantification over the rest of the universe of discourse:
Is there something which isn't that thing x and of which the term "H" is also true?
If no, then "H" is singular. If yes, then let us call "H" general.
- and -
Is there something which isn't that thing x and of which the term "H" is instead false?
If no, then let us call "H" universal. If yes, then let us call "H" special.

The twin questions stand mutually independent and resolve into four answers, conjoinable in four ways (see the table "Tetrastic versions..." above), notwithstanding issues of term purport which multiply relevant options. For the polyadic case, incorporate criteria requiring one-to-one correspondences as needed and slackening as needed to compensate for sequence variety.

One may think at first glance that one of the conjunctions, the universal-cum-singular, enframes a nearly blind window, looking out only on the case of a one-object universe. But let us practice consistency of conception, avoiding special wrinkles and complications, and classify the singular and the singulars-in-a-polyad together as singular in logical quantity, just as we class both the monadic general and the polyadic general as general. Then the monadic-or-polyadic singular-cum-universal comes forth naturally as a logical quantity corresponding to a gamut, a total population and its parameters, a universe of discourse, etc., supporting for example a collective predicate such as "30% (are) blue." (Those collective predicates are pretty hard to get without polyads.) Usually when we think of the universal, we think of something like a law, with many, even indefinitely many instances. That is actually a compound quantification; such a universal is also non-singular, i.e., also general.

Of course, in the sense that two are not three, "two" is not universal. But "two," "three," etc., are universal in the sense of being true of anything in some polyad or other; the qualities, the particular attributes, of the counted objects don't matter; only each object's being other than the others matters. Then we abstract the numbers and think of them as singulars. Thanks to its imaginative apparati, mathematics can re-create the world's logical quantitative diversities and variegation on abstract levels.

Now, since a universe-encompassing polyadic subject fully spelt out in sequenced monadics is sometimes daunting, consider a universe-encompassing relative or collective predicate; consider a universe-encompassing expressionally streamlined polyadic subject; and consider also a predicate-formative functor such as "with a (frequency) probability of 35%."

The question of variety among exhaustive sequences of the same total population's members is not a vexatious complication (raising the question of whether the total population is really "singular" or "multi-singular" or whatever you wish to call it) but instead a good complication and part of the solution to the question of what might be interesting about the monadic-or-polyadic singular-cum-universal logical quantity as a perspective. It goes to show that one should check to see whether one has defined parametric options in a consistent manner, especially in order to avoid jumping to conclusions about seemingly trivial or seemingly near-empty compounds of parametric options. That seemingly almost blind window turns out to view a populous class of research, including, and not limited to, probability theory and deductive theory of logic.

If one defines logical term quantities such as the universal, the general, and the special such that the terms may be either monadic or polyadic, then one should likewise define the singular, even if it means giving the singular another name, so as to keep the parameter of monadicity/polyadicity consistently independent of the parameter of logical term quantity. If one is proceeding exploratorily, then one’s logic should not be given special wrinkles in order to prejudge such questions as whether there’s any point to defining a monadically-or-polyadically-singular quantity. Such an anti-pre-judicial consistency, in the exploration of logical quantities, matters especially when one is interested in grasping logical quantities in a general way (general like statisticality and information) as perspectives characteristically emerging, even without formal articulate ado, as scopes in research and intelligent decision-making, performance, affectivity, cognition, etc., of whatever kind.

Because of the common philosophical failure to differentiate the singular as non-general sharply enough from the single as monadic, Lowe doesn't notice that a polyadic version of the singular could be a whole universe, and therefore sweepingly universal (in its universe of discourse), without being general and non-unique (again, in its universe of discourse) and is not a trivial almost-blind window onto a mere one-object universe. In other words, in missing some of the simple quantities, Lowe misses their conjunctive compounds. Thus he also misses the fact that the singular as usually understood actually involves a conjunctive compound of singular and special (or non-universal) in the sense that the singular, as usually understood, is not a total population. If "H" is a singular predicate, one usually assumes not only that there is some x of which "H" is true such that there exists nothing else of which "H" is true, but also that there exist, distinct from x, things of which "H" is false. That assumption is actually an option with a significance that becomes clear if by "singular" one means only "decidedly non-general" and not also "decidedly monadic." One will do that for conceptual consistency in considering logical quantity and term "adicity" or "valence" as separate dimensions.

I didn't start out hoping to find some way to include "total population" or "universe of discourse" as a logical quantity on a par with "general," "singular," etc. I hadn't given any thought to the idea of totality or universe as logical quantity. I simply followed the logic out consistently and tried to understand where it led. It leads to an old philosophical desideratum, a correlation of logical quantities to major classes of research subject matters. It even makes the old nominalist-realist wrangle seem less interesting, because now one is not confronting the same old stark dichotomy again and again. A universal such as "two" is as different from a non-universal general like "healthy," as either of them is from a non-universal singular like "Jack."

So I recognize four quantificational divisions, conjunctively compoundable in four ways, where E.J. Lowe recognizes only two logical quantities. Mine are logically more systematic and turn out to correlate to the subject matter perspectives of the major classes of research. If, for instance, one considers singulars polyadically as well as monadically, it is more natural to regard the 'special' sciences as being about singulars in a larger world. Before crying "there is no science of singulars," one should also remember that the subject matter of a science can differ from the object or objective of a science, and that the special sciences seek, as their objective, to discover laws, populations of elements, kinds, and individual histories of the subject matter, concrete singulars sometimes individually and sometimes in their multitudes. Even laws in physics take on the singular aspects of giant events, for instance the signal speed limit, which may have changed over time in relation to other fundamental physical quantities.

Insofar as more traditional categories such as substance and property are arrangeable in a pattern of nonbinding affinities with logical quantities, there again, I have four where E.J. Lowe has two. (Skip tables ►)

Now, such quantificational divisions are no more to be eschewed for parsimony than corners of the Square of Opposition; they are so systematic that it takes more information to eclectically select a few than to take them all. Occam doesn't raze exactly one or two corners of the Square of Opposition. To fail to recognize this leads to arguments over how few angels can dance on the head of a pin. If instead one listens to that which the logical structure is "trying to tell" one, then one may avoid the excessive foreshortening of the world's divisions that is echoed by the classic Saul Steinberg cartoon. For another instance, logical connectives can all be done in terms of negative alternation, and can all be done in terms of negative conjunction. But this means that the negative alternative and negative conjunctive are particularly versatile logical connectives; it does not mean that one or the other of them is really the only logical connective. Now, Lowe intends his ontology for the natural sciences, but I don't know what the natural sciences gain by minimizing or ignoring the difference between "blue" (true of this and of that, but not of some third or of some fourth thing) and a numberish universal like "three" (true of everything in one or another polyad xyz where xyz are all of them distinct objects and in a universe with more than two objects). I suspect that the real issue is an avoidance of evoking or suggesting further mountain ranges of those entities (beyond the generals or "universals" which Lowe already countenances) which nominalists dislike. Thus does the addictive battle between realism and its opponents distract from other interesting issues, distort and crop straightforward logical formalisms and their potential applications, and prevent philosophers from doing justice to the ideas to which they commit themselves in adopting a logical formalism such as that of logical quantity. For my part, I generally take the involvement of questions of a subject matter's ontological status in questions of math and science classification as an intrusion signifying that the classification is either deficient in firm and fertile constraints or just plain nebulous. - posted by The Tetrast @ 10:22 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

John Boyd's OODA loop

Correlations, not flat equations.

Boyd's OODA: 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.) - posted by The Tetrast @ 10:18 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Popper, McLuhan, Fuller, Kant, Heidegger
What would those five names be doing in one post? Nothing much. Each of the five cases involves a fourfold for which I see no strong correlation to my fourfolds.

Karl Popper's tetrad — (a sequential tetrachotomy? or a genuine tetrad? of) problem, tentative theory, (attempted) error-elimination (especially by way of critical discussion), new problem(s): “P 1 » TT » EE » P2 . ” I’ve tried but haven’t yet found a correlation. I can see that it could be argued that it’s a triad beginning to cycle.

Marshall McLuhan's tetrad — a tetrachotomy of enhancement, erosion, retrieval, reversal — I’ve tried but haven’t yet found a correlation.

Buckminster Fuller's tetrahedra — are not about specific foursomes of philosophically relevant conceptions, as far as I’ve been able to tell.

KANT'S TABLE OF CATEGORIES 1 of Quantity: Unity plurality totality 2 Quality Reality Negation Limitation 3 Relation Substance and accident  Cause and effect  Action and reaction    4 Modality Possibility -- Impossibility Existence -- Non-existence Necessity -- Contingency		TETRASTIC CATEGORIES (mine)
		Correspondence / variance (another than, double of, sum of, antiderivative of, etc.). Mode of attributability (indeed, not, if, possibly, novelly, probably, optimally, feasibly, etc.).	И	Modification, attribute, accident (firm, unsound, well, ill, steady, irregular, strong, weak, etc.). Substance, hypostasis (this man, this horse, etc.).

Kant's basic four categories -- quantity, quality, relation, modality. I don't see any special resemblance to my fours.

Martin Heidegger's fourfold — earth, sky, mortals, and divinities — I’ve tried but haven’t yet found a correlation or even a way to understand it. In "The Restriction of Being" in Introduction to Metaphysics, Heidegger discusses a four-way restriction or delimitation of Being by things which aren't non-being but which are nevertheless seen in oppositions to Being. I don't see a correlation there either. (In Heideggers's diagram the reader sees "the ought" above an upward arrow rising from "Being"; an arrow points from "Being" to "becoming" on the reader's left; an arrow points from "Being" to "seeming" on the reader's right; and beneath "Being" the reader sees "thinking" and a two-way vertical arrow between them.)
- posted by The Tetrast @ 10:08 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Walker Percy's semiotic tetrad

Walker Percy's Tetrad

Organism1 (I)
S y m b o l		R e l a t i o n   of		O b j e c t
	Relation of		Quasi- Identity (Meaning)
		I n t e r s u b j e c t i v i t y
Organism2 (Thou)

Walker Percy's tetrad of Symbol (or sign), Object, Organism₁ (I), and Organism₂ (Thou). Symbol and Object comprise a relation of quasi-identity or meaning. Organism₁ (I), and Organism₂ (Thou) comprise a relation of intersubjectivity. The two relations are sometimes shown intersecting across a diamond-shaped diagram.

Walker Percy jumbles functionally-defined semiotic elements with their bearers, sets up an ungainly tetrad of two organisms (I and Thou) and two things (object and symbol)), and that tetrad does not lend itself to generalization in terms of correlations to philosophical categories. Percy’s tetrad does not strike me as really philosophical.

Irrespectively, there might be some correlation with my foursomes, a correlation to that extent to which one may interpret one of the Organisms as the interpretant and the other Organism as the collaterally based recognition (which I call the "recognizant" or the "establishment"), or perhaps each of the Organisms as an interpretant and their supportings, checkings, & balancings of each other (in regard to symbol and object) as the recognizant — but these semiotic functions should be embodied by separate dedicated terms in the tetrad just as object and symbol are. And to some extent a single cognizant organism or at any rate a mind acts as its own cognitive support, check, & balance, even though it has learned much of how to do so from collaboration, strife, etc., with other organisms. (The recognizant is the verificatory/disconfirmatory element whereby I augment the Peircean triad to a tetrad). However, I wouldn’t tie interpretant and recognizant to being the fundamental semiotic “I” and “Thou” in whatever order (I would hold that the semiotic object is addressed to its sign, the sign to its interpretant, and the interpretant to its recognizant. I've discussed semiotics in “Semiotic triad versus tetrad”, also in “Why Tetrastic?” under “Semiotics” and in “Semiotics: collaterally based recognition, the proxy, and counting-as.”) - posted by The Tetrast @ 10:05 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Jung's four functions of consciousness
Carl Jung's four functions of consciousness — sensation & intuition, and thinking & feeling. There isn't a correlation. Despite their opposition, sensation and intuition are closer to each other than thinking and feeling are to each other. I don't want to get complicated here but, for various reasons, it doesn't seem a good, systematic fourfold. However I'm disinclined to judge it as a philosophical product; it is the work of a psychologist of homo sapiens, a psychologist, moreover, whom I haven't read in decades. In any case, it is hardly without value. I don't go along with the ESP stuff, but the difference between intuition (even minus actual ESP) and sensation is significant both on its own account and as an instance possibly of a pattern. - posted by The Tetrast @ 10:04 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

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
http://en.wikipedia.org/wiki/AQAL)

Upper-Left Quadrant (UL) "I" Interior-Individual Intentional e.g. Freud	Upper-Right Quadrant (UR) "It" Exterior-Individual Behavioral e.g. Skinner
Lower-Left Quadrant (LL) "We" Interior-Collective Cultural e.g. Gadamer	Lower-Right Quadrant (LR) "Its" Exterior-Collective Social 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).	# # # # # … * * * * * … # # # # # …
Worldcentric (Gilligan's 'Universal Care' stage).	Universal-cum-monadic-or-polyadized-singular(s) (total population & its parameters, universe of discourse, gamut).
Being-centric (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. - posted by The Tetrast @ 9:57 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

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.htm		Slavoj Zizek's example from the opera Don Giovanni (Source: Veryard Projects at http://www.users.globalnet.co.uk/~rxv/books/lacan.htm		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 Master	Struggle for mastery / domination / penetration. Based on Hegel's Master/Slave paradox.	Don Ottavio	inauthentic, inconsistent	Power. Ruling/governing arts.
Discourse of the University	Provision and worship of "objective" knowledge - usually in the unacknowledged service of some external master discourse.	Leporello	inauthentic, consistent	Wealth, means. Productive arts.
Discourse of the Hysteric	Symptoms embodying and revealing resistance to the prevailing master discourse.	Donna Elvira	authentic, inconsistent	Splendor, glamour, "wattage," etc. The affective, expressive, "consumptual" arts.
Discourse of the Analyst	Deliberate subversion of the prevailing master discourse.	Donna Anna	authentic, consistent	Honor, standing, legitimacy. The "ruminative arts" -- maths & sciences.

- posted by The Tetrast @ 9:41 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Alain Badiou's Four Discourses
Alain Badiou's Four Discourses or “truth procedures” — Art, Love, Politics, and Science — (Skip table ►)

Tetrastic 4×4 classification of aspects of humanity
which lend themselves to social compartmentalization,
containing at least 3 of Badiou's "4 Discourses."

SECOND level (the ROWS), INTER-BEHAVIORS             About   FIRST level (the COLUMNS), SECTORS		Beginnings, leadings, decision-makings	Middles, means, abilities, resources, dealings	Ends, endings, culminations, teleioses, satisfactions	Checks, ente­lechies, establi­shings, knowledge
		Subhead (sector) Appropriation, adoption, control:	Subhead (sector) Processing, production, adaptation:	Subhead (sector) Consumption, expression, conversion:	Subhead (sector) Digestion, rumination, assimilation:
Beginnings, leadings, decision- makings	Subhead (inter-behavior) Vyings, arenas:	Affairs of power, freedom.   (Badiou's "Politics.")	Business, trade, finance, wealth.	Show, games, sports, fashion, “wattage.”	Case-building, validation, standing, honor.
Middles, means, abilities, resources, dealings	Subhead (inter-behavior) Practices, cooperations, tolerances, occupational spheres & concourses:	Administration, management, compliance, adjustment.	Labor, work, collaboration.	Leisure, hobbies, repasts, celebrations, observances, recreations, pastimes.	Study, investigation, review, discussion, reporting.
Ends, endings, culminations, teleioses, satisfac­tions	Subhead (inter-behavior) Valuings, distinctive unitings, communities:	Ruling / governing valuings.	Care-how.	Tastes & valuings about feelings.    (Badiou's "Love"?)	Valuings about cognition & legitimacy.
Checks, entelechies, establish­ings, knowledge	Subhead (inter-behavior) Checks & balances, supports, disciplines:	Ruling / governing arts.	Know-how, productive arts/sciences.	Affective arts.   (Badiou's "Art.")	Maths & sciences.   (Badiou's "Science.")

“...the four generic 'conditions' of philosophy itself.... These are the only four fields in which a pure subjective commitment is possible, i.e. one indifferent to procedures of interpretation, representation or verification.” (See Badiou’s EGS faculty biography.) The Wikipedia article adds the caveat that “Badiou consistently maintains throughout his work that philosophy must avoid the temptation to attach its own truth to that of any of the discourses, a process he terms a philosophical ‘disaster’.” I see no obvious correlation here with my fourfolds. Three or possibly all four of Badiou’s Four Discourses appear in my 4x4 classification of aspects of humanity which lend themselves to social compartmentalization. There’s hardly any pattern visible in the resultant distribution in the table. So, right off the bat, I see hardly any correlation. I haven’t studied in any detail Badiou’s justifications for singling exactly those four things out, but the justifications sound unpromising. If Badiou makes a four-way distinction among object (subject matter), representation, interpretation, and verification, then, at least there, I’ll agree with him. - posted by The Tetrast @ 9:35 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Andean Tetalectics
The Andean Tetralectics of Jorge Emilio Molina, Javier Amaru Ruiz Garcia, Jorge Miranda Luizaga, & others. Their old sites are gone, just bits remain here on the WayBack Machine (at http://web.archive.org/). (More info on their Tetralectics can be found by searching on Tetralectica OR Tetraléctica). At the old sites I had found talk of the stone Gate of The Sun in Tiahuanaco, prime numbers, string theory. I’ve no idea as to whether there’s any correlation to my fours. - posted by The Tetrast @ 9:30 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Postmodernist Tetralectics
The postmodernist Tetralectics of R. Hargitai, Ö. Farkas, L+. Ropolyi, G. Veress & Gy. Vankó — there is necessarily a correlation to my Tetrastics insofar as their Tetralectics assumes the Aristotelian four causes but, beyond that, I don’t quite know what to make of it. The orientation seems systems-theoretic. They display conceptual oppositions assembled into a tetrahedron, discuss symmetry transformations, various kinds of oppositions (vertex/face, edge/edge) etc. They discuss three levels of description — (1) standard scientific theories, (2) metatheories, and (3) tetralectics. The philosopher and information theorist John Collier has given a favorable talk "Tetralectics: Ancient and modern precursors" (at the Symmetry Festival 2003 on Culture and Science). In a March 31, 2002 peirce-l message (lost from the archive and unavailable online), he links to the Hungarian group's paper and adds, "In my own work, which is unpublished, I find over and over that there is an underlying triadic symmetry to classic tetrads. The symmetry group is that of a tetrahedron. This has been a hobby of mine for over thirty years now." (He and the Hungarian group arrived at their ideas independently of each other. See Collier's Nov. 14, 2005 peirce-l mssage).
Anyway, I've looked at the “Tetralectics” paper a number of times over the past few years. It would be nice if some of the more detailed discussion which they mention became available, in particular in regard to their reinterpretation of Aristotle’s Four Causes, their mapping of theory families in physics, the discrete/continuous/global/local division, its alignment with infinite/infinite/infinite/finite, and so forth.

Tetralectics Table gathered from “Tetralectics” (authors R. Hargitai, Ö. Farkas, L+. Ropolyi, G. Veress & Gy. Vankó) at http://hps.elte.hu/~ropolyi/tetralectics.htm

Aristo­telian concept	Central Concept / Metatheory in a tetralectics of natural sciences	Theory families in physics	The Central Concepts' Sub-Concepts	Properties connected to Central Concepts/ Metatheories	Properties connected to Central Concepts/ Metatheories	Properties connected to Central Concepts / Metatheories (opposition of vertex to the opposite triangular face)
Matter	Matter (M)	Corpuscular	substrate --&-- structure	static, closed, individual	discrete, stochastic, disordered	equipositional	quality	reality	infinite
Form	Space-time (S)	Field	space --&-- time	static, open, collective	continuous, homogeneous, causal	hierarchical	quantity	reality	infinite
Efficiency	Action (A)	Variation principles	action --&-- interaction	dynamic, open, individual	global, deterministic, inhomogeneous	hierarchical	quality	possibility	infinite
Aim	Change (C)	Conservation laws	transformation --&-- equilibrium	dynamic, closed, collective	local, teleological, ordered	hierarchical	quality	reality	finite

- posted by The Tetrast @ 9:28 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

The Quadralectics of Marten Kuilman
The Quadralectics of Marten Kuilman. He seems to be particularly interested in a four-way version of dialogical structure, and in bringing it to light in old systems of thought, but his main interest right now is in applying his ideas to architecture. I have had some contact with the genial Kuilman during the past year, and he sent me some material. I’ve read some parts a number of times, explored other parts, but I really do have trouble understanding it, particularly the mathematics. I also suspect that his very European philosophical context makes his conceptions (e.g., his conception of “visibility”) harder for me to understand. In such situations, sometimes it is best to plow ahead, in hopes of catching broad gists and then working one’s way down to some of the more difficult stuff. That hasn’t worked yet for me in this case. - posted by The Tetrast @ 9:21 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

William Vallicella's Mighty Tetrad
(Actual first date of this post: December 28, 2008. Recentest significant change: January 7, 2009.)
Vallicella discusses his Mighty Tetrad in three posts linked at 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, and Feb 8, 2008, 3:01 am.

There's definitely a correlation with one of my tetrachotomies - that of power, wealth, glory, and 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.

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 power, money, sex, and, 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: power, wealth, glamour/wattage/glory (including vitality, horsepower, sex and sexuality, etc.), and, 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 will, ability, affectivity, 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.

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). - posted by The Tetrast @ 9:20 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Joel Miller's Tetrology and the Tetrastic System
Joel Miller's Tetrology and the Tetrastic System (once there, scroll down), unpublished. In the meantime, he recommends From DNA to ABC and is willing to send it to me for a $20 bill in the mail to him in Sweden; I trust him but I wonder whether he understands about the advanced state of thievery within the U.S. postal system. I have to get around to ordering his book in some more usual way; after all, he used the word “tetrastic” before I even thought of it! (Update: He now has PayPal.) (His “Majority English: the dialect of the non-native speaker,” which you’ll see if you click on From DNA to ABC above, is the good-humored title of what seems a pleasant Website for those interested in the ins and outs of English-language usage.) Anyway, his division of the concrete world into atomic, chemical, biological, and human systems may fit well with my four-way division; I just need to learn, one of these days, why he does it. - posted by The Tetrast @ 9:19 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Robert Worstell's tetrads of ideas
Robert Worstell's tetrads of ideas (e.g., Ability as analyzed into “Purpose, Confront, Responsibility and Understanding”. He has several blogs on various subjects. I didn’t grasp the pattern in his tetrads, and possibly he’s not primarily seeking a particularized, family-resemblance kind of pattern in the sense that I do. Anyway, his criteria include: interaction and mutual enhancement of a tetrad's four points; a kind of tetrahedron-like philosophical stability of such tetrad; and productive results following soon upon application in practice. He linked to the version of this post at The Tetrast. He adds that, at his current blog(s), “tetrads have been updated to ‘four-way thunks,’ but I do have a Lulu book which contains the original doctorate thesis.” - posted by The Tetrast @ 9:15 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Hyatt Carter's meta-fours
Hyatt Carter's meta-fours -- pun intended. At that link there was a discussion (with links) about various fours which he has encountered in reading, but he has revamped his Website to focus on his new book Thinking Is the Best Way to Travel, and will restore the "Meta-Fours" essay with additions eventually. The cheerful Carter's interests include religion, spirituality, process philosophy (especially Alfred North Whitehead and Charles Hartshorne), Joyce's fiction, and other things. There's no comparison for me to make to my fours, since Carter is not so much working on a particular four-fold pattern of ideas (as far as I know), as exploring four-fold patterns of ideas in general. - posted by The Tetrast @ 9:12 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

David Spooner - threes & fours in insect metamorphosis & the human spirit
David Spooner holds that three-stage and four-stage processes of insect metamorphosis find deep echoes in human experience and imagination. Insect metamorphosis --
(A) the earlier-evolved triadic and gradual hemimetabolic metamorphosis (ovum, nymph, completed imago, e.g. the grasshopper) and
(B) the tetradic and abrupt holometabolic metamorphosis, (1) from ovum, egg, (2) to larva, grub, caterpillar, (3) then pupa or chrysalis, and (4) finally the imago - butterfly, bee, moth, wasp or beetle, --
are processes which Spooner seeks in his books to show

are more crucial to natural selection than evolutionary theorists have accepted. While not disputing Darwin, I work from A.R. Wallace`s insights. If we start from the greatest works of human consciousness (Beethoven, Mozart, Melville, Shakespeare), then humanity owes as much obliquely to the insect as the ape. -- Spooner on the homepage of his Website at the Authors' Guild.

At that Website, on a discussion page, I asked Spooner a question about the Helmholz-Poincaré picture of the creative process (which I find well-correlated with my tetrastic structure): "How would you relate (or not relate) the four-stage process of egg, larva, pupa, imago to the four-stage creative process of saturation, incubation, illumination, and verification as discussed by Murray Gell-Mann on pp. 264-265 of _The Quark and the Jaguar_? The passage can be viewed at Google Books as linked via a Google search on: each-found-a-contradiction Gell-Mann" -- and Spooner responded:

Response from David Spooner to Ben UdeIΙ:
`chitinous` (so to say) 4s are zooming about the universe. They determine the structure of much of reality, thought and experimental processes. You have many that are new to me, especially in regard to that latter category, and Hyatt Carter has many more (www.hyattcarter.com). The Gell-Mann endorsement of the Helmholz-Poincaré tetradic system of discovery/experimentation is a compacted version of the philological and evolutionary cluster ova-larva-pupa-imago.

However, this latter organic process has the virtue of ultimately opening out and fusing the human species, in its long-term evolution and maturation, more profoundly with the living world of nature. {as I explain in my books from the 1995 Metaphysics to the 2005 Insect-Populated}. It draws the realm of abstract thought back towards the earth, and thereby supplements the human relation to the great apes with one to the insect world in its evolution.

It will take me a while to absorb his basic ideas. - posted by The Tetrast @ 8:47 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Stephen R. Palmquist's diagrammatic four-folds
Dr. Stephen R. Palmquist's diagrammatic four-folds. Palmquist has written books on Kant and is interested in the diagrammatic representation of structures among ideas, including ideas related by twinned two-valued parameters (my lingo, not his), which is where we cross paths. He has said that a good place to start in understanding his diagrams is Chapter 5 of his book The Tree of Philosophy. - posted by The Tetrast @ 8:46 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Richard McKeon
Richard McKeon, the pluralist philosopher, developed some four-fold classifications of philosophical issues, approaches, etc. McKeon was just recently brought to my attention, so I've barely had a chance to read him, but off the top of my head I'd say that his fourfolds differ from mine. There are at least two philosophers, Walter Watson and David A. Dilworth, who have used McKeon's fourfolds (and maybe his threefolds too), and I may attempt some comments on Watson and Dilworth eventually. Anyway, below is my rendition of a table in McKeon's 17-page paper "Philosophic Semantics and Philosophic Inquiry" which is available from a former student of his at http://net-prophet.net/mckeon/mckeon.htm. There's a link at that Webpage to a photoimage of the table, which I used. I can't render the slanting lines in html, so I made do with the slash characters. The horizontal spacing is the same, but I changed the vertical spacing to single-spaced wherever I could.

MODES OF PHILOSOPHIC INQUIRY
Modes of Being      Being	Modes of Thought   That which is	Modes of Fact   Existence	Modes of Simplicity   Experience
Being and Becoming-----------	Assimilation and Exemplification-- (models)	Reality and Approximation--	Categories of Thought (Ideas and presentations)
Phenomena and Projections----	Discrimination and Postulation---- (theses)	Process and Frame----------	Categories of Language and action (Symbols and rules)
Elements and Composites------	Construction and Decomposition---- (constituents)	Object and Immpression-----	Categories of Things (Cognition and Emotion)
Actuality and Potentiality---	Resolution and Question----------- (causes)	Substance and Accident-----	Categories of Terms

SCHEMA OF PHILOSOPHICAL SEMANTICS
Principles	Methods	Interpretations	Selections
Holoscopic	Universal	Ontic
Comprehensive————————	————Dialectical———————————————	———Ontological————————————————————	Hierarchy (transcendental)
Reflexive—————\/—————	————Operational———————\/——————	———Entitative—————————————————————	Matter (reductive)
Meroscopic       /\	Particular            /\	Phenomenal
Simple———————/——\————	————Logistic—————————/  \—————	———Existentialist—————————————————	Types (perspective)
Actional————/    \———	————Problematic———————————————	———Essentialist———————————————————	Kinds (functional)

BASIC DIVISIONS OF PHILOSOPHY
Theoretic	Physics	Philosophy	Logic
Practical	Ethics	Poetry	Rhetoric
Poetic	Logic	History	Grammar
BASIC PROBLEMS
Whole	Universal	Reality	One
Part	Particular	Process	Many

- posted by The Tetrast @ 8:43 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Pythagoras's Tetractys
Pythagoras’s Tetractys — its numerological imagery has seemed little correlated to my fours and, in some ways, quite discorrelated, except perhaps in certain of its outlines such as turn up in an account of traditional four-symbolism by Penelope Merritt). - posted by The Tetrast @ 8:39 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Mikhail Epstein on tetrads in Soviet ideological language
Mikhail Epstein (often spelt "Epshtein" in library catalogs) in his “Relativistic Patterns in Totalitarian Thinking: an Inquiry into the Language of Soviet Ideology” discusses the Soviet ideolinguistic use of tetradic (I would say “tetrachotomical”) structures arising from pairs of two-value parameters. (In a few places, Epstein refers to it as the Soviet ideologists’ “tetralectics,” apparently only in order to suggest a four-pole version of “dialectics” and not in reference or allusion to any of the other particular brands of “Tetralectics” which I’ve discussed at this blog.) Epstein offers a fascinating account of the malign use of conceptual tetrachotomies — not particularly strong tetrachotomies philosophically, in my view, but there they are, they do their jobs. Basically, two opposite actions by an ally receive laudatory labels from the ideologist, and the same two opposite actions, when carried out by an enemy, receive denunciatory labels from the ideologist. For a simple example, the Soviet ideologist might systematically call Soviet boldness “brave” and Soviet caution “prudent,” and just as systematically call U.S. boldness “rash” and U.S. caution “cowardly.” (I discuss these particular concepts in “Tetrachotomies of future-oriented virtues and vices.”) One could imagine that the pattern could be found in political rhetoric more generally, though political rhetoric is not always shaped in full awareness of such inconsistency or hypocrisy as it harbors. When, in respect of the same behavior, one applies more favorable standards to one’s allies and less favorable standards to one’s adversaries, one may fall into such patterns. There is something of that aspect of the Soviet ideologist in each of us. Mikhail Epstein analyzes the malign Soviet extreme of weaponization of language and its prolongation into an insistent quadru-venomous stream of propaganda. - posted by The Tetrast @ 8:15 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

Penelope Merritt's account of traditional four-symbolism
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.

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 next post, "Helmholtz, Poincaré, & the creative process." - posted by The Tetrast @ 8:06 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.

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. - posted by The Tetrast @ 4:48 PM 0 sets of questions or comments [top of post] [top of page] Copyright © BenjaminðA.ðUde11.