The Tetrast
Sketcher of various interrelated fourfolds.

Compare to Aristotle, Aquinas, & Peirce.

September 25, 2006.
Recentest significant edit: September 5, 2013: I am beginning a process of revising this post in order to make it more presentable, less like my notes and jottings. Update November 6, 2016: Obviously I didn't follow through, but today I change at least a few things.

Update January 16, 2017: My discussion of agent, patient, act, borne needs MUCH revision. Unfortunately I've written no detailed discussion of the topic elsewhere on my blogs. I touch on them in spots in Methods of active learning by basic faculties; also in Contrarian, partisan, insularist, conformist; and in Telos, entelechy, Aristotle's Four Causes, pleasure, & happiness.

Here are tables

for comparison of my little systems to systems of Aristotle, Aquinas, and C.S. Peirce, in an easy way to look at.

The Four Causes & Related Principles

Aristotle (Physics II 3 and Metaphysics V 2)
externalefficient cause
 end, final cause
matter, material cause
form, formal cause
middle, means
end, telos
check, entelechy

Tetrastic (elaborated)
Traditional four causes in all capitals
1. Agent.2. Bearer.3. Act.4. Borneness.
Existence (consistently extreme version).Sustainer.Consumer, exhauster.Assimilator / suppressor.
Stages as turns of becoming.Beginning.Middle, means.END, telos.Check, entelechy, standing finished.
Stages.Development, process.Culmination.Settlement, establishment.
Four human causal principles.Ability, dealing.Affectivity, feeling of good or bad, emotion.Cognition.
Static or quasi-static causes.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.Elements, media & materials, domain (universe of discourse or total population & its parameters).Kinds, varieties; species. (Neither universal nor individual.)Individuals (connected, ordered, etc.) in a larger world.
Correlated concrete phenomena.Matter.Life.Mind.
Kinetic / mechanical correlatives.Rest mass, rest energy, internal work & power.(Non-rest) energy, work, power.Internal, balanced momenta (potential & kinetic), impulses, forces.
Light-cone zones of communication and cause & effect.Inside the future light cone
(unambiguously later).
Past light cone's surface
(just now, barely now).
Inside the past light cone
(unambiguously earlier).
Mathematical time perspective.Probabilities.Information (newsiness).Bases, facts, data (for logical reasoning).
General processes.Stochastic processes.Info / communic. processes.Inference processes.
Basic subsistence.Cooking or otherwise preparing the food.Presenting & consuming the food.Digesting & reflecting on the food.
Bahavioral phases / foci.Processing, adaptation, production.Consumption, expression, conversion.Rumination, assimilation, learnings.
Inter-behaviors.Cooperation & tolerance.Community, distinctive unitings.Checks & balances.
Creative process (Helmholtz & Poincaré).Incubation.Illumination (e.g., as in "eureka!").Verification.
Tetradic semiosic stages.Representation.Interpretation.Establishment.

The Categories


Peirce (Frstness, Secondness, Thirdness)
quality (of feeling)
reaction, resistance
1. diversity/sameness
(e.g., double-of, sum-of
antiderivative-of, etc.)
2. whetherhood, modality
(e.g., y/n, maybe, iff, probably, etc.)
3. attribute, accident,
modification, property, etc.
4. substance
(e.g., this man, this horse)
Note: Peirce seemed a bit reluctant to use the word “accident” among the categories, perhaps because of the word’s double sense of coincidence (a mode of attribution) and descriptive attribute (see the Catholic Encyclopedia entry on “accident”). Why not an alternative like “property” or “attribute”? Maybe because: “Property” originally meant something like “idiosyncrasy” (not in the sense of “quirk,” but simply of “unique to something but non-essential to it”); and, through Aquinas and others, "attribute” acquired a sense of “essential attribute.” Either way, too much narrowing of the attributional mode. Also, an attribute could be a thing (e.g., a hand), not just a property or quality. I long used “accident” in accordance with Peirce. I’m not quite happy with “attribute.”

Elements of Logical Psychology

Two notes: 1. In some translations of Aristotle, "inference" means deductive inference. Meanwhile, Peirce defines reasoning as conscious, deliberate inference, deductive or otherwise. In the Tetrastic table I use Peirce's sense of "inference." 2. Apprehension here means that of which the intellectual version is conception (or, in common parlance, concept).
Aquinas, rooted in Aristotle

1. concept

2. judgment

3. reasoning

1. apprehension

2. judgment

3. inference
1. apprehension (simple / compound), association,
plotting, tracking, graphing
2. judgment (simple / compound),
apportioning, comparing, weighing, measure, counting
3. evaluation (to an apprehension),
classification, differentiation, calculation
4. inference (to a judgment),
identification / designation, ordering, reasoning
I keep changing my mind about this.

Elements of Logical Process (Semiosis)


Arrow from object to sign to interpretant.

Modes of Inference



(doesn't automatically preserve truth;
doesn't automatically preserve falsity)

(strictly ampliative) induction
(doesn't automatically preserve truth;
automatically preserves falsity)

‘forward-only’ deduction
(automatically preserves truth;
doesn't automatically preserve falsity)

reversible deduction
(automatically preserves truth;
automatically preserves falsity)
Note: In an old logic textbook you may find "strict deduction" defined as such that its premisses deductively imply, but are not deductively implied by, its conclusions. This was an application of the word "strict" as in "strict superset," "strict subset," etc. However, nowadays "strict deduction" is often taken to refer to deduction where the conclusions are relevant to the premisses in formally defined ways in a relevance logic. Hence the phrase "forward-only deduction" to refer to deduction whose premisses deductively imply, but are not deductively implied by, its conclusions.

Requisites for Beauty

order &
due magnitude;
symmetry, &
wholeness or perfection,
integritas sive perfectio
due proportion or harmony,
debita proportio sive consonantia
naturalness, due force,
due directed magnitude
harmony, due proportion, due rhythm, consistency
wholeness, structural integrity, stability

Elemental Modes of the Psyche


(a) cognitive faculties
(b) feeling of
pleasure or displeasure
(c) faculty of desire
(correlated with (a) understanding,
(b) judgment,
(c) reason)
sense of
Sense of resistance includes
will, pleasure, pain.
will & conation
dealing, handling

A little more on elemental modes of the psyche

Tetrastic 4x4 of time-orientational modes of the psyche
Time Downward arrow.Will, ConationDealing, HandlingAffectivityCognition
For almost now:Trying (out)/(for)Testing, devisingDesireFancy, "impression"
For laterSeekingPreparing, approach.Hope, ConfidenceExpectation, anticipation
For barely nowTaking, pickingAchievingPleasure, Satisf.Noticing, discernment
For earlierAdhering, habitMaintaining, skillAttachmentMemory
Some have classed desire (a feeling) outside of the feelings and instead as a kind of will or conation. Yet, the similarity between will/conation and the feeling of desire is part of a pattern. The 4x4 table above is a systematic fairground of similarities and dissimilarities. Consider for instance the column under “Will, Conation” vis-à-vis the column under “Affectivity.” Desire does resemble trying. Yet likewise, for instance, (affective) attachment resembles (volitional) adherence. Hence, to reclassify desire as a mode of will invites a general reclassification of affectivity as volition. But perhaps trying is the archtypical mode of will?—such that a resemblance to trying is a sign of being a mode of will? Yet even if one grants that there is something to that idea, why assume that the scenario depicted in the idea is unique? One also might regard memory, recognition, and knowledge as archtypical cognition. Maintenance and skill resemble them. In fact the English words “can,” “ken,” and “know” are cognate. Are maintenance and skill really cognition, while testing, preparation, and achievement are not cognition? No, and instead, it makes more sense and is more interesting to trace out the larger emerging pattern. In considering whether to conflate will/conation with desire, it’s good to consider the broader picture and to make sure of having done adequate inventory.

From the inner mind to the outer limits

Light cone times: Almost now (feasibles & optima). Later (probabilities). Barely Now (news, information). Earlier (bases, facts, data, for logical conclusions). The times “almost now,” “later,” “barely now, just now,” and “earlier”, mentioned in the above tables, point to a generalization from the ubiquitous physical case of relativity’s light cone. Now, we say, roughly 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 far oftener than we do so.

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 (as 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. 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 or pickings.

A not insignificant further dimension of division of the psyche into elemental modes

I would also divide the psyche’s elementary modes along another dimension into those classes which in the case of cognition are (1) imagination, (2) conception & intellect, (3) the senses & cultivable ‘intuition’/‘instinct,’ and (4) commonsense perception.

* * *

Promised discussion of beginnings, middles, ends, and checks/entelechies:

tryings, leadings,
mediations, means,
steadied going(s).
unsteadied going(s) .

In a Nutshell

Now, when we try, seek, pick or take, or adhere to something, sometimes it’s so direct that we don’t think of means as being saliently involved. But often enough there are intermediate stages through which we go, and intermediative things.

• If the decision-making, the beginning, is regarded as a kind of main cause, those middles appear, relative to the situation of interest, as intermediate causes, helpers, facilitating causes. Of course they’re also intermediate effects. In any case we regard them as means.

• If the end is achieved, effected, sometimes it’s so directly obvious that we don’t think of any checks as being involved. But often enough there are collateral and at least a bit later things or events to which we look. If the end is regarded as a kind of main effect, those things or events “on the side” or further in time appear, relative to the situation of interest, as side effects, after-effects, evidentiary effects, checks.

Just as in advance one may have desired and hoped for the end, likewise one may have imagined and anticipated the collateral effects, the evidences, e.g., wakes, trails, tracks, shells, etc. One then also will have hoped for them, but only because one hopes for them as signs of the end’s having been achieved. They aren’t means to the end, they’re beyond and in addition to the end in a rather similar sense as the means are beyond and in addition to the beginning, the decision-making. And, just like an end, a check can be prospective, not yet accomplished.Update July 14, 2013: The check is not only of whether the means succeeded in achieving the end, but also of whether the end was good as it seemed in advance. In advance, one looks to the prospective "check," the prospective entelechy, to consider such issues as unintended consequences and conflicts among values. See my recent post Telos, entelechy, pleasure, happiness. End of update.

We often think of an agent cause as compelling. That’s an affinity, not a rigid rule. One could also stand physically willing but not insistent for motion, and thus one will amount to a contributing agent cause of one’s motion if one does move. But let’s focus on the typical affinities among ideas. By pushing oneself, in the sense of pushing against the hardly movable ground for example, one compels one’s own motion, with a kind of physical insistence. On the other hand, we regard means as enabling rather than compelling. (The particular means may be necessary or, thanks to alternatives, unnecessary.) Now, let’s use this pattern of affinities in order to flesh out the conception of the “check,” the establishment or settlement or confirmation, as a cause. Given a goal, a prospective end or satisfaction, there is a necessity — not a compulsion but a kind of needfulness — for a means. Now, what conception stands to needfulness, as enablement stands to compulsion? A kind of reasonableness. Given that it will be established or practically knowable (at least by oneself if not by others, or even vice versa) and be a basis (for knowledge or whatever), one has reason to do something, that is, it’s reasonable to do it, in the sense that it will be real or solid or legitimate or in evidence. Why do it if it’s such that it might as well be unknown by anybody ever? Of course, sometimes one does something because it will be off the record or hidden or transitory or somehow not for real (and others will not know of it). But that is weak counter-example because the same kind of weak counter-example has always occurred in the case of goals: sometimes one does something because others will not care about it or even because it will block their aims. One note: just as an end or goal is not only about pleasure but first of all about the good — otherwise we might as well just attach electrodes to our brains' pleasure centers — likewise the check is not only about knowing and wakefulness, but first of all about the real, the legitimate, etc. To the problematics of goals, pleasures, pains, indifference, and of people acting against their own interests and ends, I come bearing reminders of the problematics of checks, knowledge, ignorance, deception, and of people acting as their own unwitting accomplices.

As a middle, a continuing, is like a staying-begun, so a check is like a staying-ended. There’s some nice simplicity and symmetry about these ideas, even as they incorporate asymmetry. We live in time-asymmetric world in which the check, the hold, the staying-ended (and, so to speak, its content) which follows upon a thing’s ending pertains to that thing more specifically, more informatively, than does a hold or holding-off which precedes the thing’s beginning. This and other asymmetries seem to have their part in the symmetries that abound.

Of course, just as a means can secondarily be an end and vice versa, so a check can secondarily be a means and vice versa, and likewise so can a check secondarily be a beginning, a decision point, etc.


Principles of the 4 causes. My conception of entelechy is somewhat nonstandard, based on ideas of stability and confirmation. I don’t seek mainly to clarify Aristotle. Unlike Aristotle and tradition, I don’t seek to stretch act and end to encompass form and entelechy. Such encompassment conflates the driven with the borne, the vibrant (or vigorous) with the firm, etc., and ramifies into conflating the driver (agent) with the bearer (patient). Systematic deeper equivalences aren’t found without recognizing the systematic distinctions nearer the surface.
  A traditional view of entelechy appears in the entry for “entelechy” in the great Century Dictionary. C.S. Peirce may have written the entry and probably at least reviewed it, since it is among the words at the relevant database at the Peirce Edition Project’s branch at the Université du Québec à Montréal (UQÀM) (Website at )
From the Century Dictionary, Vol. III, Page 1946, Entastic to Enter (DjVu):

entelechy (en-tel´e-ki), n. [ L. entelechia, Gr. ’εντελέχεια, actuality, ’εν τέλει ’έχειν, be complete (cf. ’εντελής, complete, full): ’εν, in; dat. of τέλος, end, completion; ’έχειν, have, hold, intr. be.] Realization: opposed to power or potentiality, and nearly the same as energy or act (actuality). The only difference is that entelechy implies a more perfect realization. The idea of entelechy is connected with that of form, the idea of power with that of matter. Thus, iron is potentially in its ore, which to be made iron must be worked; when this is done, the iron exists in entelechy. The development from being in posse or in germ to entelechy takes place, according to Aristotle, by means of a change, the imperfect action or energy, of which the perfected result is the entelechy. Entelechy is, however, either first or second. First entelechy is being in working order; second entelechy is being in action. The soul is said to be the first entelechy of the body, which seems to imply that it grows out of the body as its germ; but the idea more insisted upon is that man without the soul would be but a body, while the soul, once developed, is not lost when the man sleeps. Cudworth terms his plastic nature (which see, under nature) a first entelechy, and Leibnitz calls a monad an entelechy.

     To express this aspect of the mental functions, Aristotle makes use of the word entelechy. The word is one which explains itself. Frequently, it is true, Aristotle fails to draw any strict line of demarcation between entelechy and energy; but in theory, at least, the two are definitely separated from each other, and ’ενέργεια represents merely a stage on the path toward ’εντελέχεια. Entelechy in short is the realization which contains the end of a process: the complete expression of some function—the perfection of some phenomenon, the last stage in that process from potentiality to reality which we have already noticed. Soul then is not only the realization of the body; it is its perfect realization or full development. E. Wallace, Aristotle's Psychology, p. xlii.

Joe Sachs in the Energeia and Entelecheia section of his article “Aristotle (384-322 BCE): Motion and its Place in Nature” in the Internet Encyclopedia of Philosophy is dissatisfied with the traditional emphases in interpretation of what Aristotle meant by entelécheia. Sachs writes:
Entelecheia means continuing in a state of completeness, or being at an end which is of such a nature that it is only possible to be there by means of the continual expenditure of the effort required to stay there. Just as energeia extends to entelecheia because it is the activity which makes a thing what it is, entelecheia extends to energeia because it is the end or perfection which has being only in, through, and during activity.
Yet, the activity and effort turn out sometimes, in Sachs’s descriptions, to be a stable static balance of forces, for instance as with an attracted stone at rest against the attractive earth under water. We normally would not say that such a stone is active or that such a stone’s position or behavior is a continual expenditure of effort. Instead we would note the effort that stands invested and the potential energy, potential activity, thereby involved. All the same — aside from Sachs’s initially making it sound as though a stable static equilibrium couldn’t be an entelechy — his conception of entelechy is closer than the traditional one is to my deliberately altered conception of it, given his emphasis on the staying complete, not to mention his depicting it in terms of places and embeddedness in the world. And I also don’t regard all entelechy as necessarily static. Maybe my version isn’t as nonstandard as I thought!

End versus check: culmination versus standing finished

By ‘end,’ I mean a culmination, an end in the sense of télos, actualization, fulfillment. The check, on the other hand, is a kind of settlement, solidification, and holding in completeness — entelechy (see sidebar) —, be it ontic or epistemic.

The check or entelechy amounts to a kind of confirmation of things which might have been illusory or transitory. In a broader sense than is usual for the word “entelechy,” one can consider wakes, tracks, trails, shells, husks, etc., as entelechies, or as outcroppings of an entelechy of the situation.

However, the traditional emphasis, in the conception expressed by the term “entelechy,” has been on the entelechy as a having COMPLETE (or a holding or being COMPLETE), fully and not just partly actualized — rather than on entelechy as a HAVING (or HOLDING or BEING) complete - a standing finished - in a settled completion that can stand up to trials. It’s been enTELechy instead of entelECHY. That traditional emphasis on fullness of actualization (rather than on solidity, establishment), going back to the term’s orginator Aristotle, has permillennially missed something of the confirmational aspect, I think.

Hard it is to become good, harder still to stay good — that sort of thought seems to have been at the root of it, so it’s good to remember that, in a practical sense, what’s involved in staying good is not only that one fully has the good, but also that one’s good is firm and can stand up to reality’s trials and tests, whether they come thick and fast, or otherwise. It’s a good which is tried and true.

Moreover, it is simpler to regard entelechy in that way, as being a distinct principle, something further than a being-fully-completed, since one already regards the middle as being something further than a being-fully-begun. The analogy is exact down through its foundations, as will be seen in a moment. One must be regardful of the systematic conceptual structure of stayings and becomings which undergird these ideas.

Which brings us to the following:

Occam Doesn’t Raze Exactly One Corner of the Square of Opposition

One might object that “beginning, middle, end” seems so nice and complete; why add something more? Beginning, middle, end, like start, continue, stop.

Logically, however, it doesn’t seem so nice and complete at all. Instead:

Beginning, like starting at time t
X occurs? no (for some period) till t, yes (for some period) since t.
Middle, like continuing at time t
X occurs? yes (for some period) till t, yes (for some period) since t.
End, like stopping at time t
X occurs? yes(for some period) till t, no (for some period) since t.
Check, like refraining, holding at time t
X occurs? no (for some period) till t, no (for some period) since t.

Now that’s logically nice, complete, and hardly escapable, exhausting the combinatorial possibilities of the two relevant parameters.

The entelechy is traditionally associated with the form. Now, a structure is an equilibrium (be the equilibrium static, harmonic, or whatever else) among forces with some stability. Therefore the structure of a thing - even with all the mobility, flexibility, etc., which the structure may have - is a settlement or establishment of the thing, and is the kind of form (as opposed to form as aspect, figure, quality, etc.) most suited to be regarded as the entelechy. While the good has the rational character of an end, a culmination, on the other hand the true, the sound, the legitimate, have the rational character of a check, an entelechy.

It is also possible to make an entelechy the end, goal, culmination of one's action, as when one acts in order to prove something - maybe in inquiry, but also, for instance, about oneself in daily life, acting to prove oneself as being legitimately this or that, deserving of some sort of recognition or honor or accorded status, or to prove that some people do or don't deserve some status. (How many times, in practical matters, have you heard one person ask another, "what are you trying to prove?")
One can make a goal of any of the four causes, and there are 'arenas' of contention for them -
For instance one makes a goal of a beginning, a deciding, a leadership, when one vies or contends in group or mass decision-making for a decision or for a way of decision-making (politics, military battle, etc., deciding who or what gets to decide, etc.).
If it's a vying to have or be means in general, then it's for wealth, wherewithal, (e.g., business, commerce, finance, etc.) .
If it's a vying to have or be ends in general, a vying to be valued, then it's for glamour, glory, wattage, splendor (e.g., fashion, sports, popularity, notoriety, opulence, "hipness," etc.).
If it's a vying to have or be entelechies in general, a vying to be legitimized, then it's for honor, standing, etc. (e.g., case-building, discussion, debate, the formation of common opinion).

Agent, patient, act, borneness

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.
The “agent-patient” distinction was discarded long ago in fields like chemistry, yet the ideas remain useful for informal discussion. They could be more useful if they were conceived more systematically.

The agent acts on the bearer a.k.a. patient, e.g., matter, and, to the extent that the bearer suffers through to a completed change, that completed change is the act. Agent-patient-act: the ancient philosophical tradition.

(In the case of "rest" or stasis imposed by the agency, I'm not aware that Aristotle discussed "completed" stasis or the like, but suitable ideas seem to include that of a stasis culminating in some event and that of a stasis with the potential energy of the event in which it would culminate.)

Inching beyond ancient tradition.

The act is an affectedness, an acted-on-ness, of the bearer (except in the extreme case of a creation out of nothing). A bearer is affectable, but it is not always vigorously, distinctively affected; I mean that bearing and being affected aren’t to be crudely conflated, as when we think of bearing only as suffering rather than as, first of all, patience. Indeed we don’t conflate them when we think of the bearer as matter, process, etc., and of the affectedness, the act, as energy, culmination, etc. There is an equivalence between bearing and being affected, yet also distinctions between them along lines of potency vs. act, and of inside vs. outside. The perspective of inside-outside relations also arises in one’s seeing an inside as a “mini-outside.” Internal act, internal vigor, help constitute the temper, harmony, patience of a whole.

Breaking with ancient tradition.

What’s sauce for the goose is sauce for the gander. If bearer per se is to be distinguished from bearer as affected, and if bearer’s patience and endurance are to be distinguished from bearer’s affectedness (the act), then, correspondingly, agent per se is to be distinguished from agent as borne, and agency as affecting is to be distinguished from borneness, borneness manifested in the extents and ways in which agency is itself turned, opposed, balanced, stabilized, etc. However, neither Aristotle nor the Scholastics considered form first of all in terms of movements or forces balanced within a system, though this equilibrium is, if stable and basic to the system, the system’s structure (in its aspects kinetic & static) and, otherwise, a kind of state of the system. Instead Aristotle & the Scholastics emphasized more abstract and pliable conceptions of form and classed the form, along with the end, as act. So tradition passed along three principles — agent, patient, act — yet four causes — efficient, material, final, and formal.

Passion vs. Patiency and other tricky distinctions, in clarificatory arrangement. We come to a fork in the road as to the meaning of the ancient Latin verb pati, “to bear,” “suffer,” etc. — (1) “to endure, to bear up under,” and (2) “to undergo, to yield up to.” (The ancient Greek paschein had pretty much the second meaning.) A thing may to various extents both endure and yield. The first sense is primary for pati and may be associated with not only endurance but also spiritlessness, a kind of inertia; the second sense is tied to the idea of act, the driven, which, in a sense, is opposite to the patient, its patience, the enduring; the two opposed ideas are of aspects of duration, ideas, respectively, of temperate versus vigorous, and, respectively, of enduring versus briefening. As the ideas of patience and act are temporal, so the ideas of agency and, opposed to it, borneness, are spatial ideas, involving magnitudes with directionality and directional opposability. The agent is an impetus for process, development, becoming, eventuating in act. The old tradition defined ongoing change, shift, spatial or otherwise, which it called “motion,” as the state of being between potency and act. But underlying an agency is an even simpler role of mover, impeller, imparter of spatial motion which is not itself a process culminating, by its own incubative nature, in act. Spatial motion and rest (stationariness) are relative; and simple uniform motion is a changing of distance-defined relative location, which continues indefinitely if not interrupted. This is travel, not duration, and pertains most directly to an agent’s driving and impress, rather than to a patient’s enduring and incubating. (The traditional idea can be saved to a small extent: potency: a thing is at rest in its own reference frame; motion: then it gets hit and now travels or is at rest in a changed reference frame; act: finally it collides with something.)

A wrench in the works is that the word “passion” succumbed fully to the second sense of pati, the sense of “to undergo, to yield up to.” The act (or action qua act, as distinguished from action qua operation, impelling, driving) which is the acted-on-ness is, by that very stroke, the “passion” of the patient, and differs only in its perspective; the passion is the act as regarded from the receiving end, while the act is said as a deed to be of the agent, though the word “act” comes from a passive participle meaning “been made or driven.”

Anyway, this semantic choice about the word “passion,” the traditional one, obscures the more meaningful distinction outlined above between the act and the borneness, one whereby the end can be distinguished from the form at the level of causes' principles, as act and borneness.

The patient hardly exists as a patient except so long as the balance, supportedness, stability of agencies in its system — the agencies which the patient contains or has internalized — are there in some significant measure. If instead the patient yields up fully and thoroughly, it will be converted to pure act, like matter into kinetic energy. A patient may yield (pati in the second sense) fully to an agent, but basically a patient is an endurer (pati in the first sense), and a borneness is an agent’s corresponding balancement. Now, that is to make borneness sound like balanced internal agencies. Far from objectionable, that is desirable, (a) since the idea of balanced internal agencies obviously pertains to the idea of structure and therefore of the formal cause, which thereby at last has a distinct causal principle in borneness, and also (b) since nothing is wrong and something is right with agency and borneness being in some sort of equivalence, when patience and act are in some sort of equivalence. The bearer (or its patience) is in a sense internal act, internally stored, tempered act, internal vigor, in latent and patent modes, which comprises the temper and patience of a whole. For instance, rest mass (correlated to proper time, “own duration”) is equivalent to rest energy (though in order for this analogy to work in terms of the primitive terminology of “agent, bearer, acted-on, borne,” one must, among other things, consider momentum as impulse which is a suitably more “agential” idea than that of momentum per se).

The resultant tetrachotomy is a kind of square of oppositions of causes’ principles, with an axis of space along the downward diagonal, and an axis of time along the upward diagonal.
agency ~ ~ act
~ ~ ~ ~ X ~ ~ ~ ~
bearing ~ borneness

Moreover it’s worth noting that, logically, insofar as agent & patient are like “maker” and “allower/supporter,” their conceptions are subject to logical inter-transformability like their kindred conceptions necessity and possibility in simple parallel.

Why it is, that agent and patient should both of them be principles of change yet their passive-voiced versions should not, likewise unconflated, both of them be principles of change, is a question which has unfortunately gone largely unnoticed, so far as I know. It’s especially unfortunate insofar as it seems that, for the various already noted reasons, the borneness is just as valid a principle as agent, bearer, and act. Occam’s Razor isn’t blind and won’t cut here; to the contrary, if agent is the driver and act the driven, and if bearer is endurer, then borne is the endured, not the driven. The value of the simplicity of consistency should have led reasoning along this road long ago.

The agency is an initiation of change or rest (or arrest), the patience is a mediation of change or rest, the act is a culmination of change or rest, and the borneness is a settlement or resolution of change or rest. Thus those four terms reassuringly parallel the gamut of logical possibilities of change’s starting, continuing, stopping, refraining.

Note: It is not necessarily that there are always two things, agent and bearer, in various roles; one same thing may be agent and bearer; and the acted-on in question may be or become separate from the bearer in question; some of an agent’s agency may be internalized by the bearer and become stably balanced within it, in a restructuring; and so forth.

Human Versions of the Four Principles of the Four Causes

Again, agency is an initiation of change or rest. Human agency is will, volition, conation. Bearing or patiency is a mediation of change or rest. Human bearing, mediating, is ability, handling, dealing-with. Act is a culmination of change or rest. Human acted-on-ness, humanly being-affected, is affectivity. Borneness is a settlement or resolution of change or rest. Humanly being upheld, supported, is cognition. (Note: I don’t mean that cognition is something inherently frozen! Quite to the contrary.)

1. Agency ―――› will & character. ~ ~ ~ ~ 3. Acted-on-ness ―› affectivity & sensibility.
2. Bearership ―› dealing & competence. ~ 4. Borneness ―――› cognition & intelligence.

On a level where one distinguishes between will and affectivity, one should make also the same distinction between dealing (trectation, dealing-with) and cognition. It’s like the distinction between efferent (as with efferent nerves carrying signals out from the brain to the muscles) and afferent (as with afferent nerves carrying signals to the brain from sensory receptors).

Similarly, on a level where one distinguishes either (1) dealing-with from will or (2) cognition from affectivity, on that level one should make both distinctions. Between members of each pair there is a difference like that between the indirect (e.g., finesse) and the direct (e.g., force), or between that which is stabilized or steadied within a system and that which is otherwise in its involvement with the system.

Teleology as Philosophical Botany

complex dependences on
leadings, tryings,
complex dependences on
mediations, means,
steadied going(s).
complex dependences on
unsteadied going(s).
complex dependences on
We depend on checks or stages of checkedness a great deal and at least somewhat radically, anyway deeply. Our deep dependence on them is what separates us from purely instinctual animals and from vegetables, whose adjustments and adaptations in responses to conditions are pre-programmed and stop short of points beyond which we speak of design adaptations, which require evolution or intelligence and learning. We’re not quite to the point of redesigning ourselves biologically but we redesign much in our world. If a vegetable’s decoding of a signal is “disconfirmed,” then this heightens its odds of leaving the gene pool — the signal’s ‘recipient’ is in a sense the evolutionary process, which, in its trial-&-error way, is the only thing there doing anything like learning. We have brains and are sufficiently unbound to particular codes and systems of interpretation, sufficiently that we can test, check, renovate, redesign our interpretations and systems of interpretation, at least somehwat, rather than leaving that job mostly or entirely to biological evolution. And thus it is that intelligence involves verification, confirmation, inference processing rather than merely calculation, curve-fitting, information processing, and likewise it is that intelligence is not merely telic but distinctly entelechic (confirmational, etc.) and that its forms and structures do not merely instrumentally follow function but instead also record and evidence, for the intelligence itself, a function’s accomplishment, and also much more.

Multiplicities of Functions and Statuses

Agency, operation.
(Aristotelian category: ACTION.)
Capacity, caliber.
Power (force, influence), might.
Beginnings, leadings, tryings.
Manner, mode, bearingship.
(Aristotelian category: POSITION, ATTITUDE, APTNESS.)
Wealth, affluence.
Middles, mediations, means.
Acted-on-ness, passion.
(Aristotelian category: PASSION.)
Role, function.
Glory, wattage, glamour, “action.”
End(ing)s, culminations.
Condition, state, borneness.
(Aristotelian category: STATE, HAVING.)
Honor, standing, basis.
Entelechies, checks.
Yet, aren’t such evidencings and recordings a function and value? And isn’t the form then still a kind of means, following function? The answer to both questions is yes, especially from the biological viewpoint. Conversely, from the intelligential viewpoint, functions, goals, and their means can be evidentiary and can be legitimacies and bases for legitimacies. Beginning, means, end, check — each of these can work and be multifariously, in a metaboly and evolution of hows and whys. In the elementary case, the evidence of a goal’s accomplishment is not a means to that goal, nor is it that goal itself. It is also a means, an end, etc., in merely the same sense that a means itself can be a secondary end and vice versa. If one pays attention to the explanatory frame, and does not play fast and loose with shifts of reference, then it becomes clear that the entelechy, the settledness, is an original relationship not understandable merely as beginning, means, or end, and can be regarded as a kind of transformation of any of them only in such sense as the sense in which they can be regarded as transformations of one another.

Another discussion: "Mining Aristotle's Four Causes for order & balance."

* * *

Classifications of Research

Caveat: Birger Hjørland has written: “There is not today (2005), to my knowledge, any organized research program about the classification of the sciences in any discipline or in any country. As Miksa (1998) writes, the interest for this question largely died in the beginning of the 20th century.”
C.S. Peirce's classification of research
This is based mostly on his 1903 classification of the sciences in CP1.180-202. At its start in CP1.180, Peirce says: "This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all possible sciences, nor with so many branches of knowledge, but with sciences in their present condition, as so many businesses of groups of living men. It borrows its idea from Comte's classification; namely, the idea that one science depends upon another for fundamental principles, but does not furnish such principles to that other. It turns out that in most cases the divisions are trichotomic; the First of the three members relating to universal elements or laws, the Second arranging classes of forms and seeking to bring them under universal laws, the Third going into the utmost detail, describing individual phenomena and endeavoring to explain them. But not all the divisions are of this character."

Some online Peirce classifications of the sciences:
CP1.180-202 (1903)
CP1.180-202 (1903) & 1.203-283 (1902)
MS L75 (1902)
"Development of Peirce's classification of sciences - three stages: 1889, 1898, 1903" (pdf) Tommi Vehkavaara (2003)
"The outline of Peirce's classification of sciences (1902-1911)" pdf) Tommi Vehkavaara (2001)

Vehkavaara in "Development of Peirce's classification of sciences - three stages: 1889, 1898, 1903" (pdf) (2003) points out that Peirce's first published such classification may be an 1889 version found in the Century Dictionary under "Science" definition c., p. 5397. Now, "Science" is among the words in the database at the Peirce Edition Project on Peirce's contributions to the Century Dictionary at UQÀM (Université du Québec à Montréal). If Peirce indeed wrote the Century Dictionary's definition of "Science," then it's significant that maths there are divided into "pure" and "applied," and that the latter consist of (1) "mathematical philosophy" (including probability theory, which Peirce omits from later classifications), (2) "mathematical physics," and (3) "mathematical psychics" (including economics).


One sees the spirit of Peirce's nomological - classificatory - descriptive trichotomy in much of his classification. He strongly seems to be describing it in the above-quoted remark at the start of his 1903 Syllabus classification. However he uses the terms "nomological," "classificatory," and "descriptive" as labels for divisions in only the special (a.k.a. idioscopic) sciences. Possibly, for instance, Peirce did not outright call mathematics nomological because the word (like "nomothetic") refers to law-formulative tendencies in only the special sciences. The Century Dictionary does not so limit the relevant sense, but the somewhat later Oxford English Dictionary on the relevant sense of "nomological" says: "Relating to or denoting certain principles, such as laws of nature, that are neither logically necessary nor theoretically explicable, but are simply taken as true."


In CP1.180 at the start of his 1903 classification, Peirce says (see quote above) that most of his classifications of sciences (which include mathematics by his terminology) turn out to be "trichotomic," each trichotomy with its "First," its "Second," and its "Third." By such language and capitalizations Peirce usually implies correlations to his categories Photobucket. Peirce's categories: 1stness, quality (reference to a ground): ground; 2ndness, relation, reaction, resistance (reference to a correlate): [1st] relate, [2nd] correlate; 3rdness, representation (reference to an interpretant): [1st] sign, [2nd] semiotic object, [3rd] interpretant. firstness (quality of feeling), secondness (reaction, resistance), & thirdness (representation) (tintings mine). On the other hand, if Peirce had felt sure of the correlations in the case of his science classifications, he would not have been shy about more plainly outlining them in some article. My tintings of his science classifications further below are in order to bring into visual relief Peirce's trichotomical science-classificational pattern of scientific aims at (1) universal elements or laws, (2) classes, (3) descriptions and also the possible correlations to 1stness, 2ndness, 3rdness, respectively.

Now, arguably the explicit nomological - classificatory - descriptive subdivisions in the special sciences (a.k.a. idioscopy) match pretty well his account of his typical classificational trichotomy, and echo the big division into math - philosophy - special sciences and also the bigger division into discovery science - review science (a.k.a. synthetic philosophy) - practical science. The tintings of Peirce's divisions there and elsewhere are based on my reading of Peirce & my general sense about it. There are quandaries. For instance, the continuous & the singulars (things which can be at only one place per time) in their concrete multiplicity are classed in some cases alike as the business of descriptive (3 or C or iii, etc.) sections, though continuity is a 'third' and the singular is a 'second.'
Tetrastic classification of research
This is displayed (further down) in that which is traditionally called the order of being, the order of that which is more basic ontologically and, in this discussion, the order of research fields about things (laws, entities, etc.) by appeal to which we explain things. The reverse order is traditionally called the order of knowledge, the order starting from the best known and most familiar and, in this discussion, is the order of research fields about things by appeal to which we establish, confirm, corroborate things. The order of being has been favored for orderings within the special sciences. The order of knowledge has been favored for orderings within mathematics. The orders are compatible at least to the extent that they're but systematic transformations of one another with correspondingly related criteria. (A combinatorial feeling suggests that there may be two other significant orders, too.)

All the fields mentioned, including "inverse optimization theory," are actual disciplines, though inverse optimization theory is especially young, perhaps 11 or 12 years old, as a discipline. The divisions are all tetrachotomical, though if I went into the level of subclassification which Peirce does, I would make quite non-tetrachotomical classifications as well. One expects such a logical pattern at some point to yield diminishing returns and eventually to become counterproductive. The first of the four members relates to universal balancements, laws, rules, the universal which is not itself a universe but instead applies beyond the given instance. The second relates to totalities, completive divisions, and gamuts of elements and of combinations. The third relates to assortings by distinctive accordances. The fourth relates to unitary items monadic and in polyads (in a larger population or universe) and their unique pairings and orderings, partial orderings, etc.

Now, in order to put the special sciences collectively first in order of knowledge before more abstract studies which they come to apply, one will need to take "knowledge" in a sense including that of "familiarity" and this is an especially disputable point; but there are patterns clear enough to leave a considerable residuum after any such disputation.

The systematic inter-transformability of orderings would mean that one can pursue essentially the same classification questions irregardlessly of variations of views about what's more basic, the order of knowledge or the order of being?, and even irregardlessly of variations of views about the ontological status of mathematical objects, laws, etc. You may wish to call the order of being "the order of abstractness" or something like that; but whatever you call it, we'll be able to agree that you mean the opposite of the order of knowledge/familiarity.

A little more detail on how the order of knowledge reverses the order of being in the special sciences.
We establish (and verify, (dis)confirm, etc.) evaluations and interpretations. We evaluate and interpret measurements and other signs and representations. We measure and form representations of things objectified by location, connection, etc.
1. Of course, in order to verify anything in the concrete world, one needs to know about (and be a part of) concrete people doing that. That is human and social knowledge.
2. In order to evaluate, interpret, things in the concrete world, as distinctive or redundant and as, for instance, making a possibly dangerous difference to the experimenter, one needs to know about (and be a part of) life and information; life is sophisticated information processes made flesh, and is unique in its capacity to depend on differences which make hardly any difference on a strictly material level.
3. In order to measure things in the concrete world, one needs to know about (and be part of) matter and its interactions.
4. In order to locate things and identify connections in the concrete world, one needs to know about (and be a part of) motion, forces, space, time, etc. (But again, all these things need measurement, evaluation, and verification, and, remember, we’re talking order of knowledge here).
Special relativity, concerned with inertia, momentum, etc., is considered very general and basic and is based on ideas about uniform motion. Yet inertial forces do not appear under circumstances of strictly uniform motion and there would be no occasion to form a conception of inertia.
So it can be seen that in a general way the order of being and the order of knowledge are each other's reverse. There isn t a compelling need to fix upon one as being more basic; the compelling need is to specify the senses in which one means words like “foundational” and “basic.”

Tetrastic categorial correlations:
CategoryResearch focus
(more info further down)
1. Correspondences/variancesUniversalities
2. Attributional modesTotalities, elements, apportionments
3. Attributes, properties, etc.Kinds, assortings
4. SubstantiaeUnitary things, orderings, hierarchies

So, how to reconcile?: Peirce's scientific approaches trichotomy of
(1st) Universal elements or laws, (2nd) Classes, (3rd) Descriptions
with his 1stness-2ndness-3rdness-based trichotomy of
(1st) Chance, (2nd) Law, (3rd) Habit-taking,
which itself has to be reconciled with his 1stness-2ndness-3rdness-based trichotomy of
(1st) Possibility, (2nd) Actuality, (3rd) [Conditional] Necessity.
Peirce noted a movement of fields from description, into classification, and finally into dealing with universal elements or laws. Said movement reflects the 1-3-2 movement from
(1st) chance through (3rd) habit-taking to (2nd) law
-- with chance and law as habit-taking's two already encountered limits. Its reverse
(2nd) law, (3rd) habit-taking, (1st) chance,
(starting from the goal which is law) seems the ordering principle for his classification of the sciences. However, such classifications as
(A) Phenomenology, (B) Normative science, & (C) Metaphysics,
seem, as those fields study
(A) appearances, (B) norms, & (C) commonly regardable special or almost-special cases,
to follow a 1-3-2 possibility - necessity - actuality order or a 1-2-3 chance - laws - habit-taking order better than a 2-3-1 order, while simultaneously adhering to the science trichotomy of (1st) universal elements or laws, (2nd) classes, (3rd) descriptions. Peirce seems to keep the door open between his science trichotomy and others through the idea of appearance and chance as universal elements or laws, and some idea of nature's laws as somewhat arbitrary, even a form of chance, the sense which "nomological" included or came to include.

Last exit to Peircean tri-categorialism (in my view). Distinctions such as those among subject matter, method, and objective and between evolution and involution might offer a solution. Gary Richmond discusses the idea of various orderings or "vectors" in "Trikonic Analysis-synthesis and Critical Common Sense on the Web" (2006) at Richmond, who teaches communications, is alert like other Peircean philosophers to apparent conflicts in the application of Peirce's categories but seems almost unique in actively seeking to do something systematic, within a decidedly Peircean framework, about such conflicts. His orderings or vectors build on some ideas of Peirce's own, and would, even without the spur toward resolving the apparent conflicts, address the need for a systematic Peircean trichotomization (or hexachotomization) of traditional ideas like those of the order of being and the order of knowledge.


Peirce's basic error, in my view, in his typical research-classificational trichotomy ((1) universal elements or laws - (2) classes - (3) descriptions) is his conflation of two disparate, essentially mutually inverse approaches into the "classificatory" - (A) that which analyzes into basic constituents from a complete gamut or totality of alternatives, and explores combinations of constituents (as in the case of chemical elements & substances) and their properties which often differ from those of their constituents; and (B) that which differentiates and, finding or putting like with like, assorts (as in the case of biological parts and wholes of organisms, and species, genera, etc.) into increasingly broad kinds; -- the two approaches working their mazes, so to speak, from opposite ends. Of course these are simplifications as regards chemistry and biology, but true enough in their rough way.

Research foci: universalitative, completive, assortative, unicitative. The Completive-vs.-Assortative difference comes into nontrivial relief between various fields such as matter science and biology (though of course every field has its shares of both these approaches). Instead of Peirce's trichotomy of (1) universal elements or laws - (2) classes - (3) descriptions, I find in my system that there are focuses on: 1. Universalities; 2. Totalities, full complements, exhaustive divisions; 3. Species, genera, assortings; 4. Unitary things and unique orderings.

"Universality." The idea here is not simply that of "All F is G" but is instead that of the non-exhaustive universal in the sense, for instance, of "3," "500," etc., such that anything whatsoever will be one of three in a larger universe, one of five hundred in a larger universe, etc., and "3" will be any several, distinct xyz collectively whatsoever in a larger universe. It's a universal with further applications than the given one, or, at any rate, a universal with more than one application. Such is what people usually actually mean by "universal." It needs and deserves a distinct name but there is none. Anyway, the spirit is that of the so-called "miraculous jar" of positive integers and of ever more things (or at least mathematical objects) for them to be true of or applicable to.

— "Totality." My point is the exhaustiveness, the completiveness of divisions. (I don't have anything like Gödelian completeness in mind.) It's the exhaustive, the universe of discourse, the totality, the gamut (e.g., cdefgab in the universe of a plinker's notes), gamuts of theoretically possible combinations, etc. This is a logical quantity at the same level of analysis as the "universal with applications beyond the given instance."

— "Assortings." Such characterizes one's putting of like with like even before one has established a system of classes. The logical quantity is the special (in the sense of non-universal) combined with the general (in the sense of non-singular), as for instance "red" which is neither universal to things nor singular.

— I alight upon the ideas of "unicity" instead of "descriptive" or "explanatory" in order to evoke sufficient generality for this mode. The idea, in terms of logical quantity, is of the non-exhaustive monadic singular or singulars in polyad (non-exhaustive, i.e., the thing or things in question are in among more things, a larger universe, embedded in a world, instead of constituting a universe by themselves). Such is what people usually have in mind in thinking of things denoted by singular terms. (This, like each of three other logical quantities outlined above, is a conjunctive compound of simpler quantities, and together the four compounds constitute a set exhaustive of the combinatorial possibilities at their level of analysis.) The fields which, in comparison to their kin, are called descriptive, are ironically underdescribed thereby, and are often also instantiative, even consolidative, rife with multiple applications from other fields, and in fact involve anchorings, connectings, orderings, into tapestries of variegation, explanation, and (dis)verification, in which unitary things are uniquely paired, trio'ed, etc. The anchorings, linkings, orderings, hierarchizations, are themselves suitable for abstraction and general study; I call such abstract studies unicitative even when they are not descriptive.

"CA" (horizontally or vertically arranged) marks where two fields are comparatively completive & assortative respectively. Note indeed that these are comparative characterizations. Each field has its share of each of the four aspects or foci.
rules, balancings
elements, combinations, gamuts
kinds, assortings
items, etc., orderings, hierarchies
rules, balancings
Extremization, equations, topology, graph theoryDeductive math theory of optimizationCAInverse or multi-objective optimization (descriptive & inductive phases) & its mathematical formalismsSciences of motion, forces
elements, combinations, gamuts
Integration, measure, enumerative combinatorics  Probability theoryCAStatistics  Sciences of matter
kinds, assortings
Derivatives & functions, functionals, algebraDeductive math theory of information (historical overlap into abstract algebra)CACommunication/info theory (descriptive, inductive) & its mathematical formalismsSciences of life
items, etc., orderings, hierarchies
Limits, order, conditions affecting math-inductionDeductive math theory of logicCAPhilosophySciences of mind, intelligence, intelligent life
The completive-assortative difference is that between (a) assuming or establishing a total set of combinatorial elements from which one proceeds, and (b) assuming or establishing particular kinds and generalizing toward a potential total set of possibilities based on some at least putative underlying set of combinatorial elements. The twain approach each other from their opposite directions but typically seem not come together to mesh so perfectly as to become one. Anyway, they are recurrent distinct approaches.
A. Science of Discovery.
B. Science of Review.
C. Practical Science.
Peirce about Science of Review - "arranging the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science. Such is the nature of Humboldt's Cosmos, of Comte's Philosophie positive, and of Spencer's Synthetic Philosophy. The classification of the sciences belongs to this department." Previously, in his 1902 application to the Carnegie Institution (MS L75.355), Peirce had divided science thusly:
A. Theoretical Science.
  I. Science of Research.
  II. Science of Review, or Synthetic Philosophy.
B. Practical Science, or the Arts.
A. Mathematical & scientific researches.

B. Affective arts
(lit., music, visual, etc.).
C. Productive arts/sciences ("know-how").

D. Ruling/governing arts.

Important: The ordering of the fields shown just above is the opposite of their ordering as disciplines. Broader picture (for details, click here)
Affairs of power, freedomBusiness, econ. affairsSports, fashion, show, wattageDebate, case-building, honor
Management & complianceWork, labor, skill-plyingRecreation, hobbies, diversionStudy, communication
Governing / ruling valuesCare-howGratificational
Values re. cognition & legitimacy
Governing / ruling artsKnow-howAffective artsSciences & maths
Pattern to which Peirce's classifications of sciences tend to approximate:
1. Universal elements or laws;
2. Classes;
3. Descriptions.
Pattern of tetrastic classifications of sciences:
1. Factors, rules, constrainings, equilibrations
2. Elements, totalities, combinations, apportionments;
3. Particulars, differentiations, assortings;
4. Items, etc., orderings, hierarchies.
I don't try to show fields which arise as combinations of other fields.
I. Mathematics - About hypotheticals. Draws necessary conclusions.
A. Mathematics of Logic.B. Mathematics of Discrete Series.C. Mathematics of Continua & Pseudocontinua.
(Note: By 'continuum' Peirce meant a continuum of points more numerous than any Hilbertian aleph's worth. He held that such a continuum was the true subject matter of that which we now call topology, and that the reals, the complex reals, etc., constituted pseudocontinua.)
I. 'Pure' mathematics - Tends to draw equivalential conclusions. About universals that aren't universes.
Four subdivisions seem to traverse A., B., C., D. below:
1. sets (e.g. of curves) > the continuum;
2. continuous & uncountable (e.g., reals);
3. discrete & everywhere dense (e.g., rationals);
4. discrete & not dense.

(Functionals range over curves and belong in 1.)
A. (Many-to-many) equations, extremization, topology, graph theory.B. (One-to-many) integration, measure, enumerative combinatorics.C. (Many-to-one) functionals, functions, their derivatives. Algebra.
D. (One-to-one) limits, ORDER, conditions affecting math-induction applicability.
II. 'Applied' yet mathematically deep/nontrivial mathematics
Tends to draw non-reversibly deductive conclusions. About totalities, universes.
A. Deductive math theory of optimization.B. Deductive math theory of probability.C. Deductive math theory of infor­ma­tion (w/ historical overlap of research interest into abstract algebra).D. Deductive math theory of logic.
II. Philosophy, cenoscopy - About positive phenomena in general (not special classes) as available to anybody in any waking moment. Doesn't use special experiences.
Necessary philosophy or Epistemy ("Epistêmy") *Theorics*
("theôrics") (space, time)
A. Pheno- menology (a.k.a.
(incl. the CATEGORIES).
B. Normative Science.C. Metaphysics.
i. Esthe- tics.ii. Ethics.iii. Logic / Semiotics.
1.Speculative Grammar. ¹
2.Critic. ²
3.Methodeutic. ³
i. Ontology or General.ii. Psychical or Religious.
1. God.
2. freedom [& destiny].
3. immortality.
iii. Physical. (space, time, matter, etc.)
III. Abstract yet positive-phenomenally deep/nontrivial studies (cenoscopy) - Tend to draw ampliatively inductive conclusions. About the non-universal general = the non-singular special.
A. Inverse & multi-objective optimization (descriptive & inductive phases) & its mathematical formalisms.
B. Statistics.C. Communi­cation / info theory (descriptive, inductive) & its mathematical formalisms.D. Philosophy
III. Special sciences, idioscopy - About special classes of phenomena. Resorts to special experiences. (Peirce made only two broad divisions here, instead of his usual three. In his 1902 Carnegie application, he put the Psychical (as "A.") before the Physical (as "B").)
a. Physical.b. Psychical.
i. Nomological or General.
i. Molar Physics.
Dynamics &
ii. Molecular Physics.
Elaterics [pressure]
iii. Etherial Physics.
Optics &
ii. Classificatory. **
i. Crystallography
ii. Chemistry.

1. Physical.
2. Organic.
 Aliphatic &
3. Inorganic [elements, atomic weights, compounds, periodicity, etc.]
iii. Biology.
1. Physiology.
2. Anatomy.
iii. Descriptive.
Geognosy &
i. Nomological Psychics or Psychology.
i. Introspectional.
ii. Experimental.
iii. Physiological.
iv. Child.
ii. Classificatory Psychics, or Ethnology.
1. Special Psychology.
2. Linguistics.
3. Ethnology.
iii. Descriptive
Psychics, or History.

1. History proper.
2. Biography.
3. Criticism.
IV. Special sciences (idioscopy) - Tends to conclude in surmises to laws, entities, etc. About singulars among more singulars (and seeking to learn their laws, elements, kinds, uniquenesses).
A. Sciences of motion, forces.

B. Sciences of matter.C. Sciences of life.D. Sciences of mind, intelligence, intelligent life.
* Peirce's "Minute Logic" (1902) includes discussion of Epistêmy and Theôrics, and says (CP1.278 : "...[theôrics] only resort to special observation to settle some minute details, concerning which the testimony of general experience is possibly insufficient."
There's no mention of 'necessary philosophy,' 'Epistêmy,' or 'Theôrics' in the 1903 Syllabus outline classification in CP1.180-202 .

¹ Speculative Grammar includes the classification of signs.
² Critic includes the study of the modes of inference (especially the deductive, inductive, & abductive modes).
³ Methodeutic, also called 'Rhetoric' by Peirce, seems the locus of the Pragmatic Maxim and anyway includes the study of scientific method.

** Peirce in the 1903 Syllabus classification: "Classificatory physics seems, at present, as a matter of fact, to be divided, quite irrationally and most unequally, into i, Crystallography; ii, Chemistry; iii, Biology."
I've got a systematic ontology too. Triessentialism explains everything in terms of threes and triads and trinities. Take a look. And before you postulate "spirit" as the fourth and missing essence, ask yourself: do you mean a pseudo-physical realm, a pseudo-nonphysical energy, passionate feelings, wisdom, zen, or something else? If you can't define spirit, but you can give an analogy that explains it, it's not sufficient.
I don't base everything on an ontology or metaphysics,
I just generalize based on patterns which my blog discusses. As to the logical, the emotional, and the physical, you use those words in sometimes more general senses than I do, but in any case I do fit the ideas into classifications of various kinds, there's stuff in various places on my blog. The whole blog is my argument for fourfolds, I don't know how to state the argument in brief. I tried to explain why in "Why Tetrastic," but as I revised it over time, it got too long, too strident in some places, and also somewhat repetitive. It's become unwieldy, I don't know what do with it as a piece of writing.

I don't really know what you mean by "spirit," a word with many meanings. I use some obviously related ideas such as that of mind. I don't really know how to define "mind" philosophically, so if you want a definition of that or of spirit, you won't get one from me; I won't convince you of anything, and that's that. I do think of mind as something with some radical self-evolutionary capability. A mind powerfully learns. It doesn't just calculate or curve-fit, it infers, testing its interpretations and interpretive systems against experience. In my view, an inference process -- including confirmatory and verificational aspects -- is a kind of evolution, a kind of testing and accordant continual renovation and occasional re-design of an information-processing system. I don't mean that the mind is a scientist. The heart learns too, in its way.
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