This blog will consist mainly in selections adapted from longer posts in my home blog

*The Tetrast*. My four-folds are generally related to a slightly revised version of Aristotle's Four Causes (four reasons for a thing's being what it is). I disbelieve in numerology and it bores me. No paranormalism, synchronicity claims, etc., here. I call myself “the Tetrast” partly in fun at my inclination to make philosophy on the seemingly threadbare theme of a four-fold pattern. Best viewed in

*Internet Explorer*or

*Firefox*(at least as of my recentest opportunity to compare).

**Recentest significant edit: September 5, 2013.**

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

**(From "Compare to Aristotle, Aquinas, & Peirce")**

# Beginnings, middles, ends, and checks/entelechies.

Plus "entelechy" definitions from the *Century Dictionary* and from Joe Sachs (see Sidebar further below).

Archaí, beginnings, tryings, leadings, unsettlings. Mésa, middles, mediations, means, steadied going(s). Télê, ends, culminations, unsteadied going(s) . Entelecheíai, entelechies, checks, settlings. |

**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 maybe 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.

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.

SidebarMy conception of entelechy is somewhat nonstandard, based on ideas of stability and confirmation. I don’t seek mainly to clarify Aristotle (well, except when I edited Wikipedia's "Entelechy" article). 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 http://www.pep.uqam.ca/ )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.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 ending —

*télos*in the sense of ‘teleosis,’ reaching the end, actualization. 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, fully and not just partly actualized — rather than on entelechy as a HAVING 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 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 - i.e.,

*power*- 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, means*, 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

*glory, glamour, wattage*, splendor (e.g., fashion, sports, popularity, notoriety, opulence, "hipness," etc.). For "wattage" think not only candlepower but also horsepower; think vitality and, obviously, sex.

**•**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).

**(Adapted from "What of these other fours?"). Recentest significant change: October 29, 2013.**

There appears to be some structural correlation between my tetrastic classification of the fields of research and

**Max Tegmark’s theory of a four-level multiverse**in which every possibility is actualized (“everything exists”) and in which mathematical existence is real existence. I’m not saying that I think that Tegmark’s four-level multiverse picture is true (or that any multiverse picture is true). Tegmark claims that it is at least testable. (I am not a physicist and feel unprepared to evaluate his claims of testability.) What I’m saying is that there is a correlation between my tetrastic classification of the fields of research and aspects of the structure of physics-relevant ideas built by Tegmark as the structure of his claimed four-level multiverse. As for the reality of Tegmark’s four-level multiverse, your guess is as good as and maybe better than mine.

Tegmark’s Multiverse | My classification of research areas into families | Particle possibilities (feasibles/optima), probabilities, detection, & experimentation as correlating to Tegmark levels(I haven't seen this correlation, or whatever it is, posed by anybody else, but it seems implicit.) |

Level IV: includes other mathematical structures, different fundamental physical equations. | 1. Pure mathematics (analytic equations, extremization, topology, graph theory, integration, measure, enumeration, differentiation, calculation, limits, order, etc.). | (1st) IV. Feasibles & optimaVariation across mathematical structures. The particle's (wave packet's) evolution involves contributions from classically absurd (but quantum-feasible) potential trajectories and counterfactual circumstances, which mostly cancel each other out. Do they correspond, as "would-have-beens," to potential variations of a Level-I experimental setup? Yet how meaningful would that correspondence be if they involve variations in shortest distances, spacetime metrics, and mathematical structure generally, well beyond variations that we could actually carry out in our Level I experimental setup? This raises a question of mathematical equivalences between seemingly dissimilar scenarios. |

Level III: includes alternate-outcome worlds (quantum branching); same features as Level II. Works only if quantum evolution is unitary. | 2. Applied yet mathematically deep mathematics (deductive maths of: optimization, probability, information, and logic). | (2nd) III. ProbabilitiesVariation across quantum branches, corresponding to aprioristic distribution of probabilities for what the experimental particle will do at a given point in its evolution. |

Level II: includes other post-inflation bubbles, same fundamental equations of physics, but possibly different particles, constants, and dimensionality. | 3. Abstract yet positive-phenomenally deep sciences/studies (inverse optimization, statistical theory, descriptive and ampliatively-inductive areas of information theory, and philosophy). | (3rd) II. InformationVariation along one quantum branch (repeated experiment with same setup). |

Level I: includes regions beyond our cosmic horizon, “universes” or Hubble volumes in a single given inflationary bubble. | 4. Concrete empirical sciences/studies (physical, material, biological, and behavioral/social/human). | (4th) I. LogicVariation of experimental setup, an actual history (establishment of a hypothesis, theory, etc.) |

In other words, one would expect that the “city of research,” in its evolved broad layout, would naturally come consistently, if it came at all, to resemble the “sky” of constellated multiverse structures “above” it. I mean that a resemblance that goes half-way and then simply quits seems rather unsatisfying.

Another question is, of course, whether our civilization's “city of research” has evolved sufficiently for a systematic resemblance between it and multiverse structures to emerge. Whatever the case may be in that regard, I think I do see a correlation between the multiverse structures and the layout, as I see it, of research fields.

However, in the correlation, fields such as deductive logic, which Tegmark associates with Level IV, are associated instead with Level III. Deductive logic is about the structures of alternatives among predicates or propositions which, according to the quantum Many Worlds view, are all actualized thanks to quantum branching into alternatives. Deductive logic is one of a family of fields, including also the deductive mathematics of optimization, probability, and information, studying such alternatives. They are considered mathematically deep, yet are not usually called “pure” mathematics, but “applied.” (One is stuck with their distinction’s being made with the terms “pure” and “applied”; one can see how it came about, but it’s neither the most illuminating way nor even true in every relevant sense. And as Dieudonné points out in his mathematics article in the

*Encyclopedia Britannica*Fifteenth Edition, the rubric “applied” jumbles deep and trivial areas of math together. “Pure” does not.)

Now, Tegmark follows tradition in regarding formal deductive logics as the most basic area in maths. I discuss issues of this kind at greater length in my post “Logical quantities, categories of research, and categories”. To summarize here, such deductive logics are about proof, and to put them as most basic within mathematics is to order the maths in the order of knowledge and of how we know things. Yet tradition also puts physics as more basic then chemistry, biology, etc., yet that is not in the order of knowledge but in the order of being. Tradition, on these points, is inconsistent, and the neat inter-family alignment of members of the research families tends to bear this out (see table below). If Tegmark on some level liked an element of research-classificational traditionalism as “leavening” his cosmological radicalism, I’d say he should have been even more radical instead. (

**Skip tables ►)**

Universal: | Special: | ||
---|---|---|---|

General: | 1. Universal general. | 3. Non-universal general. | |

(Multi-)singular (monadic, polyadic, etc.): | 2. Universe; 'grand' polyad, gamut, etc.; total population & its parameters. | 4. (Multi-)singular (monadic, polyadic, etc.) in a larger world, i.e., special (multi-)singular. | |

Tetrastic 4x4 classification of the sciences & mathematics.

(columns)

BANDS OF

AFFINITY (rows)

generals.

gamuts, total

populations

& their

parameters.

generals

(non-singular

specials).

(monadic,

polyadic, etc.)

in a larger

world.

*Pure maths (at least some are classified below):*

*Applied yet mathematically often-deep, mathemtically duductive theories:*

*General ('domain-independent') studies of positive phenomena:*

*'Special'*

sciences:

sciences:

generals.

*Rules, constraints, equational balances:*(descriptive & inductive phases) & its mathematical formalisms.

gamuts,

total

populations

& their

parameters.

*Elements, compositions, full complements:*universal

generals

(non-

singular

specials).

*Differentiations, specializations,*

kinds,

special parts:kinds,

special parts:

communication theory

(descriptive, inductive) & its mathematical formalisms.

(monadic,

polyadic,

etc.) in a

larger

world.

*Singular-*

izations,

unique relations, orderings, hierarchies:izations,

unique relations, orderings, hierarchies:

To put logic first among maths is an inclination of many people, usually anti-Platonistic, who regard the existence of mathematical objects as a fiction, at best a convenient fiction - for them, there is no order of being, but only order of knowledge, in mathematics. That's

*not*a constraint which Tegmark needs to heed in his theory that mathematical existence is real existence.

What about the Comtean idea that the field which supplies basic principles to another field is the prior field? That's an ordering according to being, not according to learning, since the principles in question, involving laws, facts, entities, etc., are explanatory, descriptive, predictive, or verificative as contents of inferences. Deductive logic supplies principles or methods for inferring things and therefore for showing or accounting for or

*learning and knowing about*things - not principles that, as inference factors, show or account for things in other areas of mathematics, areas and principles which are not

*about*inference or its factors. Consider the concrete parallel: a study of actual methods of inference to concrete fact and even to laws covering concrete particulars would be neither physics nor prior to physics, but instead a social study, including sociology about science, also with some overlap into psychology, and would involve applications of philosophy and logic.

Now, two families of mathematics are regarded as deep, and one of them as pure and deep, and the other as applied yet (mathematically) deep. Pure mathematics includes such areas as simultaneous equations, topology, matrices, extremization, graph theory, integration, measure, enumeration, differentiation, calculation (algebra), groups, limits, and kinds of ordering e.g. well ordering. Conclusions drawn in these fields tend to be “reversibly” a.k.a. “equivalentially” deductive (in mathematical induction, the minimal case and the heredity, conjoined, are equivalent to the conclusion) and structures of equivalences are rife throughout pure mathematics. Applied yet mathematically deep mathematics consists of deductive mathematical theories of optimization, probability, information, and logic; conclusions in these fields tend to be non-reversibly deductive (though to the extent that deductive mathematical theory of information has “re-invented” group theory, it has developed pure-mathematical interests and, presumably, has drawn many conclusions through mathematical induction.) All of these applied yet deep mathematics are about

*structures of alternatives*. They are about the structures of those alternatives which all are actualized across Tegmark’s Level III, the Many Worlds of quantum physics, and they deduce from totalities to parts.

What about Level II? Now, Level III and Level II are each other’s “inverses,” Level III actualizing alternate outcomes across quantum branchings, and Level II actualizing alternate outcomes in various times and places along a single branch, so that the two levels come out the same in their features. Likewise is there a family of abstract yet positive-phenomenally deep areas of research, such as statistical theory, areas each of which deals with the inverse problem of a correlated area of applied yet deep mathematics, and each of which deals in a general way with gathering data from various actual places and times and drawing ampliatively-inductive conclusions from parts, samples, etc., to totalities. These areas pertain to phenomena in general rather than to any special class, any single sample of the concrete real (and thus are all cenoscopic in the Peircean sense). They include inverse optimization problems (which comprise a young research field though some of the problems are old), statistical theory, descriptive and ampliatively inductive areas of information theory, and the descriptive and ampliatively inductive study of logic and intelligent processes — I mean philosophy, not AI or computer research. This family of research seem to stand to Level II as the deductive maths of optimization, probability, information, and logic stand to Level III.

Finally of course, correlated to Level I, there are the concrete empirical or “special” sciences — physical, chemical, biological, behaviorial/social/human, which tend to conclude in surmises, as cogent as they can make them.

I had kind of hoped to discuss some of this with the folks at the "everything" mailing list, but the arguments there tend to revolve around computationalism (most of the active participants are genial, e.g., Bruno Marchal, and they're all intelligent). Also, they don't think that much can be said about Tegmark’s Level IV. I suspect that this is because they haven’t yet been able to incorporate extremal principles into their work as they would like, but I don't think that I convinced them that there's any particular reason to think that there's a connection.

Note:

**How to say “everything exists.”**In standard first-order logic, the phrase “everything exists” would be taken to trivially mean “that, that is, is,” or the like. Is there a way to say it in Tegmark’s sense in first-order logic at all? Is it an idea that can be logically expressed at that basic level? What would it mean if it can’t? Well, there does appear to be a way to say it in a specially restricted kind of first-order logic, by use of a special kind of quantificational functor. As for whether this leads to a coherent logical idea in less restricted logic, you be the judge. The result is, at least, a kind of statement which seems to lead to an area of logical issues raised by Tegmark’s picture, in any case, with regard to saying that every “potential” particular definite individual is actualized somewhere and somewhen, or, on the other hand, that the world altogether lacks some

*particular definite individual(s).*The objectual version of the formalism sharpens the problem by allowing the individual(s) in question to be unspecified and even unspecifiable.

Now, in defining the existential particular quantification, one may start with a finite universe of objects named by constants

*a*”

*h*”,

*a*such that...

*a*...or there is

*b*such that...

*b*... ... ...or there is

*h*such that...

*h*....” and agree to write this as

**∃**

*x*...

*x*....”

*x*ranges over only named objects

*a, b, c,*etc. Then the variable

*x*is no longer substitutional but instead is

*objectual*. To get to our new special functor will be a matter of replacing the repeated “or” with a repeated “and”.

Let’s define a functor

**Æ**”

**Æ**

*x*...

*x*....”

*a*such that...

*a*...and there is

*b*such that...

*b*... ... ...and there is

*h*such that...

*h*....” In effect one is saying that every name names something. Now, what happens when the substitutionalist requirement is dropped? In considering just what it is that

*x*now ranges over, and whether the objectual statement

**Æ**

*x*”

(Note:

**Æ**

*x*”

**∃**

*x*(

*F x*) &

**∀**

*x*(

*F x*) ”

**→**G x**∃**

*x*

**∀**

*y*( [

*F x*] & [

*F y*] ) , ”

**→**G y**Æ**

*x*”

This post has been backdated from February 17, 2009 to December 4, 2008, in order to keep it from appearing on the home page.

It contains simplified versions (friendlier to users of screen readers) of two tables in the post on Tegmark's Multiverse and the classification of the sciences and maths. The first and smaller table is "

*Simple*& conjoined logical quantities for terms (subject, predicate, etc.)". The second table is "Tetrastic 4×4 classification of the sciences & mathematics".

Universal: | Special: | |
---|---|---|

General: | 1. Universal general. | 3. Non-universal general. |

(Multi-)singular (monadic, polyadic, etc.) | 2. Universe; 'grand' polyad, gamut, etc.; total population and its parameters. | 4. (Multi-)singular (monadic, polyadic, etc.) in a larger world. |

Column One. Main heading: Universal generals. Sub-heading: Pure maths (at least some are classified below): | Column Two. Main heading: Universes, gamuts, total populations & their parameters. Sub-heading: Applied, yet mathematically often-deep, mathematically deductive theories: | Column Three. Main heading: Non-universal generals (non-singular specials). Sub-heading: General ('domain-independent') studies of positive phenomena: | Column Four. Main heading: Singulars (monadic, polyadic, etc.) in a larger world. Sub-heading: 'Special' sciences: | |
---|---|---|---|---|

Row One. Main heading: Universal generals. Sub-heading: Rules, constraints, equational balances: | Extremization, equations, graph theory, many-to-many relations. | Mathematics of optimization. | Inverse or multi-objective optimization (descriptive & inductive phases) & its mathematical formalisms. | Sciences of motion, forces. |

Row Two: Main heading: Main heading: Universes, gamuts, total populations & their parameters. Sub-heading: Elements, compositions, full complements: | Integration, measure, enumeration, one-to-many relations. | Mathematics of probability. | Statistics. | Sciences of matter. |

Row Three: Main heading: Non-universal generals (non-singular specials). Sub-heading: Differentiations, specializations, kinds, special parts: | Differentiation of functions, calculation (algebra as theory of calculation), many-to-one relations. | Mathematics of information (historical overlap into abstract algebra). | Info/ communication theory (descriptive, inductive) & its mathematical formalisms. | Sciences of life. |

Row Four: Main heading: Singulars (monadic, polyadic, etc.) in a larger world. Sub-heading: Singularizations, unique relations, orderings, hierarchies: | Limits, ordering, inference conditions, one-to-one relations. | Mathematics of logic. | Philosophy. | Sciences / studies of mind, intelligence, intelligent life. |

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