# One plenum? Many real infinities? Notes on the virtuality of order corresponding to polynomial grammaticality

Polynomials name terms that comprehend ever so much as the term is capable of bounding within a constellation of terms as incorporated by a formulaic system. the determinability of this so much is added separately, by the decision regarding which numerical domain is being put at the basis of the solution space.

What is a quantity?  It is not an Identity, it is an Invariance. It’s mode of being is neither quantum nor quantitas, it is insistence (neither ideality nor existence).

There are three principles today of its determinability (Deleuze):

1. a principle of determinability which corresponds to the undetermined as such (dx, dy) – quantitability
2. a principle of reciprocal determination corresponds to the really determinable (dY/dx) – qualitability
3. a principle of complete determination corresponds to the effectively determined (values of dY/dx) – potentiality

dx– the differential, is the Idea, its problem, and its being.

The determinability of a quantity allows for its individuation. Individuation depends upon a political and an economical vector: e) the economical vector concerns the mastering of virtues, p) the political vector concerns involving the mastered virtues in contracts of possibilities.

A differential is the contracted not-A, the inversion after:

1) “what there is” (the abounding quantity)  is being split into halves which are placed in a “presence through not being here”  which we call time and space (consideration, political vector, x),

2) the placed cuts mutually index and settle one another through naming their relations as renderings (contracting, the economic vector, x/y),

3) the named and gendered cuts (the multiplied halves) acquire an autonomy and begin to act on a stage, by introducing a there into the presence of not-being-here, a there where they send representatives of their gender (symbolization, the political vector, dx),

4) the representatives of their gender, mutually index and settle one another through naming, have been contracted as possibilities through naming their symbolicity (‘fitting together’) and diabolicity (‘keeping apart’) (negation, the economic vector, x/y),

4) have been encoded according to their organization in ideality  (infinitization, the political vector, dx) – the invariance is virtually real (not potentially real). Its reality depends upon the strength of virtues, which manifests and organizes itself in the contraction of possibilities.

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An associative cloud of concepts gathered from www.etymonline.com while breeding over the idea of what these technical notes entail:

L. symbolum “creed, token, mark,” from Greek symbolon “token, watchword”,  literally “that which is thrown or cast together,” from syn- “together” (see syn-) + bole “a throwing, a casting, the stroke of a missile, bolt, beam,” from bol-, nom. stem of ballein “to throw” (see ballistics). The sense evolution in Greek is from “throwing things together” to “contrasting” to “comparing” to “token used in comparisons to determine if something is genuine.” Hence, “outward sign” of something.

L. diabolus (also the source of Italian diavolo, French diable, Spanish diablo; German Teufel is Old High German tiufal, from Latin via Gothic diabaulus).The Late Latin word is from Ecclesiastical Greek diabolos, in Jewish and Christian use, “Devil, Satan” (scriptural loan-translation of Hebrew satan), in general use “accuser, slanderer,” from diaballein “to slander, attack,” literally “throw across,” from dia- “across, through” + ballein “to throw” (see ballistics).

L. genus (gen. generis) “race, stock, kind; family, birth, descent, origin,” cognate with Gk. genos “race, kind,” and gonos “birth, offspring, stock,” from PIE root *gen(e)- “produce, beget, be born”, gender translates translate Aristotle’s Greek grammatical term genos.

L. natura “course of things; natural character, constitution, quality; the universe,” lit. “birth,” from natus “born,” pp. of nasci “to be born,” from PIE *gene-“to give birth, beget”

people, “humans, persons in general,” from Anglo-Fr. people, O.Fr. peupel “people, population, crowd; mankind, humanity,” from L. populus “a people, nation; body of citizens; a multitude, crowd, throng,” of unknown origin

O.Fr. nacion “birth, rank; descendants, relatives; country, homeland” (12c.) and directly from L. nationem (nom. natio) “birth, origin; breed, stock, kind, species; race of people, tribe,” lit. “that which has been born,” from natus, pp. of nasci “be born” (Old L. gnasci; see genus). Political sense has gradually predominated, but earliest English examples inclined toward the racial meaning “large group of people with common ancestry.”

L. collectus, pp. of colligere “gather together,” from com- “together” (see com) + legere”to gather” (see lecture (n.)). The intransitive sense is attested from 1794. Related: Collected; collecting. As an adjective meaning “paid by the recipient” it is attested from 1893, originally with reference to telegrams.

L. distributionem (nom. distributio) “a division, distribution,” noun of action from pp. stem of distribuere “deal out in portions,” from dis- “individually” + tribuere “assign, allot”

tribute, n. id-14c., “tax paid to a ruler or master for security or protection,” from L. tributum “tribute,” lit. “a thing contributed or paid,” noun use of tributus, neuter pp. of tribuere “to pay, assign, grant,” also “allot among the tribes or to a tribe,” from tribus (see tribe). Sense of “offering, gift, token” is first recorded 1580s.

Gk. physike (episteme) “(knowledge) of nature,” from fem. of physikos “pertaining to nature,” from physis “nature,” from phyein “to bring forth, produce, make to grow” (cf. phyton “growth, plant,” phyle “tribe, race,” phyma “a growth, tumor”)

recognize, early 15c., “resume possession of land,” from M.Fr. reconiss-, stem of reconoistre “to know again, identify, recognize,” from O.Fr., from L. recognoscere”acknowledge, recall to mind, know again, examine, certify,” from re- “again” (see re-) + cognoscere “know” (see cognizance). Meaning “perceive something or someone as already known” first recorded 1530s

L. cognoscere “to get to know, recognize,” from com- “together” (see co-) + gnoscere “to know” (see notice)

L. notitia “a being known, celebrity, fame, knowledge,” from notus”known,” pp. of (g)noscere “come to know, to get to know, get acquainted (with),” from PIE *gno-sko-, a suffixed form of root *gno- (see know). Sense of “formal warning” is attested from 1590s. Meaning “a sign giving information” is from 1805.”to notify,” from notice (n.). Sense of “to point out” is from 1620s. Meaning “to take notice of”

L. individuus “indivisible,” from in- “not, opposite of” (see in- (1)) + dividuus “divisible,” from dividere “divide” (see divide). Not common before c.1600 and

L. dividere “to force apart, cleave, distribute,” from dis- “apart” (see dis-) + -videre “to separate,” from PIE root *weidh- “to separate” (see widow; also see with). Mathematical sense is from early 15c. The noun is attested from 1640s, “act of dividing;”

dis, word-forming element meaning 1. “lack of, not” (e.g. dishonest); 2. “do the opposite of” (e.g. disallow); 3. “apart, away” (e.g. discard), from O.Fr. des- or directly from L. dis- “apart, in a different direction, between,” figuratively “not, un-,” also “exceedingly, utterly,”

outrage, “to go to excess, act immoderately,” from outrage (n.). Etymologically, “the passing beyond reasonable bounds” in any sense; meaning narrowed in English toward violent excesses because of folk etymology from out + rage.

moderate, late 14c., originally of weather and other physical conditions, from L. moderatus “within bounds, observing moderation;” figuratively “modest, restrained,” pp. of moderari “to regulate, mitigate, restrain, temper, set a measure, keep (something) within measure,” related to modus “measure,”

modest “freedom from exaggeration, self-control,” from M.Fr. modestie or directly from L. modestia “moderation, sense of honor, correctness of conduct,” from modestus “moderate, keeping measure, sober, gentle, temperate,” from modus “measure, manner”

L. immoderatus “boundless, immeasurable,” figuratively “unrestrained, excessive,” from assimilated form of in- “not, opposite of” (see in- (1)) + moderatus “restrained”

L. restringere “draw back tightly, confine, check” (see restriction).  L.L. restrictionem (nom. restrictio) “limitation,” from pp. stem of L. restringere “restrict, bind fast, restrain,” from re- “back” (see re-) +stringere “draw tight”

L. decidere “to decide, determine,” lit. “to cut off,” from de- “off” (see de-) + caedere “to cut”

cut, caedere “to cut down, chop, beat, hew, fell, slay,”

L. disputare “weigh, examine, discuss, argue, explain,” from dis-“separately” (see dis-) + putare “to count, consider,” originally “to prune”