This article gathers the anthropological and historical-philosophical branch of the monograph: historical scales of cognition, the two ontological lines, time stratification, and the package system of categories.
In NAPG 2.0 the history of cognition is read as movement across stratified layers of perception, thought, and ontological world-building.
Historical types of perception form the ladder P01oP1oP02oP2oP03oP3oP04oP4. Parallel to it stands the system of pure and practical R-layers: $$R\!-\!01,\;R\!-\!02,\;R\!-\!03,\;R\!-\!04 \qquadext{and}\qquad R\!-\!1,\;R\!-\!2,\;R\!-\!3,\;R\!-\!4.$$
P − 1 fixes the dark pre-fold zone where the boundaries between dream and waking, image and event, past and present are not yet stable. P01 expresses the conciliar Now, while P1 is the ritual world of dense presence.
P02/P2 form cosmological reason: time is read off the cosmic order and the past ground. P03/P3 form critical and scientific reason: time becomes a horizon, a form of experience, and then a measurable and model-organized magnitude.
P04/P4 and R − 04/R − 4 fix package reason. The pure form R − 04 understands reality as a package-projective structure; R − 4 is its practical realization in AI. PIX(Π-field) is not a new episteme; it is the working mechanism of R − 04.
| Layer | Canonical name | Type of time | Arche-symbol |
|---|---|---|---|
| Layer | Canonical name | Type of time | Arche-symbol |
| P − 1 | Dark episteme | undifferentiated time | darkness, dream, déjà vu |
| P01 | Conciliar Now | unified present | liturgical Now |
| P1 | Ritual World | here-and-now | ritual, totem, omen |
| P02 | Pure Cosmo-Reason | cosmic measure | sphere, circle, cosmos |
| P2 | Practical Cosmo-Reason | calibrated external time | celestial grid |
| P03 | Pure Critical Reason | horizon of the future | form of intuition |
| P3 | Practical Scientific Reason | measurable model-time | mechanism, formula |
| P04 | Pure Package Reason | multiple presents | packet of horizons |
| P4 | Package Episteme | networked and layered time | network, packet, base of layers |
Each historical layer admits a two-line reading: $$P_\sigma = P_\sigma^{\Aline}\oplus P_\sigma^{\Pline}.$$
The Aristotelian line expresses locality, measure, finitude, and bodily visibility. In package-projective language this is the central-affine line.
The Platonic line expresses paradigm, depth, horizon, and the distant limit. In package-projective language this is the central-projective line.
A real historical type of cognition arises as a package superposition of these two lines, not as their simple separation.
Aristotle defines time as the number of motion; patristic thought and Augustine shift it toward the inner and salvific dimension; Locke, Berkeley, and Hume decosmologize time; Kant secures it as a form of intuition; Newton absolutizes mathematical time; Michelson–Morley reveals the crisis of the universal background; Einstein transfers time into the regime of synchronization and multiple presents.
| Author / line | Layer | What time is | Type of present |
|---|---|---|---|
| Orthodox Fathers | P01 | unified presence | conciliar Now |
| Augustine | P01oP03 | distension of the soul | tense inner Now |
| Aristotle | P02 | number of motion | locally observed Now |
| Locke | P02oP03 | duration from succession of ideas | inner flowing Now |
| Berkeley | P02oP03 | inseparable from succession of ideas | mentally retained Now |
| Hume | P02oP03 | order of changeable objects | empirical instant of transition |
| Kant | P03 | form of intuition | transcendental Now |
| Newton | P3 | absolute mathematical time | universal external Now |
| Einstein | P3 ↔︎ P4 | operational time of synchronization | multiple presents |
Aristotle expresses the strongest form of the central-affine line: a finite, local, observable cosmos of measure. Plato gives the strongest form of the central-projective line: the cosmos as image and time as image of eternity. Kant produces their critical tension, while Spengler supplies a morphological reading through the prime symbols of cultures.
For the historical layer Pσ, define the packet $$\LayerPacket{\sigma} = igl( P_\sigma^{\Aline,\Ax}, P_\sigma^{\Aline,\Ths}; P_\sigma^{\Pline,\Ax}, P_\sigma^{\Pline,\Ths} igr).$$
To every packet $\LayerPacket{\sigma}$ assign the value $$\TruthLambda{\sigma} = \Lambdaigl( P_\sigma^{\Aline,\Ax}, P_\sigma^{\Aline,\Ths}; P_\sigma^{\Pline,\Ax}, P_\sigma^{\Pline,\Ths} igr),$$ called the λ-value of the historical layer.
The value $$\TruthLambda{\sigma}=-1$$ means absolute truth of the corresponding ontological packet.
The ontological limit of the layer is defined as $$\OntLimit{\sigma} = \TruthLambda{\sigma}igl(\LayerPacket{\sigma}igr).$$ Thus the limit is not given by an external point but by the harmonically organized packet of internal lines and subspaces.
The Aristotelian and Platonic lines may be represented by functions aσ(x) and pσ(x); after Fourier transformation, their harmonically normalized ratio yields a spectral model of the λ-field of the corresponding layer.
Within NAPRLK, categories of thinking are not fixed boxes for sorting experience. They are package operators that organize event-state peaks in accordance with a historical regime of perception. Hence they cannot be described merely as a list of formal headings: each category must be read as a way of contracting event, state, scale, viewpoint, and transition.
Kantian and Aristotelian categories are not discarded but rewritten in package form. Their place is taken by such fundamental pairs as:
similarity and difference;
being and non-being;
law and regularity;
causality and determinism;
event and state.
At the same time, the Aristotelian line remains more tightly bound to locality, embodiment, and measure, whereas the Kantian line is tied to the form of experience and the conditions of possibility.
For the working redaction of the monograph it is useful to distinguish four blocks of categories:
fundamental: similarity/difference, being/non-being, law/regularity, axiom/limit of applicability;
causal: causality/determinism, event/state;
dialectical: unity of opposites, transition of quantity into quality, negation of negation;
package-geometric: scale, viewpoint, transition, transport, shift, rotation, size, dimensionality.
The last block is what decisively distinguishes NAPRLK from the classical tables of categories.
The classical Kantian distinction between analytic and synthetic judgments remains meaningful, but is rewritten in terms of support-connectivity and passage between layers.
An analytic judgment is one whose truth is unfolded inside a single support-connectivity without the production of new structural content. In package language this means that the configuration never leaves one and the same layer of agreement.
A synthetic judgment is one in which new content appears through a passage between distinct support-connectivities, or through the projective-harmonic closure of a configuration. Syntheticity is therefore not merely the “addition of a predicate”, but a structural increment of sense.
Synthetic a priori judgments are possible insofar as package geometry itself contains projective-harmonic closures that cannot be reduced to tautologies inside one layer. If a configuration closes harmonically, (ℐ, 𝒰; ℛ, r) = −1, then the trans-reper point r contributes genuinely new content without recourse to empirical observation and thus realizes synthetic a priority.
| extbfKant | Aristotle | NAPRLK |
|---|---|---|
| Quantity | Quantity | Size, scale |
| Quality | Quality | Dimensionality, viewpoint |
| Relation | Relation | Causality, transition |
| Modality | Substance / essence | Being/non-being, peak, admissibility |
| Analytic judgment | Definitional unfolding | Configuration inside one support-connectivity |
| Synthetic judgment | Increase of content | Passage between connectivities or harmonic closure |
The canonical line in this redaction is:
P1 — the ritual world;
P2 — cosmo-reason;
P3 — scientific reason;
R-04 — the pure form of package reason;
R-4 — its practical realization.
No separate P5 is introduced. The PIX-field does not constitute a new episteme; it expresses the working mechanism of R-04 at the level of peak agreement and event-state contraction.
Categories of thinking in NAPRLK must therefore be understood as dynamic package operators. They do not merely classify experience; they themselves evolve together with historical regimes of perception.