Grounding in our bio-socio-mathematical model of language-consciousness (Bakrim, 2021b, 2022d), the relations between analysis (linguistics) and synthesis (semiotics) (Bakrim, 2022c) are defined as the manifold relations between Sets, Categories and Types in a realistic theory of fields and observability/objectivity entanglement. Thus, modes of neuro-language verifiability represent the underpinnings of text configuration being a meta-observability of relevance levels following two orientations:

- Descending : representation and polynomial series of neurocognitive, linguistic and semiotic types 

- Ascending : Integration of linguistic and semiotic recursions 

Hence, suggesting the hypothesis of propositional bidirectionality (semiotic and linguistic one), in the sense that knowable and objective event unit of physical-social recursion (Soctxt  particles borne by the longitudinal pressure wave in the field of medium material wave, driving other sensory waves by way of interference) are distinguished from the structure of societal participation (Societcom) of sociological and ethno-communicational relevance in terms of double structuring (social-societal).

Therefore, regarding the relations of dynamic and immediate objects (Peirce, 1958), category-mathematics of language, in particular maps, their morphisms being modes of objectification symmetry and their neural substrates (hippocampus as the site of hypothetic dynamic objectification) (Gomez-Ramirez, 2014), enable us to widen our manifold model of reasoning to a configuration of fields from events and facts.

Furthermore, between linguistic-semiotic sciences (objectifying/observing) and cultural/ideological simulacra we notice the emergence of the non-objective axis from the anthropo-genetic hypothesis and its plasticity of social totality (Atmaspacher, 2012, Meloni, 2014) with a parallax of  viewpoint modulation on the manifold of the configured text (archetypes, prototypes and stereotypes). Non-objective herein means relying on the ascribing of viewpoints on analytic and synthetic forms on totality.

Relying on our type theoretical purpose, this non-objective paradox suggests polymorphic identity functions on a universe U being a dependent function changing the order of its arguments with dialogical poly-subjectivity on the Topos 

In order to pinpoint the bifurcation mode of the non-objective and the societal (objective) on text configuration (with logical-mathematical and neural verifiability preservation in the sense of Grothendieck’s model (A’Campo, 2016)), we verify and demonstrate that the modulations of discursive viewpoints on the manifold of text configuration take place in our previous set theoretical proposal : Pi = PrL X Ps (Bakrim, 2021a) where Pi the Pragmatic Impact is the Cartesian product of praxical levels and positional structure, opening thus our reasoning to Set-Category-type manifold and vector bundles and projection plans.

Therefore, the optic polyphonic dialogism on both sides of social-societal objectivities on one hand and Ideology (discourse); by which we mean any parallax orientation of objective truth and totality structure in both ‘unavoidable’ dealing with totality paradoxes and manipulative senses beyond the mere critical political sense, points out that the purpose of dynamic totality lies beyond externalist-internalist theories of consciousness designating the hypothesis of both dialogical and bidirectional orders from this bifurcation.

As an empirical field, we will ground in neural (our neural graph hypothesis of universality) and social-societal observation of intergeneration

A'campo, N., Ji, L., & Papadopoulos, A. (2016). “On Grothendieck's tame topology”, arXiv: Geometric Topology.

Atmanspacher, H.  (2012). “Dual-aspect monism à la Pauli and Jung”. Journal of Consciousness Studies 19 (9-10):96–120.

Bakrim, N. (2021 a). “Pragmatic impacts, representation, and regulation”, Semiotica, 2021, 147 - 168. 

Bakrim, N. (2021b). The Real-Object-Approach of Language (ROAL-Model): A Bio-mathematical Attempt on Language and Consciousness. BoD : Paris. 

Bakrim, N. (2022c). « De la Catégorialité sémiosique et langagière aux types : biomathématique linguistique-sémiotique et raisons/déraisons d’objectivité ». Upcoming.

Bakrim, N. (2022d). The Manifold Object of Language: A Bio-mathematical and Socio-mathematical Hypothesis from the ROAL-Model (3). BoD : Paris.

Gomez-Ramirez, J. (2014). A new Foundation for Representation in Cognitive and Brain: Category Theory and the Hippocampus. Springer Verlag. Berlin & New York.

HUFP  (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Frame Program.

Meloni, M. (2014). “How Biology became Social, and what it Means for Social Theory”. The Sociological Review 62 : 593–614.

Peirce, C. S. (1958). Collected Papers of Charles Sanders. Cambridge/Massachusetts: Harvard University Press.