Re-evaluating the structure of consciousness through the symintentry hypothesis.

The Projective Consciousness Model and its extension to the phenomenal selfhood model are the generic invariant structures of consciousness through five symmetries. They include the following: situated 3D spatiality; temporal integration through encompassing the three "nows" that constitute the Now; multimodal synchronic integration; relational phenomenal intentionality; and consciousness entails a pre-reflective awareness of the uniqueness of the phenomenal self. These symmetries stem from the evolution and emergence of the phenomenal self through modeling, and that is realized through the phenomenal modeling of the intentionality relationship. We propose that this set of symmetries is based on and can be explicated in terms of a more fundamental symmetry, symmetry-based modeling. The proposal stems from (a) Kant's transcendental structuralism, which asserts that "Objects" conform to models prescribed through the inherent structure of the phenomenal mind, and (b) Cassirer's proposition that a mathematical group underpins this structure. To validate our proposal, we stipulate this group defining symmetry-based modeling and its emergence and adaptation into structuring the Now. We find that Cassirer's group requires a more powerful dual quaternion operator to be able to support intentionality and the five symmetries. We propose that the efficacy of this operator stems from unifying symmetry-based modeling and intentionality as "symintentry." Symintentry, we argue, is not just a new form of symmetry but is the archetypical form of symmetry. Symintentry provides fresh insights into the nature of symmetry, intentionality, and consciousness.