Dear Donald,
Thank you for your insightful comments and important questions.
I drew the attention to the need to consider the mathematics and physics, not only in the most distant historical depth, "the beginning of Mathematica" and "the beginning of Physica", but also in the existential and ontological depth of these two fundamental sign systems. This is what called Edmund Husserl concerning geometry in "Origin of Geometry".
Mathematica and Physica have lost of certainty, moreover, they have lost the "existential certainty". It is well demonstrated by Morris Kline in "Mathematics: The Loss of Certainty" and Lee Smolin, "The Trouble with Physics."
Mathematica and Physica - two fundamental sign systems without ontological foundation (basification). This is a common problem for mathematicians, physicists and philosophers. I offered my version of the ontological justification of "fundamental knowledge" taking into account all the knowledge that mankind has accumulated.
What a way to justification (basification) of "fundamental knowledge"?
-Total ontological unification of matter at all levels of Universum as a whole in the spirit of Heraclitus - Plato - Aristotle - Cusa - Hegel as the triunity of absolute forms of existence of matter (absolute, extreme, limit states): absolute rest + absolute motion + absolute becoming;
-Method of ontological construction: every mathematical object of construction model of the ontological basis has a clear and distinct ontological interpretation;
- Super axiom and Super principle that suggest Tradition, Nature and depth etymology of the word "structure" (in Russian - "s-troe-nie", ie, the number "troe=three" in the root of the word "structure").
Trinity of absolute (limit, extreme) states of matter (each state has its own way - the vector of absolute state) substantiate the limit ideality - triune absolute state space: the absolute linear ("continuum") + absolute vortex ("discretuum") + absolute wave ("dis-continuum")= the absolute field. Each state has three dimensions: 3 linear + 3 vortex + 3 wave. The onto-geometric representants of absolute states of matter substantiate the absolute (triune) coordinate system: cube + sphere + cylinder.
This is structure of the otologic basis of fundamental knowledge - the primordial generating structure, " La Structure mティre " as ontological framework, carcass and foundation of knowledge. What keeps and develops the primordial structure of Universum? - Ontological (structural, cosmic) memory. The ontological basis of knowledge - is the construction of the primordial process of Universum before the "beginning of times", the ontological basis (construct) of eternity.
But in the words of Descartes: 竊' Dubito 竊' Ergo 竊' Cogito竊'
Kind regards,
Vladimir