When the search is for the foundations of any science, it is in fact for the invariant aspects of all the realities of that science, and not merely for the invariant aspects of some parts of the realities (object-set/s), methods, conclusions, etc. This does not suffice for science for maximizing success. This is because, any exclusive search for the foundations of the specific object-set or of the discourse of the specific object-set will further require foundations upon the totality of all specific object-sets and their discourse.
We find ourselves in a tradition that believes that proportionality quantities are to be taken as the invariables in physics. But I used to reduce into universal qualities the quantitative-structural aspect of all sciences, that are represented in mathematics as the ontological quantities dealt with in science. The real invariants of physics are not the ontological quantities or proportionalities of certain quantities being treated in physics.
The latter, being only the constant quantities, are one kind of ontological qualities, namely, (1) the quantitatively expressible qualities of processes, e.g., ‘quantity’, ‘one’, ‘addition’, etc. are explicable, respectively, as the qualities: ‘being a specific quantity’, ‘being a unity’, ‘togetherness of two or more units’, etc. The other kind is (2) the ontological qualities of processes in general (say, malleability, toughness, colour, redness, etc.) which cannot directly be expressed as ontological quantities of processes. This shows that pure ontological qualities are a more general notion than ontological quantities and includes the latter.
Explaining ontological qualities in terms of physical quantities cannot be done directly by fundamental physical quantities, but by physical properties that involve fundamental physical quantities. Properties are a mix mainly of ontological qualities and of course includes ontological quantities, of which some are the fundamental physical quantities. Hence, the invariants must be qualities that are generative of and apply to both quantities and non-quantities. These invariants then are fully qualitative.
If the invariants apply to all physical processes, these invariants are qualities ontologically universal to all of them in the specified group. Out of them are constructed properties by mixing many qualitative and quantitatively qualitative universals. Clearly, universals applying to all existents are the real invariants of all Reality – which is a matter to be discussed later.
Since universals are all qualitative and some of them are quantitative as qualities, ontological qualities are broader than mathematical in scope, because, the moment mathematics uses quantities, the use is not of quantities devoid of qualities, but instead, of the quantitative variety of general / universal qualities.
Qualities can also behave as some of the primitive notions that underlie all of physics and other sciences – but this will not exhaust the most necessary foundations of physics and other sciences, because these sciences require the general qualities of all existents, and not merely those of mathematics. These are the axiomatically formulable Categorial notions of philosophy, which latter is thus a general science.
In short, quantitative proportionalities as invariants are very partial with respect to existent processes and their totality. Naturally, philosophy too needs general qualities and not merely quantitative qualities to base the discipline.
Bibliography
(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.
(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.
(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.
(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.
(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.