HOW TO GROUND SCIENCE AND PHILOSOPHY TOGETHER AXIOMATICALLY?
Raphael Neelamkavil, Ph.D., Dr. phil.
We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. They call themselves or attempt to be as quantitative as possible. But are adequate comparisons between mathematics, physical sciences, biological sciences, human sciences, and philosophy, and adequate adaptation of the axiomatic method possible by creating a system of all exact, physical, and human sciences that depend only on the quantitively qualitative proportionalities and call them invariables?
They cannot do well enough to explain Reality-in-total, because Reality-in-total primarily involves all sorts of ontological universals that are purely qualitative, and some of them are the most fundamental, proportionality-type, quantitative invariables of all physical existents in their specificity and totality in their natural kinds. But as the inquiry comes to Reality-in-total, ontological qualitative universals must come into the picture. Hence, merely quantitative (mathematical) explanations do not exhaust the explanation of Reality-in-total.
Existence as individuals and existence in groups are not differentiable and systematizable in terms of quantitatively qualitative universals alone. Both qualitative and quantitatively qualitative universals are necessary for this. Both together are general qualities pertaining to existents in their processual aspect, not merely in their separation from each other. Therefore, the primitive notions (called traditionally as Categories) of Reality-in-total must be ontological qualitative universals involving both the qualitative and quantitative aspects. The most basic of universals that pertain properly to Reality-in-total are now to be found.
Can the primitive notions (Categories) and axioms of the said sciences converge so that the axioms of a system of Reality take shape from a set of the highest possible ontological Categories as simple sentential formulations of the Categories which directly imply existents? This must be deemed necessary for philosophy, natural sciences, and human sciences, because these deal with existents, unlike the formal sciences that deal only with the qualitatively quantitative form of arguments.
Thus, in the case of mathematics and logic there can be various sorts of quantitative and qualitative primitive notions (categories) and then axioms that use the primitive notions in a manner that adds some essential, pre-defined, operations. But the sciences and philosophy need also the existence of their object-processes. For this reason, the primitive axioms can be simple sentential formulations involving the Categories and nothing else. This is in order to avoid indirect existence statements and to involve existence in terms exclusively of the Categories.
Further, the sciences together could possess just one set of sufficiently common primitive notions of all knowledge, from which also the respective primitive notions and axioms of mathematics, logic, physical and human sciences, and philosophy may be derived. I support this view because the physical-ontological Categories involving the existence of Reality and realities, in my opinion, must be most general and fully exhaustive of the notion of To Be (existence) in a qualitatively universal manner that is applicable to all existents in their individual processual and total processual senses.
Today the nexus or the interface of the sciences and philosophies is in a crisis of dichotomy between truth versus reality. Most scientists, philosophers, and common people rush after “truths”. But who, in scientific and philosophical practice, wants to draw unto the possible limits the consequences of the fact that we can at the most have ever better truths, and not final truths as such?
Finalized truths as such may be concluded to in cases where there is natural and inevitable availability of an absolute right to use the logical Laws of Identity, Contradiction, and Excluded Middle, especially in order to decide between concepts related to the existence and non-existence of anything out there.
Practically very few may be seen generalizing upon and extrapolating from this metaphysical and logical state of affairs beyond its epistemological consequences. In the name of practicality, ever less academicians want today to connect ever broader truths compatible to Reality-in-total by drawing from the available and imaginable commonalities of both.
The only thinkable way to accentuate the process of access to ever broader truths compatible to Reality-in-total is to look for the truest possible of all truths with foundations on existence (nominal) / existing (gerund) / To Be (verbal). The truest are those propositions where the Laws of Identity, Contradiction, and Excluded Middle can be applied best. The truest are not generalizable and extendable merely epistemologically, but also metaphysically, physical-ontologically, mathematically, biologically, human-scientifically, etc.
The agents that permit generalization and extrapolation are the axioms that are the tautologically sentential formulations of the most fundamental of all notions (Categories) and imply nothing but the Categories of all that exist – that too with respect to the existence of Realit-in-total. These purely physical-ontological implications of existence are what I analyze further in the present work. One may wonder how these purely metaphysical, physical-ontological axioms and their Categories can be applicable to sciences other than physics and philosophy.
My justification is as follows: Take for example the case of the commonality of foundations of mathematics, logic, the sciences, philosophy, and language. The notions that may be taken as the primitive notions of mathematics were born not from a non-existent virtual world but instead from the human capacity of spatial, temporal, quantitatively qualitative, and purely qualitative imagination.
I have already been working so as to show qualitative (having to do with the ontological universals of existents, expressed in terms of adjectives) quantitativeness (notions based on spatial and temporal imagination, where, it should be kept in mind, that space-time are epistemically measuremental) may be seen to be present in their elements in mathematics, logic, the sciences, philosophy, and language.
The agents I use for this are: ‘ontological universals’, ‘connotative universals’, and ‘denotative universals’. In my opinion, the physical-ontological basis of these must and can be established in terms merely of the Categories of Extension-Change, which you find being discussed briefly here.
Pitiably, most scientists and philosophers forget that following the exhaustively physical-ontological implications of To Be in the foundations of science and philosophy is the best way to approach Reality well enough in order to derive the best possible of truths and their probable derivatives. Most of them forget that we need to rush after Reality, not merely after truths and truths about specific processes.
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.
The text of this discussion is short, but requires attentive reading. I suggest that it will pay rich dividends to your academic activity, no matter whether you are a scientist or philosopher.
Symmetry: A Subset of Universal Causality. The Difference between Cause and Reason
https://www.researchgate.net/post/Symmetry_A_Subset_of_Universal_Causality_The_Difference_between_Cause_and_Reason
This discussion-text is just 2.5 pages, but intense. Meant for those who are interested in a clear presentation of what symmetry and symmetry breaking are, and of how physicists and mathematicians tend to misunderstand and/or misuse these concepts.
The Universally Causal context of the concept of symmetry is explained in terms of a solidly founded system of differentiation between cause and reason.
Dr Raphael you wrote among other things:
"Both qualitative and quantitatively qualitative universals are necessary for this. Both together are general qualities pertaining to existents in their processual aspect, not merely in their separation from each other. Therefore, the primitive notions (called traditionally as Categories) of Reality-in-total must be ontological qualitative universals involving both the qualitative and quantitative aspects. The most basic of universals that pertain properly to Reality-in-total are now to be found."
Well as electrical engineer after having texted the use of complex numbers in a real time control center, determining the state of hundred of interconected nodes in a power system, that system on which we all depend, I knew that the real problem with physics with QM, and specially, the duality of wave particle, which I heard it was solved when Schrödinger presented his famous complex equation; I started in 1991, a work trying to deduce the fundamental equations of physics, based on complex numbers that were based on Euler's relation, the most beautiful equation of mathematics, as it included all numbers, even infinity as it was found when Euler was working with infinite series, so as electrical engineer, working always with energy, I knew, that duality presented in its treatment, i.e., real power and reactive power, that can only can be treated with complex numbers, being the real power more of the sort quantitative, and reactive power with its sort of strange behavior can be seen as qualitative, because sometimes its behavior is strange...So in 1991, I started to work in project that finally took me to deduce all the fundamental equations of physics, starting with pendulum formula, that as pointed out Thomas S. Kuhn:
"How else are we to account for Galileo's discovery that the bob's period is entirely independent of amplitud, a discovery that the normal science steamming from Galileo had to eradicate and that we are quite unable to document today."
This deduction can be found in my paper The Principle of Synergy and isomorphic unit unit, a revised version. In fact the Principle of synergy can be applied to all levels of reality, the physical, the biological, and the ontological, so both the qualitative and the qualitative, are included in a Basic Unit System concept, based on Euler's Relation, with which Schrödinger Wave equation can be deduced too, as is shown in that same paper. Evidently for this is necessary a real paradigm shift, not reductionist anymore. In this respect Edgar Morin wrote:
"... The real is even more unfathomable than death: if anything, it has been possible to find reasons for death, such as the second principle of thermodynamics, but no "reason for being" has yet been found. Thus, in humanity, the myth is born not only from the abyss of death, but also from the mystery of being".
Both the isomorphism of principles and laws in the different levels of reality, and the fact that in all of them we find order, organization and beauty, is what makes us think of the possibility of a unified science based not precisely on "a particle of God" or on an ultimate component of matter that would give us the key to everything and therefore reductionist in its very philosophical starting point, but on a unifying conceptual principle, such as the same principle of synergy, which presents the possibility of being applied at different levels of reality, just like a good engineering tool, in which the reductionist character that can lead us to meaningless analogies or to damage with the tool the very thing we intend to reconstruct or repair, must necessarily be absent.
Dr. Edgar Paternina, thanks for the intervention. Although the concept of the qualitative is different from what you seems to have understood, I should thank you with great joy that you opened up for me a few more new insights. I have just jotted down those new insights. But it will take a few years before I develop them.
Now as to what is qualitative: Anything that we can speak of the many members of a natural kind can be either a pure quality or a composition of many qualities. Any notion that we can find to be not composed of more than one attribute of the members of one and the same natural kind is a quality. Having color, having the color red, etc. may be treated as pure qualities. But having the color red in a context (say, chemical, biological, etc.) already implies the composition of more than one color with each other in the concept. This is a property.
I remain very general about these things because I do not find enough clarity about this in none of the physicists and philosophers that I know. Of course, my knowledge and acquaintance are very limited.
Please note again: Most of the attributes that we find in common parlance and also in the sciences (say, the attributes of a chemical substance) are all properties, and not qualities. Properties are the concatenation of a quality composed with other related qualities.
The Fallacies of Space, Time, and Spacetime in Physics
https://www.researchgate.net/post/The_Fallacies_of_Space_Time_and_Spacetime_in_Physics
Physical and Exact Sciences and Axiomatic Philosophy: Introducing Grounding (long text)
https://www.researchgate.net/post/Physical_and_Exact_Sciences_and_Axiomatic_Philosophy_Introducing_Grounding_long_text
There are common principles like that of sufficient reason. The rest is -- politely, I'm silent. See the difference between maths and physics, e.g. Huygens, Traité de la Lumière.
Raphael Neelamkavil
I have replied to your cited text as follows:
You: "This is similar in effect to Newton and his followers thinking honestly and religiously that at least gravitation and perhaps also other energies are just miraculously non-bodily actions at a distance without any propagation particles / wavicles."
My reply: This is just wrong, read the 'Definitions' in the 'Principia' and other texts by Newton ('Principia', letters to Bentley). It is thus not necessary to read more of your text if you are so careless in this fundamental issue.
If you go a little deep into the various contemporary logics, you will know that the principle of sufficient reason is not to have the same effect in every situation.
Newton, Huygen, etc. have lived in an era where this has not been recognized. Hence the crude nature of their definitions.
I agree in the sense that the pioneers beat cutting through the thicket - roads are built later.
``Since the Principia is one of those works everyone talks of but no one reads, anything said about it other than the usual honey-sauced eulogy must stand up against righteous indignation from all sides. But it is a work of science, not a bible. It should be studied and weighed—admired, indeed, but not sworn upon. It has its novelties and its repetitions, its elegant perfections and its errors, its lightning abbreviations and its needless detours, its extraordinary standards of rigor and its logical gaps, its elimination of stated hypotheses and its introduction of unstated ones.''
(Truesdell, Essays in the History of Mechanics, 1968, 88 quoted after Simonyi, A Cultural History of Physics, 2012, Quotation 4.12, p. 307)
Anyway, Newton's formula for the force of gravity is a mathematical expression. It is useful fapp in his time but it is not a physical theory.
"But it is a work of science, not a bible. It should be studied and weighed—admired, indeed, but not sworn upon. It has its novelties and its repetitions, its elegant perfections and its errors, its lightning abbreviations and its needless detours, its extraordinary standards of rigor and its logical gaps, its elimination of stated hypotheses and its introduction of unstated ones."
I FULLY AGREE.
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https://www.researchgate.net/post/Causality_and_Statistics_Their_Levels_of_Effect_and_of_Explanation
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https://www.researchgate.net/post/Einstein-Podolsky-Rosen_Paradox_and_Non-Locality_Is_Einstein_a_Monist
Spacetime Curvatures, Gravitational Waves, Gravitons, and Anti-Gravitons: Do They All Exist?
https://www.researchgate.net/post/Spacetime_Curvatures_Gravitational_Waves_Gravitons_and_Anti-Gravitons_Do_They_All_Exist
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https://www.researchgate.net/post/The_Fate_of_Source-Independence_in_Electromagnetism_Gravitation_and_Monopoles
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https://www.researchgate.net/post/The_Ontology_behind_Physics
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