PHYSICAL AND EXACT SCIENCES AND AXIOMATIC PHILOSOPHY:

INTODUCING GROUNDING

Raphael Neelamkavil, Ph.D., Dr. phil.

1. WHY SHOULD PHYSICS AND COSMOLOGY BE GROUNDED?

I get surprised each time when some physicists tell me that either the electromagnetic (EM) or the gravitational (G) or both the forms of energy do not exist – that EM and G are, are "existent" neither like nor unlike material bodies – but that EM and G are to be treated or expressed as mathematical waves or particles propagated from material objects that of course exist for all sciences.

Some of them put in all their energies to show that both EM and G are mere mathematical objects, fields, etc., and not physically existent objects or fields of energy emissions that then become propagations from material bodies. If propagation from material bodies, then their nature too would have to be similar to that of material bodies!!! This is something that the mathematical realists of theoretical physics and cosmology cannot bear!!!

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. But I admit that I explained certain things in the first paragraph above as if I myself were a Newtonian. This has been on purpose.

Even in the 21st century, we must be sharply aware that from the past more than 120 years the General Theory of Relativity with its various versions and especially its merely mathematical interpretations have succeeded in casting and maintaining the power of a terrifying veil of mathematical miracles on the minds of many scientists – miracles such as the mere spacetime curvature being the meaning of gravitation and all other sorts of fields. The mathematics did not need existence, and hence gravitation did not exist! But the same persons did not create a theory whereby the mathematics does not need the existence of the material world and hence the material world does not exist!!

A similar veil has been installed by quantum physics on the minds of many physicists and their audience too. We do not discuss it here. Hence, I have constructed in four published books a systemic manner of understanding these problems in cosmology and quantum physics. I do not claim perfection in any of my attempts. Hence, I keep perfecting my efforts in the course of time, and hope to achieve some improvement. The following is a very short attempt to summarize in this effort one important point in physics, cosmology, and the philosophy of physics and of cosmology.

There exists the tradition of lapping up whatever physicists may say about their observable and unobservable constructs, based on their own manner of using mathematics. The mathematics used are never transparent. Hence, the reader or the audience may not have the ability to makes judgements based on the minimum physical ontology expected of physicists. I believe that this should stop forever at least in the minds of physicists. Moreover, physicists are not to behave like magicians. Their readers and audience should not practice religious faithfulness to them. Nor should physicists expect it from them.

2. ONTOLOGICALLY QUALITATIVE NATURE OF INVARIANTS

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.

3. DIFFERENCES IN FOUNDATIONS: EXACT AND NATURAL SCIENCES AND PHILOSOPHY

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 Reality-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.

4. SYSTEMIC FOUNDATIONS VS. EXISTENCE/TS, NON-EXISTENCE/TS

4.1. Basis of Axiomatizing Science and Philosophy

The problem of axiomatizing philosophy, and/or philosophy of science, and/or all the sciences together is that we need to somehow bring in the elemental aspects of existence and existents, and absorb the elemental aspects of non-existence and non-existent objects that pertain to existents. Here it should be mentioned that axiomatizing mathematics and logic does not serve the axiomatization of philosophy, and/or philosophy of science, and/or all the sciences together. So far in the history of philosophy and science we have done just this, plus attempts to axiomatize the sciences separately or together by ignoring the elemental aspects of non-existence and non-existent objects that pertain to existents.

Existence (To Be) is not a condition for the possibility of existence of Reality-in-total or specific processual objects, but instead, To Be is the primary condition for all thought, feeling, sensation, dreaming, etc. All other conditions are secondary to this. If To Be is necessary as the condition for the possibility of any philosophy and science as discourse, we need to be axiomatic in philosophy and science about (1) existence (To Be, which is of all that exist) and/or (2) the direct and exhaustive implications of existence.

It is impossible to define existence without using words that involve existence. But it is possible to discover the exhaustive implications of To Be in order to use them in all discourse. Therefore, towards the end of this short document, I shall name what could be the inevitable primitive notions that are exhaustive of To Be and that may be used to create axioms for both philosophy and science together.

To put it differently, I attempt here to base all philosophy and science on the concept of existence of Reality-in-total as whatever it is, by deriving from the concept of the existence of all that exist the only possible (i.e., the exhaustive) implications of To Be.

Of course, the basic logical notions of identity and contradiction will have to be used here without as much danger as when we use them in statements on other less fundamental notions. I would justify their use here as the rational inevitabilities in the foundations – not as inevitabilities in the details that issue later. The inevitabilities in the later details need never to be realized as inevitabilities, because To Be implies some fundamental notions which will take case of this.

That is, the various ways in which the principles of identity and contradiction should be seen as inexact and inappropriate may be discovered in the in fields of derivation beyond the provinces of the fundamental Categorial implications of To Be. This latter part of the claims is not to be discussed here, because it involves much more than logic – in fact, a new conception of logic, which I would term as systemic logic.

Let me come to the matter that I promise in the name of the foundations of ‘Axiomatic Philosophy and Science’. First of all, to exist is not to be merely nothing. In this statement I have taken access to the Laws of Identity, Non-Contradiction, and Excluded Middle at one go in that whatever is, must be whatever it is, and not its opposite which is nothing but nothing, nor a middle point between the two extremes.

Therefore, existence must always be non-vacuous. That is, the primary logical implication of To Be is the non-non-being of whatever exists. But such a logical implication is insufficient for the sciences and philosophy, because we deal there with existents. Hence, let us ignore the logical implication as a truism. The existential implications of To Be are what we need.

I have so far not found any philosopher or scientist who derived these implications. But let us try, even if the result that obtained may be claimed by many ancients and others as theirs. In fact, theirs were not metaphysical / physical-ontological versions. Their epistemic versions of the same have been very useful, but have served a lot to misguide both philosophy and science into give “truth/s” undue importance in place of “Reality”. My claim about the exhaustive physical(-ontological) implications of To Be that I derive here is that they do not incur this fallacy.

To Be is not a thing. It is, as agreed at the start, the very condition for the possibility of discourse: philosophy, science, literature, art … and, in general, of experience. The To Be of existents is thus not a pre-condition for To Be – instead, it is itself the source of all conditions of discourse, not of existence.

4.2. Extension, Change, Universal Causality

If To Be is non-vacuous, it means that all existents are something non-vacuously real. Something-s need not be what we stipulate them to be, both by name and qualifications. But the purely general implication is that existents are something-s. This is already part of philosophical activity, but not of the sciences. We need to concretize this implication at the first tire of concrete implications. Only thereafter are sciences possible.

To be something is to be non-vacuous, i.e., to be in non-vacuous extendedness. However much you may attempt to show that Extension does not follow from the notions of To Be, something, etc., the more will be extent of your failure. You will go on using the Laws of Identity, Contradiction, and Excluded Middle, and never reach any conclusion useful for the sciences. Then you will have to keep your mouth and mind shut. I prefer for myself meaningful discourse in science and philosophy – when I meditate I shall attempt to keep my mind and lips as “shut” as possible.

As said above, Extension is one of the primary physical-ontological implications of To Be. Nothing exists without being extended, without being in Extension. Extended something-s are not just there in Extension. If in Extension, everything has parts. Thus, having parts is one of the primary implications of being something in existence. I term it alternatively also as Compositionality.

It is the very implication of being something that something-s are in Change. The deepest and most inevitable form of implication of Change is this: nothing that is in existence with parts can have the status of being something existent without the parts impacting at least a few others. This is the meaning of Change: impact-formation by extended parts. Any existent has parts existing in the state of impact formation in other parts and in themselves.

Hence, Change is the only other implication of To Be, not second to but equally important as Extension. I call it differently also as Impact-Formation. The notion of motion or mobility does not carry the full weight of the meaning of Change.

There cannot be any other implication equally directly derivable from To Be as Extension and Change can be. In other words, all other implications can be found to be sub-implications of Extension-Change, i.e., involving only Extension-Change. Showing them as involving only Extension-Change would suffice to show their sub-implications status with respect to Extension-Change.

Existence in Extension-Change belongs to anything existent, hence ubiquitous – to be met with in any existent. This is nothing but existence in the ubiquitously (to be met with in any existent) extended form of continuance in ubiquitous (to be met with in any existent) impact formation. What else is this but Universal Causality?

If you say that causation is a mere principle of science – as most philosophers and scientists have so far thought – I reject this view. From the above paragraphs I conclude that Causation is metaphysically (physical-ontologically) secondary only to existence. Everybody admits today that we and the universe exist. But we all admit that every part of our body-mind and every existent in the world must be causal because we are non-vacuously existent in Extension-Change.

This means that something has been fundamentally wrong about Causality in philosophy and science. We need to begin doing philosophy and science based fully on To Be and its implications, namely, Extension-Change-wise continuance, which is nothing but being in Universal Causation. It is universal because everything is existent. Universal Causality is the combined shape of Extension-Change. Causation the process of happening of Extension-Change-wise continuance in existence. Causality is the state of being in Extension-Change-wise continuance in existence.

4.3. Now, What Are Space and Time?

Note that what we measurementally and thus epistemically call as space is metaphysically to be termed as Extension. Space is the measuremental aspect of the primary quality of all existents, namely, of Extension. That is, space is the quantity of measurement of Extension, of measurements of the extended nature of existents. In this sense, space is an epistemic quality.

Further, note also that what we call time is the measuremental aspect of the primary quality of all existents, namely, of Change. If there is no impact-formation by parts of existents, there is no measurement called time. Hence, time is the epistemic quality of measurements of Change, which is the impact-formation tendency of all existents.

Immanuel Kant termed space as the condition for the possibility of sensibility, and Edmund Husserl called it as one of the fundamental essences of thought. Space and time in Kant are epistemic since they are just epistemic conditions of possibility; and essences in Husserl are epistemic, clearly as they are based on the continuous act of epochḗ.

Nothing can exist in epistemic space-time. That is, language and mind tend to falsely convert space and time into something that together condition existents. Thus, humans tend to believe that our measuremental concepts and derivative results are all really and exactly very essential to existent something-s, and not merely to our manner of knowing, feeling, sensing, etc.

This is the source of scientific and philosophical misconceptions that have resulted in the reification of the conclusions and concepts of thought and feeling. Thus, this is also the source of conceptual insufficiencies in philosophical and scientific theories. Scientism and scientific and mathematical instrumentalism justify these human tendencies in the name of pragmatism about science and thought.

Reification of certain statistical conclusions as probabilities and the metaphysicization of probable events as the only possible events are not merely due to the above sort of reification. It is also by reason of the equivocation of probability with possibility and the reification of our scientific and statistical conclusions of probabilities as real possibilities. Humans tend to forget that a certain amount of probability is exactly and properly the measure of the extent of human capacity (and by implication, of human incapacity), at a given instance and at a given measuremental moment of history, to use instruments to get at all the existents that are the causes of a given process.

As we know, To Be is not a Category / Quality. It is the very condition that is the same as the existence of something-s as whatever they are. This is a tautology: To Be is To Be. If To Be is a metaphysical notion, the physical-ontologically and scientifically relevant metaphysical implications of To Be are Extension-Change. These are the highest and only highest Categories of all philosophy and science. Universal Causality is the notion of combination of Extension-Change. It is not an indirectly derived notion.

If scientists tend to relegate such notions as philosophical, they are trying to be practical in a silly manner. Even scientific results need the hand of proper and best possible formulations of notions and theoretical principles. Theoretical principles (say, of causation, conservation, gravitation, matter, mass, energy, etc., which may clearly be formulated in terms of Extension-Change-wise existence and existents) must be formulated in the most systemic manner possible.

I would call Extension, Change, and the combination-term Universal Causality not merely as the highest metaphysical Categories. They are the very primitive terms in addition to terms like ‘existent’, ‘matter-energy’, etc., which are necessary for an axiomatic formulation of the foundations of the sciences. Hence, we need to formulate axiomatically both philosophy and science.

Universal Causality may hereafter also be taken as an axiom in philosophy and the sciences. An axiom is a formulated basic principle. In that case, why not formulate also the primitive notions (Categories) of Extension and Change as axioms? In short, the difference between mathematical-logical axiomatic foundations and physical-philosophical axiomatic foundations is that in the former set primitive notions are not axioms, and in the latter primitive notions may be formulated as axioms.

In the light of the above discussion, it becomes clear that Einstein’s postulation of gravitation and matter-energy as space-time curvatures is at the most a formulation of these notions in terms of the mathematical necessity to use space-time (epistemic) measurements and theorize based on them in theoretical physics.

Einstein was immersed in the neo-positivism and logical positivism of his time. Hence, he could not reason beyond the use, by mathematics, of quantitative notions as concrete measurements. Scientists and philosophers who still follow Einstein on this sort of a misguided reification of epistemic space and time are taking refuge not on Einstein but on his theoretical frailties. Even today most scientists and philosophers are unaware that quantities are in fact quantitatively characterized pure qualities – and not properties that are combinations of qualitative and quantitatively qualitative notions.

Minkowski formulated the mathematics of space-time and thus reduced space-time into a sort of ether in which physical processes take place gravitationally. Einstein put gravitation into this language and mistook this language (the language of mathematical space-time) to be the very matter-energy processes that curve according to gravitational processes. For the mathematics this is no too great error, because it worked. This is why some physicists even today consider gravitation and/or all energy forms as ether, as if without this stuff in the background material bodies would not be able to move around in the cosmos! A part of the cosmos is thus being converted into a background conditioner!

Only formal functioning has so far been found necessary in mathematics. Derivation from the metaphysical sources of existents and non-existents has not so far been found necessary in mathematics. But, note here also this: for more than 100 years physicists and philosophers of physics lapped up this substitution of the language of mathematics for the actual, physically existent, processes, which otherwise should have been treated also metaphysically, and if possible, in a manner that is systemically comprehensive of the sources of all sciences.

The implications of existence, non-existence, existents, and non-existents too can help to make the mathematical adaptations work pragmatically. Hence, clearly it does not suffice that only the mathematical formalism attained so far be used in physics and the sciences. The project of science, philosophy, mathematics, and logic must grow out of their limits and become parts of a systemic science with foundations in the implications of existence, non-existence, existents, and non-existents.

I have been attempting to explain in these pages a limited realm of what I otherwise have been attempting to realize. I show only that there are two physical-ontological Categories and some derived axioms (out of these many axioms, only one is discussed here, i.e., Universal Causality), using which we need to formulate not merely philosophy but also physics and other sciences.

But I suggest also that the existence-related and non-existents-related mathematical objects too must be formulated using some primitive terms and axioms that are compatible with the philosophical and physical primitive terms and axioms that may facilitate a systemic approach to all sciences.

4.4. Why Then Is Science Successful?

The awarding of the Nobel Prize 2023 for quantum informatics to Alain Aspect, John F. Clauser, and Anton Zeilinger does not, therefore, mean that all of quantum physics and their assumptions and results are ‘the realities’ behind the ‘truths’ formulated. Instead, it means only that the truths they have formulated are relatively more technology-productive within the context of the other truths and technologies that surround them in physics. Quantum informatics works at a level of effects where we involve only those movements and processes that result in the resulting discoveries, general truths, and the derivative technology.

Similarly, the successes of engineering, informatics, medical processing technology, and the medical science that (as of today) are based on these need not be a proof for the alleged “absolute truth status” of the theories based on Newtonian physics, of molecular and atomic level chemistry and biology, etc. These sciences use only certain contextual levels of interaction in the physical world.

Recollect here the ways in which occidental philosophers dating at least from Parmenides and Heraclitus and extending up until today have been mistaking space and time as (1) two metaphysical categories, or (2) as mere existents, or (3) as illusions.

Oriental philosophies, especially Hindu and Buddhist, have been the best examples of rejecting space-time as metaphysical and as equivalent to permanent substances in a manner that made some Occidental thinkers to look down on them or to reject all of them. In the course of conceptualization that is typical of humans, having to create further theoretical impasses is necessarily to be avoided as best as we can. Such an ideal requires the help of Extension, Change, and Universal Causality.

In the foregoing paragraphs I have only hinted at the necessity of axiomatic philosophy and science. I have only suggested some basic notions in this systemic science. I do also use these notions and some axioms developed from them to formulate a new philosophy of mathematics. I have already published some books based on these and have been developing other such works. I hope to get feedbacks from earnest minds that do not avoid directly facing the questions and the risk of attempting a reply to the questions themselves.

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.