MATHEMATICS AND CAUSALITY:

A SYSTEMIC RECONCILIATION

Raphael Neelamkavil

What are the bases of the problem of incompatibility of causality with mathematics and its applications? I suggest that it is the dichotomy between mathematical continuity and discreteness on the one hand and the incompatibility of applying any of them directly on the data collected / collectible from some layers of phenomena from some layers of nature. I clearly point at the avoidance, by expressions like ‘from some layers of phenomena from some layers of nature’, of the centuries of epistemological foolishness, because this is the point at which phrases and statements involving ‘data from observation’, ‘data from phenomena’, ‘data from nature’ etc. are very gross, without epistemological and ontological astuteness.

If causal continuity between partially discrete “processual” objects is the case, then the data collected / collectible cannot be the very processual objects or provide all knowledge about the processual objects. But mathematics and all other research methodologies are based on human experience and thought based on experience. Hence, it is important to define the limits of applicability of mathematics to the physics of data is the only way to approximate beyond the data and the methodologically derived conclusions beyond the data.

The same may be said also about logic and language. Logic is the broader rational picture of mathematics. Language is the symbolic manner of application of both logic and its quantitatively qualitative version, namely, mathematics, with respect to specific fields of inquiry. Here I do not explicitly discuss ordinary conversation, literature, etc. We may do well to instantiate logic as the formulated picture of reason. But reason is limited to the procedures of reasoning by brains. What exactly is the reason that existent physical processes undergo? How to get at conclusion based on but beyond data and methods? If we may call the universal reason of Reality-in-total with a name, it is nothing but Universal Causality.

How to demonstrate this as the case? ((To be developed further.))

A caveat is in place here: When I write anything here, you have the right to ask me constantly for further justifications. And if I have the right to anticipate some such questions, I will naturally attempt to be as detailed and as systemic as possible in my formulation. Each sentence is merely a part of the formulation. After reading each sentence you may pose me questions, which certainly cannot all be answered well within the sentences or after the sentences in question.

Hence, I tend to be as systemic as possible in each of the following sentences. Please do not accuse me of being too complex in my expressions. Your (and our) mathematics, physics, and logic can be very complex and prohibitive for some. But would we all accuse these disciplines or the readers if the readers find them all complex and difficult? I do not create such a state of affairs in these few sentences, but there are complexities here too. Hence, I express my helplessness in case any one of you finds these statements complex.

Insistence on mathematical continuity in nature is a mere idealization. It expects nature to obey our merely epistemic idealization where processes outside are vaguely presented primarily by the processes themselves in a natural manner, represented by the epistemic activity of the brain in a natural manner, and idealized via concepts expressed in words and sentences by the symbolizing human tendency to capture the whole of the object by use of a part of the human body-mind. The symbolizing activity is based on data, but the data are not all we have.

Insistence on mathematical continuity in nature as a natural conclusion by application of mathematics to nature is what happens in all physical and cosmological (and of course other) sciences insofar as they use mathematical idealizations to represent existent objects and processes. Logic and its direct quantitatively qualitative expression as found in mathematics are powerful tools. But, as being part of the denotative function of symbolic language, they are tendentially idealizational. By use of the same symbolizing tendency, it is perhaps possible to a certain extent to de-idealize the same symbols in the language, logic, and mathematics being used to symbolically idealize representations.

Merely mathematically following physical nature in whatever it is in its part-processes is a debilitating procedure in science and philosophy (and even in the arts and humanities), if this procedure is not de-idealized effectively. If this is possible at least to a small and humble extent, why not do it? Our language, logic, and mathematics too do their functions although they too are equally unable to capture the whole of reality in whatever it is, wholly or in in parts, too far beyond the data and their interpretations!

This theoretical attitude of partially de-symbolizing the effects of human symbolizing activity by use of the same symbolic activity accepts the existence of processual entities as whatever they are. Perhaps such a generalization can give a slightly better concept of reality than is possible by the normally non-self-aware symbolic activity in language, logic, and mathematics!

This theoretical attitude facilitates and accepts in a highly generalized manner the following three points:

(1) Mathematical continuity (in any theory and in terms of any amount of axiomatization of logical, mathematical, physical, biological, social, and linguistic theories) is totally non-realizable in nature as a whole and in its parts: because (a) the necessity of mathematical approval of any sort of causality in such a cosmology and by means of its systemic physical ontology falls short miserably in actuality, and (b) logical continuity of any kind does not automatically make symbolized representation activity adequate enough to represent the processual nature of entities as derivate from data.

(2) Absolute discreteness in nature, which, as of today, is ultimately of quantum-mechanical type based on Planck’s constant, continues to be a mathematical and physical misfit in the physical cosmos and its parts (may not of course be so in non-quantifiable “possible worlds” due to their absolute causal disconnection) and is a mere common-sense mathematical compartmentalization: (1) because the aspect of the causally processual connection between any two quanta is logically and mathematically alienated in the physical theory of Planck’s constant, and (2) by reason of the “epistemology of box-type thinking” (see Ruth Edith Hagengruber, Uni-Paderborn) implied by the non-self-aware symbolic activity of body-minds.

(3) Hence, the only viable and thus the most reasonably generalizable manner of being of the physical cosmos and of biological entities is that of existence in an extended (having parts) and changing (extended entities and their parts impacting a finite number of others in a finite amount) manner. Existence in Extension-Change-wise manner is nothing but causation. Thus, every existent is causal. There is no minute measuremental iota of time wherein such causal existing ceases in any existent. this is CAUSAL CONTINUITY BETWEEN PARTIALLY DISCRETE PROCESSUAL OBJECTS.

The attitude of treating everything as causal my also be characterized by the self-aware symbolic activity by symbolic activity itself, in which certain instances of causation are avoided or increased or avoided incrementally. This is at the most what may be called freedom. It is fully causal, but causal not in a specific set of manners and causal in some other specific set of manners.

PHYSICS and COSMOLOGY even today tend to make the cosmos either (1) mathematically presupposedly continuous, or (2) discrete with defectively ideal mathematical status for continuity and with perfectly geometrical ideal status for specific beings, or (3) statistically indeterministic, thus considered partially causal, or even considered non-causal in the interpretation of statistics’ orientation to epistemically logical decisions and determinations based on data. If not, can anyone suggest proofs for an alleged existence of a different sort of physics and cosmology until today?

A topology and mereological physical ontology of CAUSAL CONTINUITY BETWEEN PARTIALLY DISCRETE PROCESSUAL OBJECTS, fully free of discreteness-oriented category theory, geometry, functional analysis, set theory, and logic, are yet to be born. Hence, the fundamentality of Universal Causality in its deep roots in the very concept of the To Be (namely, in the physical-ontological Categories of Extension and Change) of all physically and non-vacuously existent processes, is yet alien to physics and cosmology till today.

LINGUISTIC PHILOSOPHY and even its more recent causalist child, namely, DISPOSITIONALIST CAUSAL ONTOLOGY (1) attribute an overly discrete nature to “entities” without ever attempting to touch the deeply Platonic (better, geometrically atomistic) shades of common-sense Aristotelianism, Thomism, Newtonianism, Modernism, Quantum Physics, etc., and without reconciling the diametrically opposite geometrical tendency to make every physical representation continuous, (2) logically comatose about the impossibility of linguistically definitional approach to the processual demands of existent physical objects without first analyzing and resolving the metaphysical implications of existent objects irreducibly being in finite EXTENSION and CHANGE, and (3) hence, unable to get at the CAUSALLY CONTINUOUS (neither mathematically continuous nor geometrically discontinuous) nature of the physical-ontologically “partially discrete” processual objects in the physical world.

PHENOMENOLOGY has done a lot to show the conceptual structures of ordinary reasoning, physical reasoning, mathematical and logical thinking, and reasoning in the human sciences. But due to its lack of commitment to building a physical ontology of the cosmos and due to its purpose as a research methodology, phenomenology has failed to an extent to show the nature of causal continuity (instead of mathematical continuity) in physically existent, processually discrete, objects in nature.

HERMENEUTICS has just followed the human-scientific interpretative aspect of Husserlian phenomenology and projected it as a method. Hence, it was no contender to accomplish the said fete.

POSTMODERN PHILOSOPHIES qualified all science and philosophy as being perniciously cursed to be “modernistic” – by thus monsterizing all compartmentalization, rules, laws, axiomatization, discovery of regularities in nature, logical rigidity, etc. as an insurmountable curse of the human project of knowing and as a synonym for all that are unapproachable in science and thought. The linguistic-analytic philosophy in later Wittgenstein too was no exception to this nature of postmodern philosophies – a matter that many Wittgenstein followers do not notice. Take a look at the first few pages of his Philosophical Investigations, and the matter will be more than clear.

THE PHILOSOPHIES OF THE SCIENCES seem today to follow the beaten paths of extreme pragmatism in linguistic-analytic philosophy, physics, mathematics, and logic, which lack a FOUNDATIONAL CONCEPT OF CAUSALLY CONCRETE AND PROCESSUAL PHYSICAL EXISTENCE.

Hence, it is useful for the growth of science, philosophy, and humanities alike to research into the CAUSAL CONTINUITY BETWEEN PARTIALLY DISCRETE “PROCESSUAL” OBJECTS.

https://www.researchgate.net/post/Mathematical_Continuity_in_Nature_Vs_Causal_Continuity_between_Partially_Discrete_Processual_Objects_Have_patience_to_read_till_the_end

Humans in this age, by inventing and using mathematical models and trying to match them with natural phenomena, are free to know the world. The mentioned models have their own logic and causality! And experience has shown that they do not have a significant relationship with nature! And there will always be an inevitable distance between our models of nature, the motivation to reduce this distance may be another request for scientific efforts!

I believe it is common knowledge that mathematics and its applications cannot prove causality directly. What are the bases of the problem of incompatibility of physical causality with mathematics and its applications in the sciences and in philosophy? The main but general explanation could be that mathematical explanations are not directly about the world but are applicable to the world to a great extent. Hence, mathematical explanations can at the most only show the ways of movement of the processes and not demonstrate whether the ways of the cosmos are by causation.

No science and philosophy can start without admitting that the cosmos exists. If it exists, it is not nothing, not vacuum. Non-vacuous existence means that the existents are non-vacuously extended. This means they have parts. Every part has parts too, ad libitum, because each part is extended. None of the parts is an infinitesimal. They can be near-infinitesimal. This character of existents is Extension, a Category directly implied by To Be.

Similarly, any extended being’s parts are active, moving. This implies that every part has impact on some others, not on infinite others. This character of existents is Change. No other implication of To Be is so primary as these. Hence, they are exhaustive.

Existence in Extension-Change is what we call Causality. If anything is existent, it is causal – hence Universal Causality is the trans-science physical-ontological Law of all existents. By the very concept of finite Extension-Change-wise existence it becomes clear that no finite space-time is absolutely dense with existents. Hence, existents cannot be mathematically continuous. Since there is change and transfer of impact, no existent can be absolutely discrete in its parts or in connection with others.

Can logic show the necessity of all existents being causal? We have already discussed how, ontologically, the very concept of To Be implies Extension-Change and thus also Universal Causality.

What about the ability or not of logic to conclude to Universal Causality? In my argument above and elsewhere showing Extension-Change as the very exhaustive meaning of To Be, I have used mostly only the first principles of ordinary logic, namely, Identity, Contradiction, and Excluded Middle, and then argued that Extension-Change-wise existence is nothing but Universal Causality if everything existing is non-vacuous in existence. For example, does everything exist or not? If yes, let us call it non-vacuous existence. Hence, Extension as the first major implication of To Be. Non-vacuous means extended, because if not extended the existent is vacuous. If extended, everything has parts.

A point of addition now has been Change. It is, so to say, from experience. Thereafter I move to the meaning of Change basically as motion or impact. Naturally, everything in Extension must effect impacts. Everything has further parts. Hence, by implication from Change, everything causes changes by impacts. Thus, we conclude that Extension-Change-wise existence is Universal Causality. It is thus natural to claim that this is a pre-scientific Law of Existence.

In such foundational questions like To Be and its implications we need to use the first principles of logic, because these are the foundational notions of all science and no other derivative logical procedure comes in as handy. In short, logic with its fundamental principles can help derive Universal Causality. Thus, Causality is more primary to experience than the primitive notions of mathematics.

In my opinion, mathematics itself may not be able to prove causality, but because it is a tool, it is itself causal. If we assume that causality is prior and eternal, we implicitly accept that it cannot be proven by anything and it is a simple matter. Mathematics is not able to identify simple things and can only confirm or reject multiple things!

I also think that mathematics is a tool for human understanding, and through it, infinite different forms can be extracted for the physics of the world or how phenomena occur, without all of them becoming reality in our world!

Mathematics is a very useful and not versatile tool for chaining or systematically ordering human thoughts in coherent frameworks, and so far we have seen that none of the cosmological and physical mathematical models have been completely consistent with the real world. !

We live in a world where there are materials, forces and energy and rules, which work together!, and we have been able to understand this world with scientific methods to the extent that it is useful and practical for us, but not What it is, but also how we communicate between its components!

We are always amazed and confused when we identify the wisdom of the world!

One of our poets named Sohrab Sepehri says: Our job is not to identify the secret of the rose, but our job is to float in the enchantment of the rose!

This time what you said is not clear to me.

Mathematics is a conceptually symbolizing tool. The brain-level processes behind it are causal, sure. But mathematical considered as such is not causal.

I did not claim that causality is simple and eternal in the sense you meant. But what is meant by "Mathematics is not able to identify simple things and can only confirm or reject multiple things"? Kindly tell me the difference or similarity in what you meant.

Math is able to imagine many or infinite things. No two opinions on this. Hence the high measure of applicability of math to physics and science as such.

About the final esthetical comments in your intervention, I have no problems.

In my previous statement, I mean by simple topics, topics that are indivisible, or in other words, not made up of parts, and the other are compound topics that are made up of parts.

Therefore, I think, that mathematics cannot distinguish what are indivisible subjects like causality.

The work of mathematics is to research and determine relationships between inseparable subjects, for example, mathematics does not know what the essence of a number is, but it knows what is meant by prime numbers.

Perhaps the answer to the question whether mathematics comes first or experience is decisive, in other words, mathematics, at least in its initial form, was formed from the human effort to simulate real experiences with numbers and parameters, and has continued to evolve over time. (but not necessarily only by experience).

Also, in my opinion, a system of mathematical rules is causal, but its compliance with a phenomenon from the real world does not necessarily prove its causality.

Scientific experience has shown that the phenomena of the world are different from what is modeled by mathematics.

Sir, was my statement clear this time? I would appreciate it if you could tell me.

Seyed Mohammad Mousavi, I have a suggestion. I shall cite a few phrases or sentences from your intervention here. Would you just take a look at them and make those phrases clearer?

(1) simple topics, topics that are indivisible. INDIVISIBLE TOPICS?

(2) mathematics cannot distinguish what are indivisible subjects like causality. INDIVISIBLE SUBJECTS? WHY DO YOU SAY CAUSALITY IS INDIVISIBLE?

(3) mathematics does not know what the essence of a number is. THE ESSENCE OF A NUMBER?

etc.

It is due to this sort of parts of your sentences that I find it difficult to get what you write. Please do not feel that I am belittling you. Instead, my request is to just clarify things. What I have been doing to avoid this problem is to read my statements a few more times and make changes in them. There have been occasions where I just wrote things and did not edit it. And there I have made mistakes too. However well I express myself, I try to edit it again and again.

Yes, sure, I will do what you said.

Mathematically, space is the "thing" that can curve. Hence, Einstein and all others might have called it as the thing that in fact is curving in physical processes, including gravitational. But is this not a mathematical heresy in physics?

Mathematics is not physics. It can only help physics. Why can and why should math try to be physics and call "space" as a thing? Now, if space is renamed into a medium, will it become ether?

Should space or space-time curve in gravitational processes, or should existent matter-energy fields curve?

The Irretutable Argument for Universal Causality. Any Opposing Position?

Very very short. https://www.researchgate.net/post/The_Irretutable_Argument_for_Universal_Causality_Any_Opposing_Position

You may like the new discussion session: GRAVITATIONAL COALESCENCE PARADOX. It is the kernel of an idea on which I have reflected more than 35 years by now, have presented arguments to some cosmologists, and have got support.

https://www.researchgate.net/post/Gravitational_Coalescence_Paradox_GCP

All impact transfers within and between entities are extended-changing. Impact transfer is nothing but the activity called Causation. Existents are in extended-changing causal process. The relation of one impact transfer process towards the constitution of another is Causality. Hence, everything is in causal process. If anything non-causal exists, it must lose contact with causal processes and cannot be connected with anything else so to result from causal processes or non-causal processes.

That is, Causality is a derivative Category pertaining to all existents. It is derived from putting together Extension and Change. Causality (the relation) and causation (the action / activity) are act-based. In general, without direct reference to the causal aspect, and with direct reference to the entity-aspect, one can say denotatively: everything is an extended-changing process. (“Everything is in process” means adjectivally: “Everything is processual”) In fact, Causation and Processuality are interchangeable; the manner of definition alone differs. But a unit process is a set of cause and effect.

To help obtain some more clarity on what we discuss here, I think the following discussion will be of use -- especially the question by Richard Marker and my reply:

https://www.researchgate.net/post/The_Irrefutable_Argument_for_Universal_Causality_Any_Opposing_Position

Richard Marker: One more point: So far we have been speaking of the various laws of science / natural laws. Just one among them was causality. Now, if the very physical existence is Extension-Change-wise, and if Extension-Change-wise existence is itself Causality, then every existent must be causal. This is Universal Causality, and it becomes a pre-scientific Law. I call it a metaphysical / physical-ontological Law because IT IS THE LAW OF THE VERY POSSIBILITY OF BEING TAKEN AS PHYSICALLY EXISTENT. Extension and Change are the only and the exhaustive meanings of To Be. In that case, these two Categories must have a superior Categorial position in both philosophy and the sciences.

Today I have revised the basic initial text of this discussion.

If an electron A at a specific spacetime loses a certain number of quanta of energy (say, 100 quanta), naturally its total energy has come down. Or, will anyone claim that it has thus increased or that it is in a constant state? Now imagine that it is accelerated later by other forces.

Suppose that another electron B at another spacetime. It has not lost so many quanta of energy (say, only 50 quanta). It is also being accelerated similarly with the same amount of energy – of course, whether our measurement of the acceleration energy in the two cases is absolutely exact is yet another ambiguous matter, but we suppose that they are equal.

Will the latter be at a better position in the total energy content than the former? Or, will it be claimed that their energy, mass, etc. after received equal acceleration from outside are equal, merely because they are both electrons? Moreover, we know that in the path that both the electrons take there will be various other physical influences which we do not determine and cannot. In short, the mass, energy etc. of the two electrons will never be equal at any physical state. And we know that nothing in the world is in a static state.

That is, our generalized determination of an exact mass for an electron need not be the exact energy, mass, etc. of an electron in various physically processual circumstances. At normal circumstances within a specific chemical element, and when freed from it, the electron will have different values. This shows that no electron (in itself) will be identical in all its properties with any other. Our description of these properties may be considered as identical. But this description in physics is meant merely for pragmatic purposes! One cannot now universalize it and say that the mass, energy, etc. of electrons everywhere is the same everywhere.

What about the values (mass, energy, etc.) of other particles like photon, neutrino, etc.? I believe none can prove their case to be otherwise.

That is, there is nothing in the world, including electrons, quarks, photons, neutrinos, etc., which has an exact duplicate anywhere else. This is the foundation for the principle of physical identity.

Is Mathematics an Exact Science? If Yes, and If Not, Why?

Why are numbers and shapes so exact? ‘One’, ‘two’, ‘point’, ‘line’, etc. are all exact. But irrational numbers are not so. If notions like ‘one’, ‘two’, ‘point’, ‘line’, etc. are defined to be so exact, then it not by virtue of the exactness of these substantive notions, but instead, due to their being adjectival: ‘being a unity’, ‘being two unities’, ‘being a non-extended shape’, etc. A quality cannot be exact, but may be defined to be exact. It is in terms of the exactness attributed to these notions by definition that the adjectives ‘one’, ‘two’, ‘point’, ‘line’, etc. are exact. This is why the impossibility of fixing these (and other) substantive notions as exact miss our attention. If in fact these are inexact, then there is justification for the inexactness of irrational numbers too. If numbers and shapes are in fact inexact, then not only irrational numbers but all mathematical structures should remain inexact except for their having been defined as exact. Thus, mathematical structures, in all their detail, are a species of qualities, namely, quantitative qualities.

https://www.researchgate.net/post/Is_Mathematics_an_Exact_Science_If_Yes_and_If_Not_Why

Reification of Concepts in Quantum Physics?

https://www.researchgate.net/post/Reification_of_Concepts_in_Quantum_Physics

I have revised the lead text (see directly under the title of the discussion: Mathematics and Causality: A Systemic Reconciliation). Now it has become 8 pages in A-4. See the link below.

I believe your questions may be answered here in my humble manner. Further questions and suggestions are most welcome. Thanks.

https://www.researchgate.net/post/Mathematics_and_Causality_A_Systemic_Reconciliation

Non-integer rational numbers are not the direct notion of anything existent. Even a part of a unit process has the attribute ‘unity’ in all the senses in which any other object possesses transpire. For this reason, natural numbers have Categorial priority over rational numbers, because natural numbers are more directly related to ontological universals than other sorts of numbers are. Complex numbers, for example, are the most general number system for their sub-systems defined mathematically, but this does not mean that they are more primary in the metaphysics of ontological universals, since the primary mode of numerically quantitative qualities / universals is that of natural numbers.

Why Are Numbers and Shapes So Exact?

https://www.researchgate.net/post/Why_Are_Numbers_and_Shapes_So_Exact

How to philosophize? How to philosophize in the sciences?

https://www.researchgate.net/post/How_to_philosophize_How_to_philosophize_in_the_sciences

Do Electromagnetic and Gravitational Quanta (EM Quanta and Gravitons) Gravitate from Within?

https://www.researchgate.net/post/Do_Electromagnetic_and_Gravitational_Quanta_EM_Quanta_and_Gravitons_Gravitate_from_Within

Do electromagnetic and gravitational wavicles exist? Before using them in physics, it must be determined whether they exist, for them to exert causally real physical effects. Existents cannot be vacua, and hence, they must exist, and hence they are

(1) in Extension (each having a finite number of finite-content parts), because if not extended, EM quanta would be non-existent, and

(2) in Change (existents, which are always with parts, possessing parts which always exert finite impacts on a finite number of others, inclusive of exertion of finite impacts on some parts within), because anything that has no change is not in existence.

An existent without own parts and own exertion of impacts will be imaginable as existent. Anything that is not in Extension-Change is non-existent – a physical-ontological fact at the foundations of physics, which most physicists (and other scientists) forget while performing their statistical and other related miracles!

This much for an introduction. Now, what are the implications of such existence in the case of EM wavicles and gravitons?

ELECTROMAGNETIC AND GRAVITATIONAL QUANTA

If electromagnetic and gravitational wavicles are EXISTENT, then they possess also EXTENSION and CHANGE. They are not absolutely geometric particles, instead, they are elongated at various dimensions.

Let us assume the following as a general principle in physics: Anything physical issues gravitons, which are the basic attractive forces within physical existents.

If an existent energy wavicle is thus a matter wavicle with extension, it must also issue gravitons! In that case, the only stuff in the cosmos that cannot themselves issue further gravitons from within are gravitons themselves. What can this work to in physics and cosmology? I believe that we need a revolution from this viewpoint. This is a proposal that waits being tested by future physics and astrophysics.

Gravitons too are extended and changing wavicles. But they are themselves the wavicles possessing also their parts that attract each other, and are long-range in nature. If they issue sub-gravitons, they will naturally be kept attracted within the issuing sources, because the parts from which they are supposed to be issued are themselves attractive by nature and other matter and energy particles attract each other basically by means of issuing gravitons.

But naturally, gravitons too must be existent, and hence possess parts. What would be the sort of parts that gravitons can possess? Repulsons or Gravitons? Sub-repulsons or sub-gravitons? I think that they cannot themselves be repulsons and sub-repulsons, because repulsons and sub-repulsons without coherence will not stick together as parts of gravitons. Gravitons cannot issue gravitons themselves, since this is self-creation. But they can possess sub-gravitons as parts, but these need not be of the same power as their totality that each graviton is.

In any case, one thing should be accepted: BOTH ELECTROMAGNETIC AND GRAVITATIONAL QUANTA MUST ISSUE THEIR OWN WAVICLES OF ATTRACTION. IN THE CASE OF ELECTROMAGNETIC QUANTA, THE ISSE IS THAT OF GRAVITONS (and whatever other sub-wavicles that might be there for them to give rise to). IN THE CASE OF GRAVITONS, THE PARTS WILL HAVE TO BE SUB-GRAVITONS (plus whatever other sub-wavicles that might be there for them to give rise to).

I have been revising this short discussion paper of mine in RG. It is an attempt to correct some basic attitudes in physics. Just now I have written an introduction to it. Please read it here. In a few days I shall upload the whole lead-text of this discussion for your reading and comments. Here please find only the introduction:

FOUNDATIONS OF AXIOMATIC PHILOSOPHY AND SCIENCE

1. INTRODUCTION

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, but are to be treated or expressed as waves or particles propagated from material objects that of course exist. Some of them put in all their energies to show that both EM and G are mere mathematical fields, and not physically existent fields of energy propagations from bodies.

This is similar in effect to Newton and his followers thinking honestly and religiously that gravitation and other energies are just miraculously non-bodily actions at a distance without any propagation particles / wavicles.

Even in the 21stcentury, we must be sharply aware that from the past more than 120 years the General Theory of Relativity and its various versions 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.

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

Questioning the Foundations of Physical Constants, Properties, and Qualities

https://www.researchgate.net/post/Questioning_the_Foundations_of_Physical_Constants_Properties_and_Qualities

How to Ground Science and Philosophy Together Axiomatically?

https://www.researchgate.net/post/How_to_Ground_Science_and_Philosophy_Together_Axiomatically

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.

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

Causality and Statistics: Their Levels of Effect and of Explanation

https://www.researchgate.net/post/Causality_and_Statistics_Their_Levels_of_Effect_and_of_Explanation

Einstein-Podolsky-Rosen Paradox and Non-Locality: Is Einstein a Monist?

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

The Fate of “Source-Independence” in Electromagnetism, Gravitation, and Monopoles

https://www.researchgate.net/post/The_Fate_of_Source-Independence_in_Electromagnetism_Gravitation_and_Monopoles

Can what are termed "mathematically consistent" natural laws necessarily be physically consistent? If they can be, then mathematics becomes physics (and for that matter it becomes any other mathematical science). But if math is different from all these sciences, the adequacy and applicability of math to physics and other sciences cannot be 100%. If that is the case, it is very important that physics (and other sciences) be helped constantly to choose the most suitable math. This help can come from the same science/s only in a partially realizable manner. Nor can math take up this task fully well. Hence, a generic science beyond all these including math and logic must take charge of improving the remaining portions of inadequacy and inapplicability of math to physics and the sciences. Which could that science be? I hold that this most general science need not contain all that philosophy has so far understood itself to be. But something of the philosophy of these sciences combined with the philosophy of math, logic, etc. would be an ideal option.

Essential Reason in Physicists’ Use of Logic: And in Other Sciences Too!

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Here a serious and somewhat complex matter to discuss:

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