MATHEMATICS VS. CAUSALITY:
A SYSTEMIC RECONCILIATION
Raphael Neelamkavil, Ph.D., Dr. phil.
1. Preface on the Use of Complex Language
2. Prelude on the Pre-Scientific Principle of Causality
3. Mathematical “Continuity and Discreteness” Vs. Causal Continuity
4. Mathematics and Logic within Causal Metaphysics
5. Mathematics, Causality, and Contemporary Philosophical Schools
1. Preface on the Use of Complex Language
First of all, a cautious justification is in place about the complexity one may experience in the formulations below: When I publish anything, the readers have the right to ask me constantly for further justifications of my arguments and claims. And if I have the right to anticipate some such possible questions and arguments, I will naturally attempt to be as detailed and systemic as possible in my formulation of each sentence here and now. A sentence is merely a part of the formulated text. After reading each sentence, you may pose me questions, which certainly cannot all be answered well within the sentences or soon after the sentences in question, because justification is a long process.
Hence, my sentences may tend to be systemically complex. A serious reader will not find these arguments getting too complex, because such a person has further unanswered questions. We do not purposely make anything complex. Our characterizations of meanings in mathematics, physics, philosophy, and logic can be complex and prohibitive for some. But would we all accuse these disciplines or the readers if the readers find them all complex and difficult? In that case, I could be excused too. I do not intentionally create a complex state of affairs in these few pages; but there are complexities here too. I express my helplessness in case any one finds these statements complex.
The languages of both science and philosophy tend to be complex and exact. This, nevertheless, should be tolerated provided the purpose is understood and practiced by both the authors and the readers. Ordinary language has its worth and power. If I give a lecture, I do not always use such formal a language as when I write, because I am there to re-clarify.
But the Wittgensteinian obsession with “ordinary” language does not make him use an ordinary language in his own works. Nor does the Fregean phobia about it save him from falling into the same ordinary-language naïveté of choosing concrete and denotative equivalence between terms and their reference-objects without a complex ontology behind them. I attempt to explain the complex ontology behind the notions that I use.
2. Prelude on the Pre-Scientific Principle of Causality
Which are the ultimate conditions implied by the notion of existence (To Be), without which conditions implied nothing exists, and without which sort of existents nothing can be discoursed? Anything exists non-vacuously. This implies that existents are inevitably in Extension (having parts, each of which is further extended and not vacuous). The parts will naturally have some contact with a finite number of others. That is, everything is in Change (impacting some other extended existents).
Anything without these two characteristics cannot exist. If not in Change, how can something exist in the state of Extension alone? And if not in Extension, how can something exist in the state of Change alone? Hence, Extension-Change are two fundamental ontological categories of all existence and the only two exhaustive implications of To Be. Any unit of causation with one causal aspect and one effect aspect is termed a process.
These conditions are ultimate in the sense that they are implied by To Be, not as the secondary conditions for anything to fulfil after its existence. Thus, “To Be” is not merely of one specific existent, but of all existents. Hence, Extension-Change are the implications of the To Be of Reality-in-total. Physical entities obey these implications. Hence, they must be the foundations of physics and all other sciences. Theoretical foundations, procedures, and conclusions based on these implications in the sciences and philosophy, I hold, are wise enough.
Extension-Change-wise existence is what we understand as Causality: extended existents and their parts exert impacts on other extended existents. Every part of existents does it. That is, if anything exists, it is in Causation. This is the principle of Universal Causality. In short, Causality is not a matter to be decided in science – whether there is Causality or not in any process under experiment and in all existents is a matter for philosophy to decide, because philosophy tends to study all existents. Science can ask only whether there occurs any specific sort of causation or not, because each science has its own restricted viewpoint of questions and experiments and in some cases also restrictions in the object set.
Thus, statistically mathematical causality is not a decision as to whether there is causation or not in the object set. It is not a different sort of causation, but a measure of the extent of determination of special causes that we have made at a given time. Even the allegedly “non-causal” quantum-mechanical constituent processes are mathematically and statistically circumscribed measuremental concepts from the results of Extended-Changing existents and, ipso facto, the realities behind these statistical measurements are in Extension-Change if they are physically existent.
Space is the measured shape of Extension; time is that of Change. Therefore, space and time are epistemic categories. How then can statistical causality based only on measuremental data be causality at all, if the causes are all in Extension-Change and if Universal Causality is already the pre-scientific Law under which all other laws appear? No part of an existent is non-extended and non-changing. One unit of cause and effect may be called a process. Every existent and its parts are processual.
And how can a so-called random cause be a cause, except when the randomness is the extent of our measuremental reach of the cause, which already is causal because of its Extension-Change-wise existence? Extension and Change are the very exhaustive meanings of To Be, and hence I call them the highest Categories of metaphysics, physical ontology, physics, and all science. Not merely philosophy but also science must obey these two Categories.
In short, everything existent is causal. Hence, Universal Causality is the highest pre-scientific Law, second conceptually only to Extension-Change and third to Existence / To Be. Natural laws are merely derivative. Since Extension-Change-wise existence is the same as Universal Causality, scientific laws are derived from Universal Causality, and not vice versa. Today the sciences attempt to derive causality from the various scientific laws!The relevance of metaphysics / physical ontology for the sciences is clear from the above.
Existents have some Activity and Stability. This is a fully physical fact. These two Categories may be shown to be subservient to Extension-Change and Causality. Pure vacuum (non-existence) is absence of Activity and Stability. Thus, entities, irreducibly, are active-stable processes in Extension-Change. Physical entities / processes possess finite Activity and Stability. Activity and Stability together belong to Extension; and Activity and Stability together belong to Change too.
That is, Stability is neither merely about space nor about Extension. Activity is neither merely about time nor about Change. There is a unique reason for this. There is no absolute stability nor absolute activity in the physical world. Hence, Activity is finite, which is by Extended-Changing processes; and Stability is finite, which is also by Extended-Changing processes. But the tradition still seems to parallelise Stability and Activity with space and time respectively. We consider Activity and Stability as sub-Categories, because they are based on Extension-Change, which together add up to Universal Causality; and each unit of cause and effect is a process.
These are not Categories that belong to merely imaginary counterfactual situations. The Categories of Extension-Change and their sub-formulations are all about existents. There can be counterfactuals that signify cases that appertain existent processes. But separating these cases from some of the useless logical talk as in linguistic-analytically tending logic, philosophy, and philosophy of science is near to impossible.
Today physics and the various sciences do at times something like the said absence of separation of counterfactual cases from actual in that they indulge in particularistically defined terms and procedures, by blindly thinking that counterfactuals can directly represent the physical processes under inquiry. Concerning mathematical applications too, the majority attitude among scientists is that they are somehow free from the physical world.
Hence, without a very general physical ontology of Categories that are applicable to all existent processes and without deriving the mathematical foundations from these Categories, the sciences and mathematics are in gross handicap. Mathematics is no exception in its applicability to physical sciences. Moreover, pure mathematics too needs the hand of Extension and Change, since these are part of the ontological universals, form their reflections in mind and language, etc., thus giving rise to mathematics.
The exactness within complexity that could be expected of any discourse based on the Categorial implications of To Be can only be such that (1) the denotative terms ‘Extension’ and ‘Change’ may or may not remain the same, (2) but the two dimensions of Extension and Change – that are their aspects in ontological universals – would be safeguarded both physical-ontologically and scientifically.
That is, definitional flexibility and openness towards re-deepening, re-generalizing, re-sharpening, etc. may even change the very denotative terms, but the essential Categorial features within the definitions (1) will differ only meagrely, and (2) will normally be completely the same.
3. Mathematical “Continuity and Discreteness” Vs. Causal “Continuity”
The best examples for the above are mathematical continuity and discreteness that are being attributed blindly to physical processes due to the physical absolutization of mathematical requirements. But physical processes are continuous and discrete only in their Causality. This is nothing but Extension-Change-wise discrete causal continuity. At any time, causation is present in anything, hence there is causal continuity. This is finite causation and hence effects finite continuity and finite discreteness. But this is different from absolute mathematical continuity and discreteness.
I believe that 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 within 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.
It is good to note that mathematics is a separate science as if its “objects” were existent, but in fact as non-existent and different from those of any other science – thus creating mathematics into an abstract science in its theoretical aspects of rational effectiveness. 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.
Moreover, the basic notions of mathematics (number, number systems, points, shapes, operations, structures, etc.) are all universals / universal qualities / ontological universals that belong to groups of existent things that are irreducibly Extension-Change-type processes. (See below.)
Thus, mathematical notions have their origin in ontological universals and their reflections in mind (connotative universals) and in language (denotative universals). The basic nature of these universals is ‘quantitatively qualitative’. We shall not discuss this aspect here at length.
No science and philosophy can start without admitting that the cosmos exists. If it exists, it is not nothing, not non-entity, 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 of the concept of To Be, which belongs to Reality-in-total. These arguments show us the way to conceive the meaning of causal continuity.
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. In fact, space-time is no ontological affair, but only epistemological, and existent processes need measurementally accessible finite space for Change. 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 to be causal? We have already discussed how, ontologically, the very concept of To Be implies Extension-Change and thus also Universal Causality. Logic can only be instrumental in this.
What about the ability or not of logic to conclude to Universal Causality? In my arguments 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 is the first major implication of To Be. Non-vacuous means extended, because if not extended the existent is vacuous. If extended, everything has parts. Having parts implies distances, however minute, between all the near-infinitesimal parts of any existent process. In this sense, the basic logical laws do help conclude the causal nature of existents.
A point of addition now has been Change. It is, so to say, from experience. But this need not exactly mean an addition. If existents have parts (i.e., if they are in Extension), the parts’ mutual difference already implies the possibility of contact between parts. Thus, I am empowered to 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 and the need for there to be contacts between every near-infinitesimal set of parts of existents, everything causes changes by impacts. In the physical world this is by finite impact formation. Hence, nothing can exist as an infinitesimal. Leibniz’s monads have no significance in the real world.
Thus, we conclude that Extension-Change-wise existence is Universal Causality, and every actor in causation is a real existent, not a non-extended existent, as energy particles seem to have been considered and are even today thought to be, due to their unit-shape yielded merely for the sake mathematical applications. It is thus natural to claim that Causality is a pre-scientific Law of Existence, where existents are all inwardly and outwardly in Change, i.e., in impact formation – otherwise, the concept of Change would lose meaning.
In such foundational questions like To Be and its implications, the first principles of logic must be used, 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 (Extension-Change) is more primary to experience than the primitive notions of mathematics. But the applicability of these three logical Laws is not guaranteed so well in arguments using derivative, less categorial, sorts of concepts.
I suggest that the crux of the problem of mathematics and causality is the dichotomy between mathematical continuity and mathematical discreteness on the one hand and the incompatibility of applying any of them directly on the data collected / collectible / interpretable from some layers of the phenomena which are from some layers of the object-process in question. Not recognizing the presence of such stratificational debilitation of epistemic directness is an epistemological foolishness. Science and philosophy, in my opinion, are victims of this. Thus, for example, the Bayesian statistical theory recognizes only a statistical membrane between reality and data!
Here I point at the avoidance of the problem of stratificational debilitation of epistemic directness, by the centuries of epistemological foolishness, by reason of the forgetfulness of the ontological and epistemological relevance of expressions like ‘from some layers of data from some layers of phenomena from some layers of the reality’.
This is the point at which it is time to recognize the gross violence against natural reason behind phrases and statements involving ‘data from observation’, ‘data from phenomena’, ‘data from nature / reality’ etc., without epistemological and ontological sharpness in both science and philosophy to accept these basic facts of nature. As we all know, this state of affairs has gone irredeemable in the sciences today.
The whole of what we used to call space is not filled with matter-energy. Hence, if causal continuity between partially discrete “processual” objects is the case, then the data collected / collectible cannot be the very processual objects and hence cannot provide all knowledge about the processual objects. But mathematics and all other research methodologies are based on human experience and thought based on experience.
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 the sciences and by means of its systemic physical ontology falls short miserably in actuality, and (b) the logical continuity of any kind does not automatically make linguistically or mathematically symbolized activity of representation adequate enough to represent the processual nature of entities as derivate from data.
(2) The concept of absolute discreteness in nature, which, as of today, is ultimately of the quantum-mechanical type based on Planck’s constant, continues to be a mathematical and partial misfit in the physical cosmos and its parts, (a) if there exist other universes that may causally determine the constant differently at their specific expansion and/or contraction phases, and (b) if there are an infinite number of such finite-content universes.
The case may not of course be so problematic in non-quantifiable “possible worlds” due to their absolute causal disconnection or their predominant tendency to causal disconnection, but this is a mere common-sense, merely mathematical, compartmentalization: because (a) 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 (b) the possible worlds have only a non-causal existence, and hence, anything may be determined in this world as a constant, and an infinite number of possible universes may be posited without any causal objection!
It is usually not kept in mind here by physicists that the epistemology of unit-based thinking – of course, based on quantum physics or not – is implied by the almost unconscious tendency of symbolic activity of body-minds. This need not have anything to do with a physics that produces laws for all existent universes.
(3) 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 manner (extended entities and their parts impacting a finite number of other existents and their parts in a finite quantity and in a finite duration). Existence in the Extension-Change-wise manner is nothing but causal activity.
Thus, insofar as everything is existent, every existent is causal. There is no time (i.e., no minute measuremental iota of Change) wherein such causal manner of existing ceases in any existent. This is causal continuity between partially discrete processual objects. This is not mathematizable in a discrete manner. The concept of geometrical and number-theoretic continuity may apply. But if there are other universes, the Planck constant of proportionality that determines the proportion of content of discreteness may change in the others. This is not previsioned in terrestrially planned physics.
The attitude of treating everything as causal may also be characterized by the self-aware symbolic activity by symbolic activity itself, in which certain instances of causation are avoided or enhanced, all decrementally or incrementally as the case may be, but not absolutely. This, at the most, is what may be called freedom.
It is fully causal – need not be sensed as causal within a specific set of parameters, but as causal within the context of Reality-in-total. But the whole three millennia of psychological and religious (contemplative) tradition of basing freedom merely on awareness intensity, and not on love – this is a despicable state of affairs, on which a book-length treatise is necessary.
Physics and cosmology even today tend to make the cosmos either (1) mathematically presupposedly continuous, or (2) discrete with defectively ideal mathematical status for causal continuity and with perfectly geometrical ideal status for specific beings, or (3) statistically indeterministic, thus being compelled to consider everything as partially causal, or even non-causal in the interpretation of statistics’ orientation to epistemically logical decisions and determinations based on data. If this has not been the case, can anyone suggest proofs for an alleged existence of a different sort of physics and cosmology until today?
The statistician does not even realize (1) that Universal Causality is already granted by the very existence of anything, and (2) that what they call non-causality is merely the not being the cause, or not having been discovered as the cause, of a specific set of selected data or processes. Such non-causality is not with respect to all existents. Quantum physics, statistical physics, and cosmology are replete with examples for this empirical and technocratic treachery of the notion of science.
A topology and mereologically clean physical ontology of causal continuity between partially discrete processual objects, fully free of absolutely continuity-oriented or absolutely discreteness-oriented category theory, geometry, topology, 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 alien to physics and cosmology until today.
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.
4. Mathematics and Logic within Causal Metaphysics
Hence, it is important to define the limits of applicability of mathematics to the physics that use physical data (under the species of various layers of their origin). This is the only way to approximate beyond the data and the methodologically derived conclusions beyond the data. As to how and on what levels this is to be done is a matter to be discussed separately.
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 human reason is limited to the procedures of reasoning by brains. What exactly is the reason that existent physical processes constantly undergo? How to get at conclusions based on this reason of nature – by using our brain’s reasoning – and thus transcend at least to some extent the limitations set by data and methods in our brain’s reasoning?
If we may call the universal reason of Reality-in-total by a name, it is nothing but Universal Causality. It is possible to demonstrate that Universal Causality is a trans-physical, trans-scientific Law of Existence. This argument needs clarity. How to demonstrate this as the case? This has been done in an elementary fashion in the above, but more of it is not to be part of this discussion.
Insistence on mathematical continuity in nature is a mere idealization. It expects nature to obey our merely epistemic sort of idealizations, that is, in ideal cases based mostly on the brain-interpreted concepts from some layers of data, which are from some layers of phenomena, which are from some layers of the reality under observation. Some of the best examples in science are the suppositions that virtual worlds are existent worlds, dark energy is a kind of propagative energy, zero-value cosmic vacuum can create an infinite number of universes, etc.
The processes outside are vaguely presented primarily by the processes themselves, but highly indirectly, in a natural manner. This is represented by the epistemic / cognitive activity within the brain in a natural manner (by the connotative universals in the mind as reflections of the ontological universals in groups of object processes), and then idealized via concepts expressed in words, connectives, and sentences (not merely linguistic but also mathematical, computerized, etc.) by the symbolizing human tendency (thus creating denotative universals in words) 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 as end results. We can mentally recreate the idealized results behind the multitude ontological, connotative, and denotative universals as existents.
As the procedural aftermath of this, virtual worlds begin to “exist”, dark energy begins to “propagate”, and zero-value cosmic vacuum “creates” universes. Even kinetic and potential energies are treated as propagative energies existent outside of material bodies and supposed to be totally different from material bodies. These are mere theoretically interim arrangements in the absence of direct certainty for the existence or not of unobservables.
Insistence on mathematical continuity in nature as a natural conclusion by the 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 and extrapolate further beyond them. Mathematical idealizations are another version of linguistic symbolization and idealization.
Logic and its direct quantitatively qualitative expression as found in mathematics are, of course, 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 side-effects of the same symbols in the language, logic, and mathematics being used in order 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 well, although they too are equally unable to capture the whole of Reality in whatever it is, wholly or in parts, far beyond the data and their interpretations! Why not de-idealize the side-effects of mathematics too?
This theoretical attitude of partially de-idealizing the effects of human symbolizing activity by use of the same symbolic activity accepts the existence of processual entities as whatever they are. This is what I call ontological commitment – of course, different from and more generalized than those of Quine and others. 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.
5. Mathematics, Causality, and Contemporary Philosophical Schools
With respect to what we have been discussing, linguistic philosophyand even its more recent causalist child, namely, dispositionalist causal ontology, have even today the following characteristics:
(1) They attribute an even now overly discrete nature to “entities” in the extent of their causal separateness from others while considering them as entities. The ontological notion of an object or even of an event in its unity in analytic philosophy and in particular in modal ontology forecloses consideration of the process nature of each such unity within, on par with interactions of such units with one another. (David Lewis, Parts of Classes, p. vii) This is done 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) They are logically comatose about the impossibility of the exactly referential definitional approach to the processual demands of existent physical objects without first analyzing and resolving the metaphysical implications of existent objects, namely, being irreducibly in finite Extension and Change and thus in continuous Universal Causality in finite extents at any given moment.
(3) They are unable to get at the causally fully continuous (neither mathematically continuous nor geometrically discontinuous) nature of the physical-ontologically “partially discrete” processual objects in the physical world, also because they have misunderstood the discreteness of processual objects (including quanta) within stipulated periods as typically universalizable due to their pragmatic approach in physics and involvement of the notion of continuity of time.
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, and even metaphysical grounding as insurmountable curses 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 Wittgenstein’s 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 and forget about absolute mathematical continuity or discontinuity in nature. Mathematics and the physical universe are to be reconciled in order to mutually delimit them in terms of the causal continuity between partially discrete processual objects.
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.
Math can be applied to causality by having a symbol to represent causality. Equality means simply that 2 quantities have the same number and units value. But a board 2 meters long + a board 3 meters long may = 5 board meters of lumber but isn't the same as a board 5 meters long. Also, a changing magnetic field causes an electric field but that electric field does not cause the same magnetic field. The electric field causing a magnetic effect is in another of Maxwell's equations.
John Hodge, thanks. I do not yet understand how the mathematical and causal aspects of these can be connected.
Dear Raphael Neelamkavil
You wrote: "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."
The process of answering questions about an initial statement turns out to be a process of clarifying-by-inclusion specific aspects of the initial statement, then taken in context as a more general formulation.
Further answers to further questions establish a logical structure associative by inclusion, causal by nature, that clarifies more and more details of the initial general statement.
If at some point, some further question cannot be answered, then maybe the initial general statement requires to be modified so that this unanswerable question can now be answered without jeopardizing the previously formulated answers to the set of previous questions.
Or alternately, if the initial statement cannot be modified without jeopardizing the set of previously formulated answers, then maybe insufficient information is available to answer this question, and more research is required.
Seems to me that this goes for articulated languages as well as for mathematics.
Does this make sense to you?
Best Regards, André
I wrote that paragraph in order to defend the complex sentences: "Hence, I tend to be as systemic as possible in each of the following sentences." Did you read that?
I did not use it to show that I will go on modifying the same claims.
Dear Raphael Neelamkavil
Yes I read your entire text.
You wrote: "I did not use it to show that I will go on modifying the same claims."
That's not what I was implying. I was talking about any statement in general, in line with your analysis.
Best Regards, André
Raphael Neelamkavil
For example,
Some physical conditions are measured and produce a number or a function of numbers such as he changing magnetic field. Merely saying tis set of numbers equals another set of numbers, which may be measured, may also suggest the reverse sequence. Little physics in this correlation of calculations. But to say the former set causes another set is physics and does NOT suggest the reverse also happens - that is the curl of the electric field does not cause a changing magnetic field. The physics is in the causation, not the correlation. That is the evolution needed in Quantum Mechanics.
John Hodge, did I say anything against this? What do you want to communicate? Formulate it clearly.
Do numbers cause anything? I ask only how they do.
If, as you say Raphael Neelamkavil, within the following context:
"phrases and statements involving ‘data from observation’, ‘data from phenomena’, ‘data from nature’ etc. are very gross, without epistemological and ontological astuteness", I agree entirely that mathematics and causality are reconcilable. Furthermore, that all the sciences serve to inform the systemic reconciliation of the whole account of Reality within that context.
Ann Van Ryn, I thank you for the understanding and the ability to see the point. We never construct a foolproof system/s. But we can try to...
I have sent you a personal message via RG.
Raphael
Howdy Raphael Neelamkavil,
What good news, another real philosopher has entered the field! We amateurs do our best....
My respect for your efforts is in no way altered, but I must observe a few things:
So mathematics is idealized in applications to natural processes. I agree, and I agree with the concern you raise about that misleading human activity, but what makes me feel that the formal jargon of philosophy, epistemology and ontology, is not recognized as equally idealized and misleading?
My mathematics educated daughter scoffed at philosophy because some reciter of philosopher’s writings said things she thought were dumb. I pointed out that a being a student of philosopher’s writings does not make one a philosopher. Doing philosophy is very different, the words used notwithstanding.
I shall soon (burglars please ignore) be spending hours on the Little Sahara sand dunes enjoying the overlapping ripples in the sand as present reality overlays past truth, and observing the traces of beetles walking up a sandslide due to their weight as “what now guys?” I shall prepare a responsible (well, to me) affirmative view of your “Mathematics and Causality: A Systemic Reconciliation” because I want to, but I shall be away for a while.
(So what if it is personal, persons matter and cold sterility is mendacity.)
Happy Trails, and Good Fortune, Len
Leonard Hall, thanks. Very good.
I will revise the text soon. Today or tomorrow I shall replace the text of the original document here above (under the lead question) with the revised version. Just now I found some errors in my formulation.
About philosophy. It is a vast jungle or desert, just as math, physics, and every other field of study is. I am mostly into the philosophy of physics and of cosmology.
I am of the opinion that the jargon feeling comes when we are not into that area of study or research. Moreover, being able to find what we seek in philosophy is not so easy as is in math or physics! I started at the age of 13 with serious reading and reflection in philosophy. And during studies I never bothered of getting great points in the exams. I just read, reflected, and wrote down my own ideas.
The view that humans have on the world is influenced by the cognitive method that has been formed. All the fields of knowledge and science that you mentioned together have made a cognitive method in the current time, which identifies the world with this dominant method!
We know the one in which our thinking frame is located! To look at the world in a different way and to adopt a different method, one must work without all these fields and with a method that penetrates into the cause of the phenomena! Is there mathematics and logic that the resulting physical and cosmological models have the least distance from the principle of current phenomena in the world?! Our language is unable to express what is actually happening! Maybe a world like David Boehm's holographic world is the solution to our problem! And in fact, an important part of the truth of the world is hidden in the hidden world! The part that we need to understand the world's phenomena! Or the invention of logic, mathematics and a new scientific and epistemological language is needed?! In my opinion, the result of the phenomenological method will not say anything about the causal layers of this world! The phenomenological method helps us to work without knowing the world and gives us a way of living and using most of the capacities of this world without knowing it. Previously, Newton claimed a method for understanding physics with wrong assumptions about space and time, which lasted for a while! These assumptions are based on the feeling and philosophy of that history, which was also manifested in the language of that time! It cannot be said, now these wrong assumptions have stopped! And maybe the current path of epistemology and cosmology, with incorrect and limiting assumptions, will not bring us to the true knowledge of the world.....
Seyed Mohammad Mousavi, thanks.
I do not think that a unique method with the quality of the holographic would take off. I do not find how this will work except in computer simulations. Such simulations could be useful, but would they lead us closer to the stuff of the "object/s"?
I hope that constant quality augmentation in all methods and sciences is a natural and sure possibility. Beyond this, what to expect?
Leonard Hall, I have now revised the text and replaced the old one. For your ease, I put it here below.
MATHEMATICS AND CAUSALITY:
A SYSTEMIC RECONCILIATION
Raphael Neelamkavil
A caveat is in place here about the complexity one may experience in the formulation: 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 find the arguments being too complex. We do not purposely make anything complex. Our (and your) characterizations of meanings in mathematics, physics, philosophy, and logic can be 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.
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 causality with mathematics and its applications? 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, it can only show the ways of movement of the processes and not demonstrate whether the ways are by causation.
But 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. We shall encounter the logical aspect of the question later.
I suggest that the crux of the problem here is the dichotomy between mathematical continuity and mathematical discreteness on the one hand and the incompatibility of applying any of them directly on the data collected / collectible / interpretable from some layers of the phenomena which are from some layers of nature or of the reality in question. Not recognizing this is an epistemological foolishness. Science and philosophy, in my opinion, are victims of this.
I point at the avoidance of the problem, by the centuries of epistemological foolishness, by reason of the forgetfulness of the ontological and epistemological relevance of expressions like ‘from some layers of phenomena from some layers of the reality’. This is the point at which it is time to recognize the gross violence against reason behind phrases and statements involving ‘data from observation’, ‘data from phenomena’, ‘data from nature / reality’ etc., without epistemological and ontological astuteness.
The whole of what we used to call space is not filled with matter-energy. Hence, if causal continuity between partially discrete “processual” objects is the case, then the data collected / collectible cannot be the very processual objects and hence cannot 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 (under the species of various layers of their origin). This 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 human reason is limited to the procedures of reasoning by brains. What exactly is the reason that existent physical processes constantly undergo? How to get at conclusions based on this reason and thus transcend at least to some extent the limitations set by data and methods?
If we may call the universal reason of Reality-in-total by a name, it is nothing but Universal Causality. It is possible to demonstrate that Universal Causality is a trans-physical, trans-scientific Law of Existence. This argument needs clarity. How to demonstrate this as the case?
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.
Insistence on mathematical continuity in nature is a mere idealization. It expects nature to obey our merely epistemic sort of idealizations (in ideal cases, based mostly on the brain-interpreted data from some layers of phenomena, which are from some layers of the reality under observation). Some of the best examples in science are the suppositions that virtual worlds are worlds, dark energy is a kind of propagative energy, zero-value cosmic vacuum can create an infinite number of universes, etc.
The processes outside are vaguely presented primarily by the processes themselves, but highly indirectly, in a natural manner. This is represented by the epistemic activity of the brain in a natural manner, and then idealized via concepts expressed in words, connectives, and sentences (not merely linguistic but also mathematical, computerized, etc.) 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. We create idealized results as existents.
Thus, virtual worlds begin to exist, dark energy begins to propagate, and zero-value cosmic vacuum creates universes. Even kinetic and potential energies are treated as propagative energies existent outside of material bodies and supposed to be totally different from material bodies.
Insistence on mathematical continuity in nature as a natural conclusion by the application of mathematics to nature is what happens in all physical and cosmological (and of course other) sciences insofar as they use mathematical idealizations (another version of linguistic symbolization and idealization) to represent existent objects and processes and extrapolate further beyond them. Logic and its direct quantitatively qualitative expression as found in mathematics are, of course, 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 side-effects of the same symbols in the language, logic, and mathematics being used in order 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 well although they too are equally unable to capture the whole of reality in whatever it is, wholly or in in parts, far beyond the data and their interpretations! Why not de-idealize the side-effects of mathematics too?
This theoretical attitude of partially de-idealizing the effects of human symbolizing activity by use of the same symbolic activity accepts the existence of processual entities as whatever they are. This is what I call ontological commitment – of course, different from and more generalized than those of Quine and others. 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 the sciences and by means of its systemic physical ontology falls short miserably in actuality, and (b) logical continuity of any kind does not automatically make linguistic or mathematical symbolized representation activity adequate enough to represent the processual nature of entities as derivate from data.
(2) The concept of absolute discreteness in nature, which, as of today, is ultimately of the 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: (a) 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 (b) because the epistemology of unit-based thinking (not, of course, based on quantum physics) is implied by the almost unconscious tendency of symbolic activity of body-minds.
(3) 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. Any existence in Extension-Change-wise manner is nothing but causal activity. Thus, insofar as everything is existent, every existent is causal. There is no time (i.e., no minute measuremental iota of Change) wherein such causal manner of existing ceases in any existent. This is causal continuity between partially discrete processual objects. This is non-mathematizable.
The attitude of treating everything as causal may 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, all incrementally, not absolutely. This, at the most, is what may be called freedom. It is fully causal – causal not in a specific set of manners, but 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 causal continuity and with perfectly geometrical ideal status for specific beings, or (3) statistically indeterministic, thus compelled to consider everything as partially causal, or even 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?
The statistician does not even realize (1) that Universal Causality is already granted by the very existence of anything, and (2) that what they call non-causality is merely a specific process’ not being the cause, or not having been discovered as the cause, of a specific set of selected data or processes. Such non-causality is not with respect to all existents.
A topology and mereologically clean physical ontology of causal continuity between partially discrete processual objects, fully free of absolutely continuity-oriented or 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.
With respect to what we have been discussing, linguistic philosophyand even its more recent causalist child, namely, dispositionalist causal ontology have even today the following characteristics:
(1) They 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) They are logically comatose about the impossibility of the exactly referential definitional approach to the processual demands of existent physical objects without first analyzing and resolving the metaphysical implications of existent objects, namely, being irreducibly in finite Extension and Change and thus in Universal Causality.
(3) Hence, they are 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 and forget about absolute continuity or discontinuity in nature. Mathematics and the physical universe are to be reconciled in order to mutually delimit in terms of the causal continuity between partially discrete processual objects.
Hence, it is useful for the growth of science, philosophy, and humanities alike to research into the causal continuity between partially discrete “processual” objects and forget about absolute continuity or discontinuity in nature. Mathematics and the physical universe are to be reconciled in order to mutually delimit in terms of the causal continuity between partially discrete processual objects.
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 CASE OF STATISTICAL CAUSALITY:
As a way to relativize or to reduce to non-consummative the substitution of causation by statistical recognition and interpretation of causation, I would subscribe to Phil Dowe’s announcement about his work in causation: “[…] the whole approach of using statistical relations to analyse causal mechanisms will be challenged. It will be argued: (1) that causal production cannot be analysed in terms of statistical relations, and (2) that causal interactions cannot be analysed in terms of statistical relations.” [Phil Dowe 2000: 79]
What is the import of this claim?
Does he really question statistical interpretations?
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.
Existents have some Activity and Stability. This is a fully physical fact. These two categories may be shown to be subservient to Extension-Change. Pure vacuum (non-existence) is absence of Activity and Stability. Thus, entities, irreducibly, are active-stable processes in Extension-Change. Physical entities / processes possess finite Activity and Stability. Activity and Stability together belong to Extension; and Activity and Stability together belong to Change too. That is, Stability is not merely about space; and Activity is not merely about time. But the tradition still seems to hold so. We consider Activity and Stability as sub-categories, because they are based on Extension-Change, which together add up to Universal Causality; and each unit of cause and effect is a process.
These are not Categories that belong to merely imaginary counterfactual situations. The Categories of Extension-Change and their sub-formulations are all about existents. There can be counterfactuals that signify cases that appertain existent processes. But separating these cases from useless logical talk is near to impossible in linguistic-analytically tending logic, philosophy, and philosophy of science.
Today physics and the various sciences do something like this in that they indulge in particularistically defined terms and procedures, blindly thinking that these can directly represent the physical processes under inquiry. Concerning mathematical applications too this is the majority attitude among scientists. Hence, without a very general physical ontology of Categories that are applicable to all existent processes, all sciences are in gross handicap.
The best examples are mathematical continuity and discreteness being attributed to physical processes, which are continuous and discrete only in their Causality. This is nothing but Extension-Change-wise discrete causal continuity. At any time causality is present in anything, hence there is causal continuity. But this is different from mathematical continuity and discreteness.
I HAVE REVISED THE DISCUSSION TEXT OF THIS QUESTION AS FOLLOWS:
MATHEMATICS AND CAUSALITY:
A SYSTEMIC RECONCILIATION
Raphael Neelamkavil
A caveat is in place here about the complexity one may experience in the formulations below: When I write anything here, you have the right to ask me constantly for further justifications for what I write. 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. Our (and your) characterizations of meanings in mathematics, physics, philosophy, and logic can be complex and prohibitive for some. But would we all accuse these disciplines or the readers if the readers find them all complex and difficult?
It is common knowledge that mathematics and its applications cannot prove causality directly. What are the bases of the problem of the incompatibility of causality with mathematics and its applications? 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, it can only show the ways of movement of the processes and not demonstrate whether the ways are by causation.
But can logic show the necessity of all existents being causal? I suggest that the crux of the problem here is the dichotomy between mathematical continuity and mathematical discreteness on the one hand and the incompatibility of applying any of them directly on the data collected / collectible / interpretable as derived from some layers of the phenomena which are from some layers of nature or the reality in question. Not recognizing this is an epistemological folly. Science and philosophy, in my opinion, are victims of this.
I point at the avoidance of the problem, by the centuries of epistemological folly, by reason of the forgetfulness of the ontological and epistemological relevance of expressions like ‘from some layers of phenomena from some layers of the reality in question’.
This is the point at which it is time to recognize the gross violence against reason behind THE MUTUAL CONFUSION OF phrases and statements involving ‘data from observation’, ‘data from phenomena’, ‘data from nature / reality’ etc., without epistemological and ontological astuteness.
The whole of what we used to name "space" is not filled with matter-energy. Hence, if causal continuity between partially discrete “processual” objects is the case, then the data collected / collectible cannot be the very processual objects and hence cannot provide all knowledge about the processual objects.
The sciences and all research methodologies are based on human experience and thought based on experience. But mathematics, though from experience, is as though not from experience. It quantifies qualities, and hence are qantitatively qualitative in its way of treatment of its objects.
Hence, it is important to define the limits of applicability of mathematics to the physics of data (under the species of various layers of their origin). This 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 human reason is limited to the procedures of reasoning by brains. What exactly then is the reason that existent physical processes constantly undergo? How to get at conclusions based on this reason and thus transcend at least to some extent the limitations set by data and methods?
If we may call the universal reason of Reality-in-total by a name, it is nothing but Universal Causality. It is possible to demonstrate that Universal Causality is a trans-physical, trans-scientific Law of Existence. This argument needs clarity. How to demonstrate this as the case?
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 of the concept of To Be.
Existence in Extension-Change is what we call Causality. If anything is existent, it is causal – hence Universal Causality is the trans-scientific 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 as transfer of impact, no existent can be absolutely discrete in its parts or in connection with others.
Insistence on mathematical continuity in nature is a mere idealization. It expects nature to obey our merely epistemic sort of idealizations (in ideal cases, based mostly on the brain-interpreted data from some layers of phenomena, which are from some layers of the reality under observation).
Some of the best examples for inflicting mathematical continuity and discreteness in science are the suppositions that 'virtual worlds are absolutely discrete worlds', 'dark energy is a kind of propagative energy', 'zero-value cosmic vacuum can create an infinite number of universes', etc.
The processes outside the mind are vaguely presented primarily by the processes themselves, but highly indirectly, in a natural manner. This is represented by the epistemic activity of the brain in a natural manner, and then idealized via concepts expressed in words, connectives, and sentences (not merely linguistic but also mathematical, computerized, etc.) 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 that we have. We then create the mathematically and linguistically idealized results as existents.
Thus, virtual worlds begin to exist, dark energy begins to propagate, and zero-value cosmic vacuum creates universes from nowhere. Even kinetic and potential energies are treated as propagative energies, as existent outside of material bodies and as supposed to be totally different from material bodies.
Insistence on mathematical continuity in nature as a necessary conclusion by the application of mathematics to nature is what happens in all physical and cosmological (and of course other) sciences insofar as they use mathematical idealizations (another version of linguistic symbolization and idealization) to represent existent objects and processes and extrapolate further beyond them.
Logic and its direct quantitatively qualitative expression as found in mathematics are, of course, 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 side-effects of the same symbols in the language, logic, and mathematics being used in order 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 well, although they too are equally unable to capture the whole of reality in whatever it is, wholly or in parts, far beyond the data and their representations. Therefore, why not de-idealize the side-effects of mathematics too?
This theoretical attitude of partially de-idealizing the effects of human symbolizing activity by use of the same linguistic symbolic activity accepts the existence of processual entities as whatever they are. This is what I call ontological commitment – of course, different from and more generalized than that proposed by Quine and others.
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 the sciences and by means of its systemic physical ontology falls short miserably in actuality, and (b) logical continuity of any kind does not automatically make linguistic or mathematical symbolized representation activity adequate enough to represent the processual nature of entities as derivate from data.
(2) The concept of absolute discreteness in nature, which, as of today, is ultimately of the 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: (a) 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 (b) because the epistemology of unit-based thinking (not, of course, based on quantum physics) is implied by the almost unconscious tendency of symbolic activity of body-minds.
(3) 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. Any existence in Extension-Change-wise manner is nothing but causal activity. Thus, insofar as everything is existent, every existent is causal. There is no time (i.e., no minute measuremental iota of Change) wherein such causal manner of existing ceases in any existent. This is causal continuity between partially discrete processual objects. This is NOT MATHEMATIZABLE.
The attitude of treating everything as causal may also be characterized by the self-aware symbolic activity by symbolic activity itself, in which certain instances of causation are enhanced or avoided, all incrementally, not absolutely. This, at the most, is what may be called freedom. It is fully causal – causal not in a specific set of manners, but 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 by allowing defectively ideal mathematical status for causal continuity and with perfectly geometrical ideal status for specific beings, or (3) statistically indeterministic, thus compelled to consider everything as partially causal, or even 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?
The statistician does not even realize (1) that Universal Causality is already granted by the very existence of anything, and (2) that what they call non-causality is merely a specific process’ not being the cause, or not having been discovered as the cause, of a specific set of selected data or processes. Such non-causality is not with respect to all existents.
A topology and mereologically clean physical ontology of causal continuity between partially discrete processual objects, fully free of absolutely continuity-oriented or 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 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.
With respect to what we have been discussing, linguistic philosophy and even its more recent causalist child, namely, dispositionalist causal ontology have even today the following characteristics:
(1) They 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) They are logically comatose about the impossibility of the exactly referential-definitional (strictly denotative) approach to the processual demands of existent physical objects without first analyzing and resolving the metaphysical implications of existent objects, namely, being irreducibly in finite Extension and Change and thus in Universal Causality.
(3) Hence, they are unable to get at the causally continuous (neither geometrically 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 purpose.
Postmodern philosophies qualified all logic, math, 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 the 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.
Howdy Raphael Neelamkavil,
Thank you for your continuing improvement of exposition in this work. I recall being bewildered by "Universal Causality" when I first encountered it many months ago: I find this latest definition quite clear. Whether it is valid is separate from my understanding of your meaning. Many other points are becoming more lucid as well, again, thank you.
My earlier observations have been tempered by recollection of the movie biography of Louis Pasteur in which Joseph Lister is also featured. Movie accuracy is irrelevant here since the important affect is that I realized an overview for your effort that rings true for me: You are seeking an improvement in "doing Physics" that avoids infection from mathematics qualities that mislead research. Close enough since your version is more important:
"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 well, although they too are equally unable to capture the whole of reality in whatever it is, wholly or in parts, far beyond the data and their representations. Therefore, why not de-idealize the side-effects of mathematics too?"
This written, and your effort affirmed, I must honestly note that while this all rings true in the universe as you conceive it, there are differences in our universes. Application of your development to my universe does raise questions. A point of agreement is contained in my "My Skin Is Not My Surface" work and my initial "Indiscrete Number Theory" version that has evolved to Object-oriented Number Theory. They derive from efforts to conceive an eddy in a stream as an individual with integrity that interacts (your "change as transfer of impact") with other eddies in the stream (or persons in a community.) It is an "indiscrete" individual with integrity. In this way, your "the existents are non-vacuously extended. This means they have parts." strikes me as similar. Unfortunately, I need clarification of "parts" in the "extended" state of the existents. You go on to write: "Every part has parts too, ad libitum, because each part is extended. None of the parts is an infinitesimal. They can be near-infinitesimal." I think this point could be clarified since it implies that portions (all?) of extension are fragmented. Your set of parts in an individual extension is effectively unbounded, up to being infinitesimal. The latter would require the extended thing be the result of a limit process, which could hardly be allowed because it's result is not a member of the set used and therefore would not exist. If they are not infinitesimal, are not the "smallest" discrete? I wonder here. Incidentally, the history of common sense trash about infinitesimals is very human error, like many similar absurdities at the present time.
(Is discrete or continuous actually the problem? I don't think so, or that words are the problem you address, and the abuse of words cannot be prevented by forbidding them. Other words may be abused as well.)
"What exactly is the reason that existent physical processes constantly undergo? How to get at conclusions based on this reason and thus transcend at least to some extent the limitations set by data and methods?" is excellent in my view. In my work my focus on process is an effort to have the reason that existent physical processes constantly undergo at the core of the effort. It describes well my efforts to find the mind movie that presents the nature of Nature, a movie that is deeper than visual because it includes "reason" as you use it here.
On the devil's advocate side, questioning things brings out that you write of things having extension and forbid the existence of a "volume" that could contain that extension. "Space is the measured shape of Extension" from your "Irrefutable Argument" piece does not cover my need for a volume, say a vacuum state that is not the "false vacuum" of Inflationary Universe theory. Your Space definition only says that, did such a volume exist we could call the occupied portion space, but then we are stuck with it also existing. Further, you allow the extension to have "parts" and yet write nothing about internal "impacts" that are as logical as many other details here, given external impacts and responses to them. What is(are) the "reason(s)" specifying Change as it is Caused by impacts. Also, If appears several places - what if "it" isn't, "they" are not.
Well, enough of this. You have several posts on this topic and I must not try to address them all. About the same fraction of humanity is capable of doing philosophy, natural or other, as is capable of playing a violin or your favorite instrument. I wish some individuals wouldn't try to do philosophy and thereby create the quite off-the-wall excesses to which you object and that appear in every era, like Descartes' "vortices." Cogito ergo sum is brilliant but it does not explain planetary motions in vortices, or prove "I" is contained in a corporeal object.
By the way, as you also appreciate, many scientists act responsibly and use "idealized" versions of theories well. Much of the appearance of irresponsibility comes from the populace demanding thrills and the go-betweens who thrive on this addiction. Remember the cholesterol scare a few decades ago which lasted a while until someone pointed out "good cholesterol" and the insanity waned. I think your effort is important as in the Pasteur/Lister note above, but factory workers tolerate safety lectures and ignore them in practice (lots of experience there), so implementation of your concerns in scientific activity will be an interesting process, or per Spock of Star Trek, "fascinating."
Finally, I think the following paragraph is epistemological and ontological astuteness gone mad, or perhaps is to idealized: "This is the point at which it is time to recognize the gross violence against reason behind THE MUTUAL CONFUSION OF phrases and statements involving ‘data from observation’, ‘data from phenomena’, ‘data from nature / reality’ etc., without epistemological and ontological astuteness." Epistemology and ontology have no stronger absolute meaning than energy, momentum or charge! “data from observation” has meaning!
Your view is well expressed and getting better with each version - a work in progress. Others will find there what they see, and I wish you good fortune in the endeavor, but I have a sparkling mountain stream happily solving the problem of a few rocks in a rapids to understand, so I'll amble off for a while.
Happy Trails, Len
Leonard Hall, thanks. I read your intervention fully, just now. Most of the questions and suggestions are familiar to me since I have been working on it in various books. Currently I am on a new book: CAUSALITY IN PHYSICS, MIND, LANGUAGE, AND AI: PROCESS METAPHYSICS OF SPACE-TIME, UNOBSERVABLES, UNIVERSALS, AND VIRTUAL POSSIBLE WORLDS. Just about 200 pages. The English version is ready. Am now working on the Italian version. Later, someone will translate it into Spanish. I decided not to translate it into German since most German-speaking persons interested in this theme would already be in a position to read the English.
In this work I am elaborating on most of the questions you have already sounded. One day, as I get time, I shall write a detailed reply to your intervention. This week my hands are full. Incorporating the corrections (from two Italians) on the Italian version, some classes and talks to attend, etc. occupy me now.
In any case, as I read your response, I realized that some aspects (like infinitesimality) need more clarification in ResearchGate. In the said book, I have done it. But I promise to respond with answers to all that you asked and opined.
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
Leonard Hall, one question on procedure. Do you like that I revise this lead question of the discussion in a manner that I reply also to your questions? This is what I prefer. But if you want a specific post on the questions you have raided, I can do that. The problem is that in any case I must revise the lead text. Am planning to develop it into a few pages; and writing an additional intervention specifically to your questions would mean repetition of many things said in the lead text.
Reification of Concepts in Quantum Physics?
https://www.researchgate.net/post/Reification_of_Concepts_in_Quantum_Physics
Howdy Raphael Neelamkavil,
"Philosophy (from Greek: φιλοσοφία, philosophia, 'love of wisdom')" Wikipedia quote. Philosophy is a condition that one does not control, like actual love of a spouse rather than just desire, infatuation, or lust for a partner. Since our first encounters I have found enrichment of "my wisdom" (which is dangerous to self-evaluate) in our exchanges, but I'm not trying to settle anything. In wisdom as in science I believe we're floating along mid-stream, more ignorant and unwise that full of either knowledge or wisdom. I was scolded severely at the U. S. Army Atmospheric Sciences Laboratory at White Sands Missile Range for making an affirmative comment about one of two optical turbulence measurement systems by an aggressive advocate of one of the systems who was engaged in combat over them with his supervisor. I pointed out my opinion could do little damage, and I think the same is true here. I'm just following along, interacting (intervening?) on points of interest to me and discovering new things and ideas along the way, like I did on vacation when I watched and recorded a 2 cm black beetle rotating a 3 mm cluster of sand grains as if licking something it found on its surface. I'd never seen a beetle do that before, interesting, and the body parts it used were new to me because I know so little about beetles. You are free from any constraint on my part as to how you contribute to your discussion.
On exactness: on my second reading of the Blue and Brown Books of Wittgenstein when I got it right, I found the awareness that "language of the people" is unsuited to philosophic investigations, and that is just fine because philosophers are in the wrong to rip language from its native use and use it in strange ways (latter wording mine). Jargon, the patois of a specific discipline with each term carefully defined and used with that definition is needed for philosophic investigation. The words are then as exact as their definition and their use! I live in Idaho. My car license plate reads "Famous Potatoes" and raises the question you have raised "What does one potato mean?" Myriad answers when looks to the object, but "one" here is a counting number and "how many" has been rigorously specified although "how much" remains a mystery.
On irrational numbers I quote a reply from Spiros Konstantogiannis to one of my questions: "Using the so called least upper bound (or supremum) property of the real numbers, which is a statement that expresses the completeness of the real numbers; i.e. the fact that every convergent real sequence converges in the real numbers; i.e. its limit is also a real number, it can be straightforwardly shown that there exists a positive real number x such that x2=2 and that that number is unique. Then x is defined to be the square root of 2. Hence, even though the square root of 2 cannot be calculated precisely, it is well defined; its definition is rigorous. Both the existence and uniqueness of the square root of 2 are derived from the completeness of R."
So, is mathematics an exact science in "the language of the people?" Well, no, but it is an exact science in the language of mathematics, and that (physics) "has nothing to do with – or better, it is independent of – mathematics" from the same post is even stronger than your position as I understand it. Is philosophy exact in the language (jargon, patois?) of philosophy - not if one is wise, but it can be precise, accuracy unknown.
1 as a counting number is not the same thing as 1 as a real number, although real numbers can be used to count - it goes on and on. Perhaps this is our most significant difference in world views: I seem to be more willing for common notions and partial understanding to go along together, choosing which to use in specific cases, than I used to be and you seem to be. Have I learned, or just become confused by the idea that living can not, and need not, be that precise or accurate? Hmmm.
Happy Trails, Len
Leonard Hall,
Since you have asked me here some questions that belong to the discussion session on "Math and Causality", I shall write on it here as I have promised, after a four-day engagement with some immediate work.
My replies to the questions on number, irrational number, etc. will be posted there: https://www.researchgate.net/post/Is_Mathematics_an_Exact_Science_If_Yes_and_If_Not_Why
Kindly show understanding for this. This is to help others who would like to experience your reflections and mine on this.
Howdy Raphael Neelamkavil,
Okay, one may find helping others in things I try to do. I know you are busy and I am confident you answer thoughtfully and swiftly within that constraint. I find multiple postings of similar ideas difficult as well. Fortunately it is quite simple to jump between posts with links. We certainly provide others with different ways to view the world. I did think I was responding to an earlier post on this thread. Not to worry.
I think my treatment of separating counting numbers from real numbers as essentially different is sound. Any effort to make them the same will fail, like mating mice and elephants, and it is not necessary. As in so many cases the problem lies in overlapping use of symbols, like "can" meaning "to dismiss" or "to prepare preserves," or "a metal container." 1 and 1.0 are just as different as mice and elephants. (The 1.0 is a valuable afterthought, I think.)
To be repeated on the other thread.
Happy Trails, Len
I think the differences between kinds of number do not matter in my definitions, because my definitions are pre-mathematical and based on the basic math behind evolutionary biology. Thus, when a cat jumps over a small pit in front of it, it does not see whether the pit is to be seen as one pit in the natural numbers or the broader real numbers. It has a vague experience of the unity of the pit. Hence, I do not have to bother even about complex numbers!
A conversation between Paul Healey and me in Academia.edu (today):
paul healey6 hrs ago
Raphael and or Peter, do either of you think a causal explanation of gravity, not for Newtonian mass is possible? Recently I have read some criticisms of Newton’s general inverse square law for it, so wondering if any other explanations have been proposed. Here’s a link that looks relevant: https://arxiv.org/pdf/1604.03441.pdf
Thanks for any feedback in advance.
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Raphael Neelamkavil Ph.D.,Dr.phil., Cosmology + Math'l Physics; Phil. of Science + Scientific, Analytic, Process, Digital, ... Systemic Metaphysics & Epistemology< 1 min ago
I have not worked on it directly in the form of a theory. But I would suggest that anything must be causal and hence also gravitons. I said 'gravitons', not merely gravitation as a mathematically treated gross phenomenon! Why should everything be causal? I shall try to explain, very simply.
As you know, any mathematical proof for causation is not a proof at all, since math cannot touch it. Math can only see or show some of the ways in which causation works.
Let me first explain causality in a new manner; and then return to gravitation.
You do believe that whatever exists, exists. Now apply the law of contradiction. Whatever does not exist, does not. Let us name the latter as pure vacuum, non-entity, etc. If anything is not vacuous, it should have some extension, i.e., should have parts.
This is, therefore, a self-evident implication of the notion of To Be. I call it the metaphysical / physical-ontological Category of Extension, because it is one of the basic natures of all existents. Now, anything in Extension is not infinitely intense, i.e., there are not all the same extended stuff.
The additional information needed here is empirical: that there are movements in such extended stuff. If so, then it means that everything extended has some movement, which automatically should affect something else -- but not affect all else. This is impact generation. I call it the metaphysical / physical-ontological Category of Change.
If something in Extension has Change, such an existence is "already impact generation (Change) by parts (Extension)". This is what we used to call Causality. That is, the very two implications of To Be, when taken together, is nothing but THE UNIVERSAL LAW OF CAUSALITY. Everything existent must be causal.
Now, back to gravitons. If they are just a non-existent but mathematical construct, we do not have to bother about them. But if they are existent (which is the only other possibility), then they too must be causal.....!
Leonard Hall, I have revised the lead text (see directly under the title of this discussion). Now it has become 8 pages in A-4. 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
Exactly! And this is perhaps why physicists can do their theoretical stuff without speaking of causation.
True. But due to the enormity of the sense of power given by math, many physicists tend to depend on math and call their own discipline as independent of causation!
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. For this reason, natural numbers have Categorial priority over rational numbers. Complex numbers, for example, are the most general number system, 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.
No Detriment to the Sciences, but Only Enhancement: By the above claim no one in the sciences needs to get threatened or feel being robbed of their own powers. Philosophy is not an attack on the sciences. It is at the very least a wake-up call for the sciences to grow in their foundations, methods, theoretical breadth and depth, and experimental connection with the broadest possible causal horizons behind theory. The fact is that any conversation about the above aspects of science automatically becomes philosophy of science. They can happily forget all other functions of philosophy.
Howdy Raphael Neelamkavil,
I finally recognized a problem, and after looking up “category” I can find “extension” for objects as something that can be said about them without acknowledging the volume that must exist also to contain them. That’s trivial when meanings of words in use are specified. (I did read through the Britannica Great Books (1952 ed.), but I did not memorize them, even Immanuel Kant’s volume!)
Now to clarify, in our opening contact under your inquiry Can the Primitive Notions (Categories) and Axioms of Mathematics, Physics and Philosophy Converge? there is a serious communication problem in either English or Philosophy, because Categories are not Primitive Notions! “A category is that which can be said of everything in general, that is, of anything that is an object.” (Wikipedia, “Category.”) “In mathematics, logic, philosophy, and formal systems, a primitive notion is a concept that is not defined in terms of previously-defined concepts." (Wikipedia “Primitive Notions.”) Categories in Philosophy Jargon are predicates and Primitive Notions are undefined bases for a discipline. “Point,” “line,” “contains” (Wikipedia examples) of primitive notions are not at all like the categories “extension,” “impact,” “change” as you use them in your Mathematics and Causality: A Systemic Reconciliation. If we have to become natives in Philosophy Jargon to read your stuff, please be more careful!
This written, I can remove my concern about a volume containing extension as expressed in an earlier post. As for extension having parts in all objects and for the parts in an individual object to be indeterminate up to unbounded in count but not infinitesimal, I find it less obvious, however categorical. Impacts of these “existents” and having “impacts cause” remain in need of definition and explanation in my world, but at least I have learned what you mean by categories in your world.
Past experiences encouraged me to skip this post as a waste of time for both of us, then I recognized my observation above about Philosophy Jargon versus "translated from philosophical language into normal" [thank you Igor Bayak on the Reification of QM thread] as a general problem, and I wondered whether either of us could be comprehended at a glance. My reference to Aristotle's words, or Kant's words, or Neelamkavil's words, was sound because unbeknownst to me I had identified a source of confusion. I need to know when a set of letters refers to Philosophy Jargon or "normal language." Ahhh. This opening may be very nice for me, especially when your motivations for a development and conclusion in your world lead me astray in my world. The mixed language problem is real: I'll watch for it, please help.
Happy Trails, Len
Dear Leonard Hall, thanks. I was waiting for you comment.
I am aware of the distinction between category in phil and primitive notions in math. But in phil, there are no other primitive notions. We do use sentences to explain both category and primitive notions, but this is post factum within the system. For these reasons, I have used them as the same.
Concerning near-infinitesimality: Consider an electron. It does not have an infinite number of finite (here, near-infinitesimal) parts. It has only a finite number of them. Only if we speak of infinitesimals do we have an infinite number of them in a finite-content particle / wavicle. Thus, this is evident.
Now about impacts: First of all, if anything is non-vacuous, it is extended, having parts. Hence Extension is one major implication of To Be. Every part has a finite amount of motion. This is what is called impact-formation. This is Change, the second major implication of To Be. Now how to reach causation? The very existence (to be) in Extension-Change is to be called Causation. Impacting alone is not causation, because it is just Change. Instead, Change should be in and by Extended objects. This is already Causality. Hence, everything existent is in causation: Universal Causality. This is a pre-scientific law.
In a book I am able to go into details. But when I write a short intervention or discussion material, I do not remember to keep every important point in it. That is all.
Thanks for the interest.
Howdy Raphael Neelamkavil,
I was looking for a recalled exchange in this work when I discovered a mild alternative:
https://www.earlymoderntexts.com/assets/pdfs/descartes1642_3.pdf
Objections to the Meditations and Descartes’s Replies René Descartes
Objections to the second meditation
Reply (5) What I wrote about the imagination will be clear enough to those who study it closely, but it isn’t surprising if those who don’t meditate on it find it very obscure.
Clearly I take too much time, and what is being used has been wasted again. I should have followed the impression to "skip it," since I do not find answers to my questions or my observations or validity in my asking for explanation of something that is only believed assertion in what I read in your post.
I learn from almost anything, directly, contrarily, analogously, even by a trigger for insight where the connection is so deep the process of aHa! remains a mystery to me as much as to others, so I'm okay here. On the other hand, being so regularly overwritten or retold points I claimed to have studied is wasting too much of your time. It's time to leave.
Happy Trails, Len
Leonard Hall, your interventions are always welcome and held in esteem. I will try to reply in the way in which I can. On many thing I need to learn more and have more insights. True.
Thanks.....
Raphael
causality is mistaken (( it so seems )) by Mr Neelamkavi for non-causal explanations that involve a "because without cause" since they do not derive their explanatory power by virtue of describing the world's network of [ natural ] causal relations ,,,,,,,
Reza Sanaye, I do not give any non-causal explanation. I try to do it all causally. I do not know why you say so.
Howdy Raphael Neelamkavil,
Okay, of course, since all is well meant. We shall keep trying. Fortunately, both dictionary and encyclopedia are online a mere tab away. I have no new observations at the moment, and aside from "category" treated above, nothing to change right now.
Happy Trails, Len
I have revised the basic text of the following discussion substantially:
Criteria to Differentiate between Virtuals and Existents in Scientific Theories
https://www.researchgate.net/post/Criteria_to_Differentiate_between_Virtuals_and_Existents_in_Scientific_Theories
Howdy Raphael Neelamkavil,
I have read through your revised basic text and I have found it pleasant, interesting and informative. It is quite readable and I thank you for the effort you expended: it was worth it to me and I enjoy exploring any philosophy I can understand. Your distinctions among denotables and your association of them with the activities of scientists and the real and virtual appearances of the world strike me as a much better treatment, more true-to-life, than earlier posts. Good show!
Of course, I'm still me. I find this post relevant to the ongoing function of scientists in extending and enriching that about which we already know; I remain skeptical about how deeply it may aid discovery of actually new knowledge. However, I do remain confident we will have individuals who cannot suppress it within themselves, aHa! They are rare and open lifetimes of work for others, hopefully the latter under the guidance of your concerns about how to do science well.
Happy Trails, Len
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
Friends,
Kindly read the following chain-conversation between an earnest scholar with insight into philosophy, the physical sciences, and logic::::
Alessandro Rizzo added a reply
2 days ago
Logic, as we commonly understand it, is a system of thought based on the reasoning capabilities of the human mind. It allows us to take premises, apply rules, and arrive at conclusions. We view these principles as universal due to their applicability to the wide range of situations we encounter in our daily lives.
However, when we push beyond the confines of human experience and begin to probe the complexities of the universe, we find instances where these principles appear to falter. Traditional logic isn't always equipped to handle the strange, often counterintuitive phenomena observed in realms such as quantum physics.
Particles can exist in multiple states simultaneously in a quantum superposition, an assertion that seems to defy the Law of Non-Contradiction. Entangled particles influence each other instantaneously over vast distances, which challenges our logical understanding of cause and effect.
These instances do not necessarily mean our logical principles are incorrect, but they highlight that our traditional logical framework may be incomplete. It's like trying to comprehend a three-dimensional object with two-dimensional understanding—our perspective is inherently limited.
While the principles of logic remain powerful tools for navigating the world as we perceive it, we must remain cognizant of their limitations. They represent one dimension of a multifaceted reality, and unlocking a more comprehensive understanding of the universe may require us to augment, or even transcend, our conventional logic.
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Raphael Neelamkavil added a reply
2 days ago
Alessandro Rizzo,
This is a very good realization: "However, when we push beyond the confines of human experience and begin to probe the complexities of the universe, we find instances where these principles appear to falter." Mostly it is so. The whole of analytic logic is developed for just for normal life-situations, technically scientific applications, and today for direct computer applications. Of course, this need not be the case with math. Math has a wider set of background considerations today. Ordinary logic is always based on direct needs.
But the following is difficult from the viewpoint of the realistic necessities behind the formulation of the foundations of any sort of logic. "Particles can exist in multiple states simultaneously in a quantum superposition, an assertion that seems to defy the Law of Non-Contradiction. Entangled particles influence each other instantaneously over vast distances, which challenges our logical understanding of cause and effect."
Either it is because such physics is extremely fragile; otherwise it is because any sort of logic cannot really apply to such physics. Even counterintuitive forms of logic falter there!
Hence, I have been following a different course of thought in order to conceptualize what basically would be problematic in quantum, statistical, and other sorts of counterintuitive physics. You can see some such works of mine in very short summary forms in some of my discussion questions (suggested at the end of this intervention).
I recognize that you are an informatics person. An information for you: Just today I have finished the work of a 200 pp. book in English and Italian:
COSMIC CAUSALITY CODE AND ARTIFICIAL INTELLIGENCE: ANALYTIC PHILOSOPHY OF PHYSICS, MIND, AND VIRTUAL WORLDS
and
IL CODICE DI CAUSALITÀ COSMICA E L’INTELLIGENZA ARTIFICIALE: FILOSOFIA ANALITICA DI FISICA, MENTE, E MONDI VIRTUALI.
Now I must begin searching for a publisher....
Here are the said suggestions to some of my discussions in RG:
https://www.researchgate.net/post/The_Irrefutable_Argument_for_Universal_Causality_Any_Opposing_Position
https://www.researchgate.net/post/Criteria_to_Differentiate_between_Virtuals_and_Existents_in_Scientific_Theories
https://www.researchgate.net/post/Reification_of_Concepts_in_Quantum_Physics
https://www.researchgate.net/post/Gravitational_Coalescence_Paradox_GCP_Introduction_to_Gravitational_Coalescence_Cosmology
https://www.researchgate.net/post/Mathematics_and_Causality_A_Systemic_Reconciliation
https://www.researchgate.net/post/Linguistic_Philosophys_Inconsistencies
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Alessandro Rizzo added a reply
2 days ago
Dear Raphael Neelamkavil,
Your exploration of the philosophical underpinnings of quantum physics is both thought-provoking and challenging. As someone who has grappled with the mysteries of the quantum world, I appreciate your efforts to question and redefine our understanding of these complex concepts.
You rightly point out the limitations of conventional logic when applied to quantum phenomena. Indeed, the quantum world often seems to defy our everyday understanding of reality. Quantum superposition and entanglement, for instance, challenge our intuitive grasp of cause and effect, as well as the principle of non-contradiction. However, I would argue that this does not necessarily mean that these principles falter, but rather that they take on new meanings in the quantum realm.
Your concept of Universal Causality is intriguing. The notion that everything that exists is in causation, even quantum-mechanical processes, is a bold one. I would argue, however, that causality in the quantum realm may not be as straightforward as in the macroscopic world. Quantum mechanics often deals with probabilities rather than certainties, which adds a layer of complexity to our understanding of causality.
Your criteria for differentiating between "virtuals" and "existents" is an interesting approach to understanding scientific theories. The idea that anything not in Extension-Change is non-existent is a compelling one. However, I would caution against too rigid a definition of existence. The quantum world has shown us that reality can be far stranger than we might imagine.
Your discussion of reification in quantum physics raises important questions about the nature of mathematical entities like wave functions. It's true that we must be careful not to confuse our mathematical models with the physical reality they represent. However, these models have proven to be remarkably successful in predicting the behavior of quantum systems, which suggests that they capture some essential aspect of quantum reality.
Finally, your analysis of potential energy and the wave function collapse is insightful. These concepts are indeed more complex than they might appear at first glance. However, I would argue that they are useful tools for understanding and predicting the behavior of physical systems, even if they do not correspond exactly to physical entities or processes.
Your exploration of these topics is a valuable contribution to the ongoing dialogue about the nature of quantum reality. However, there are a few points to discuss.
1. **Universal Causality**: While your concept of Universal Causality is intriguing, I believe that causality in the quantum realm may not be as straightforward as in the macroscopic world. Quantum mechanics often deals with probabilities rather than certainties, which adds a layer of complexity to our understanding of causality. It's not that causality doesn't apply, but rather that it may manifest in ways that are not immediately intuitive.
2. **Existence and Non-Existence**: Your criteria for differentiating between "virtuals" and "existents" is an interesting approach. However, I would caution against too rigid a definition of existence. The quantum world has shown us that reality can be far stranger than we might imagine, and phenomena that don't fit neatly into our conventional understanding of existence may still have significant physical implications.
3. **Reification in Quantum Physics**: Your discussion raises important questions about the nature of mathematical entities like wave functions. However, while we must indeed be careful not to confuse our mathematical models with the physical reality they represent, these models have proven to be remarkably successful in predicting the behavior of quantum systems. This suggests that they capture some essential aspect of quantum reality, even if they don't correspond exactly to physical entities or processes.
4. **Potential Energy and Wave Function Collapse**: Your analysis of these concepts is insightful. However, I would argue that they are useful tools for understanding and predicting the behavior of physical systems, even if they do not correspond exactly to physical entities or processes. The wave function collapse, for instance, may not be a physical process in the conventional sense, but it is a crucial concept in the interpretation of quantum mechanics.
I appreciate your efforts to challenge conventional wisdom and push the boundaries of our understanding. Even though we may not agree on all points, such dialogue is essential for the advancement of science.
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Raphael Neelamkavil added a reply
2 days ago
Alessandro Rizzo, thanks a lot for the fine formulations. Very wise and thoughtful. Congrats. At the end of this intervention I give 2 of my discussions, which are on the QM and Statistical notions that are involved in physics. Let me express just a few thoughts hereunder, with an introductory statement: I have been into this field of publication at least for more than 2 decades; but by way of reading and reflection, I have been in it for more than 3 decades.
Our statistical measures, e.g., of the position of an electron at a given time, does not depend on the model of statistical interpretation that we give, but instead, they depend on the very statistically managed measurements and their proportions of certainty of discovery, prediction, determination, or definition thus achieved. Hence, the varied successes of QM and statistical physics at this level in predicting the related phenomena are all due to the application of the mathematical apparatus, and the model thus achieved, to physical instruments.
That is a sort of algorithm-driven instrumentalization, in a general sense. This, e.g., is exactly why quantum informatics and the various quantum technologies can have success stories.
Let me illustrate this sort of success with a simple example. There are two leaves on a tree at a distance of one meter, but one over the other. Drops of water fall onto the first, and get flown onto the second. We create a signaling system as the drops fall on the first and the second leaves. The nature of light signals take care of the technology behind the signaling. We do not have to bother why light signaling is the way it is!
Here we know that the drops are not exactly spherical / globular. But, for the purpose of mathematical applications, we consider them as spherical drops and reduce them even into the shape of points for the sake of "mathematical precisioning" within the context of the mathematics available -- but which does not harm the signaling. We know clearly that theoretically these are not absolute truths or models...!
The signaling system is related directly to the temporal and spatial approximations of the falling of the drops on the two leaves. As the signals fall on another electronic device (at a distance), and the signals trigger a certain motion on the device. Using this system, let us suppose that we can instrumentalize some other physical process. Whatever the actual physical process and the shapes involved in fact are, the system works and produces the expected results!
We may later give a detailed physical explanation of the approximations involved in the implementation of the theory of, say, "Water Drop Signaling". These are not merely interpretations, but also closer approximations to what is happening in the reality externally to our interpretation. Note clearly: the theoretical model and approximations used in it are all just approximations of what really is the case in nature. We are not able to delve into all the processual layers of the object set and unearth all possible explanations of the processes and all their layers.
In order to apply our theory of the specific and precisioned processes with all their complexity in physics, we need to create instruments that work in accordance with this new theory and other related these physical and other theories which work only at a certain level of instrumentation in the given case. What works at the electronic level need not work at the nano level of physical activity.
We cannot also finalize our theory by stating that whatever works at the nano level is final and that there are no deeper layers within the object set. Even as we discover deeper layers and begin to formulate methods of instrumentation at that level, the instruments can continue to work without any hindrance. The only thing is that the instruments can further be made more precisioned and more effective. This does not work as an argument against the existence of the deeper layers beyond the nano structures!
That is, this means that the first set of interpretations and their instruments can go on to work and produce technological successes. They will continue to yield successes. This is why even now Newtonian physics yields many successes, especially at the engineering level!
Similarly, the successes of QM need not suggest that they capture some essential aspect of quantum reality in a very exact manner. Of course, this is the case to a certain extent (say, statistically), but this certainly at a certain narrowly real interpretational level.
The statistics here is a model, and therefore, is based on the measures of our ability to capture the causes and the processes within a given circumstance and sample. Statistics is thus the admission of the extent of reach into the exact correspondence of the truth projected by our measurements with respect to what is actually happening in the object process!
But this fact of lack of absolute truth in our models and theories does not affect the successes at the level of application of the possible experimental results of the theory! Now you see clearly that what quantum physicists call as the statistical truths of quantum physics are not truths but models, using which there are certain instruments and their theory of apparatus-wise obedience of quantum physics.
This is also the case with respect to Relativity. Just take the case of the Lorentz factor: Root of [(1 - (v-squared) divided by (c-squared)]. What does it in fact mean? That I am willing to measure the movement process (v) of a particle only in terms of the experimentally rather well determined / fixed luminal and luminally comparable energy propagations c.
But this means also (and exactly) that, since I use luminal velocity as the criterial velocity (merely because I have natural vision and instrumentational vision at the level of c at this epoch of the history of advancements in science), my calculation forbids v from exceeding the luminal velocity limit c!!!
Does this mean that there should not be superluminal velocities?
If there are real-valued (not complex-valued) superluminal velocities, whereby the superluminal velocity in question is C1, C2, etc., which can replace the c, and c can be placed at the place of v in the nominator, in the Lorentz factor. Thus, we have a real solution for the EPR problem, too!
After all, the c is not fixed or fixable as an absolute constant except by a convention that has proved it to be so in our region of the universe, and not for all the possibly existing worlds! Using this convention, we can continue to make our Water Drops Signaling work. But this success in measuring the lack of temporal lag in the working of the instrument need not mean that c is a universal constant for all the regions of the cosmos.
The cosmos may have a finite number of local universes or even an infinite number of them. In both the cases -- and in the latter case surely -- c may be replaced with C1, C2, etc. in other regional universes. That is, the highest possible velocity within a big bang local universe anywhere in the infinite-content cosmos can only be determined by the maximum density achieved at any one big bang of the given local universe, in a series of its oscillations between bangs and crunches. (I have treated this in my book of 2018 and in some discussions in RG, which will be given at the end of this reply.)
Nevertheless, miraculously clear and working precision is to be had in many scientific theories and experiments, both on earth and in the outer space, using this special theory of relativity! Even QM uses the Lorentz factor freely!
Should these successes mean that the Lorentz factor should be an eternally fixed proof for the so-called criterial limit-nature of c?
Now I believe we can think of a possible solution for the EPR problem! I have suggested one such in 3 of my works. I think, therefore, that what we need is a range of differently-valued c and the many relativity theories in terms of them.
I have discussed such questions in detail, including a detailed theoretical solution to the EPR problem, in three of my printed books (2014, 2015, and 2018).
I should salute you for your openness and genuineness of scientific spirit, which permit you to see many important points in the notion of theory formation in science and philosophy. Not merely of my ideas, but also of others ideas.
I am a mad man. I have dedicated my life to some such projects in the form of books. To avoid peer reviewers' ire is not easy. Hence, I may not get the most renowned publishers to publish my books. I should also forget about publishing articles in reputed peer-reviewed journals! This is my fate, and also my pleasure. I think some future acceptance (at least after a few years or decades of my death) is forthcoming.
And kindly take a look at the following discussion sessions. I think you will enjoy them. And thereafter I give a SET 2 of discussion links, which give the discussions on the cosmological problems suggested above.
SET 1:
https://www.researchgate.net/post/What_are_the_basic_insecurities_of_physics_especially_of_statistical_physics
https://www.researchgate.net/post/Is_Causality_Necessary_in_Physics_Philosophy_and_Other_Sciences_in_Place_of_Statistical_Bayesian_and_Other_Theories_of_Causality
SET 2:
https://www.researchgate.net/post/Can_the_cosmic_or_local_black_hole_singularity_be_of_infinite_density_and_zero_size
https://www.researchgate.net/post/Source-Independent_Velocity_of_Pure_Energy_vs_Causality_vs_Superluminal_Velocities
https://www.researchgate.net/post/If_the_cosmos_is_1_finite-content_or_2_infinite-content_Is_there_finite_or_infinite_creation
https://www.researchgate.net/post/Gravitational_Coalescence_Paradox_GCP_Introduction_to_Gravitational_Coalescence_Cosmology
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Alessandro Rizzo added a reply
1 day ago
Dear Raphael Neelamkavil,
Your thoughtful and extensive response is deeply appreciated. The time and dedication you've devoted to these intricate concepts shine through, and your perspective brings a refreshing viewpoint to our discourse.
You assert that our statistical measures in physics are heavily influenced by the mathematical models we've formulated, a position that resonates with accuracy. These models, while approximated by nature, have served as the bedrock of our comprehension of quantum mechanics, enabling us to generate predictions from this understanding. However, as you astutely pointed out, this doesn't necessarily indicate that these models encapsulate the entire scope of quantum reality. Perhaps it's more accurate to state they represent our best tools available for interfacing with and comprehending the quantum world, given our current technological capabilities and conceptual understandings.
Your analogy of abstracting water droplets to points for mathematical precision provides an excellent illustration. Fundamentally, the models we employ in physics are simplifications of reality, designed to encapsulate the most pivotal aspects of the physical phenomena we investigate. But it's crucial to avoid mistaking these models for reality itself. They merely represent our best current methods of describing and predicting reality.
Your comments concerning the Lorentz factor and the speed of light are strikingly thought-provoking. Indeed, the assumption that the speed of light is the ultimate speed limit in the universe is underpinned by empirical observations within our observable universe and within the framework of the theory of relativity. The concept of superluminal speeds would require us to radically revise our understanding of the universe.
Your courage and determination to challenge the established scientific framework are admirable. Authentic progress in science often originates from those brave enough to question the status quo and expand the boundaries of our understanding. I'm confident that your work will find the audience and appreciation it deserves, for the truth in science has a peculiar way of making itself known, irrespective of its immediate reception.
The possibilities you suggest, such as various relativities predicated on differing c values, are genuinely captivating. This kind of innovative thinking often ushers in paradigm shifts in scientific thought.
Your ongoing commitment to these questions is inspiring, and I anticipate with eagerness the exploration of the discussions you've linked. I hold firm in my belief that science thrives on open discourse and a diversity of perspectives. Hence, although we may not concur on all points, the value of dialogue is irrefutable.
Thank you for your participation in this intellectually stimulating conversation.
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Raphael Neelamkavil added a reply
19 hours ago
Alessandro Rizzo, I have revised my previous reply and detailed it further, also extending its cosmological implications. In fact, I had written the earlier version of the response in a hurry, in about 15 to 20 minutes. Hence the revision of the same.
Please see also the SET 2 list of RG discussions, given at the end of the revised response. These are the cosmological ones. Thanks.
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Alessandro Rizzo added a reply
15 hours ago
Dear Raphael,
Embracing your insights, the light cast by statistical measures in our understanding of quantum mechanics is impressive. They serve as a beacon in the labyrinth of quantum phenomena, born from the marriage of algorithms and instrumentalization.
The water drop signaling system, as you've painted, is a vivid illustration of mathematical approximations at work. Science walks a tightrope between reality and approximation, juggling precision with pragmatic simplicity. The certainty of mathematics may not always mirror the uncertainties of reality, and vice versa.
The discussion of various levels of physical activity and the evolution of our tools to meet these levels holds significant weight. As we continue to broaden our understanding, we must also adapt and refine our toolkit. A set of tools apt for one scenario might not apply to another.
In addressing the interpretations of quantum reality, you are pushing the envelope, provoking us to reevaluate our grasp of the universe. Though we navigate the quantum realm with the compass of statistics and models, we must stay mindful that these are but the footprints of reality - giving us direction, but also concealing a sea of unknowns.
Your exploration of the Lorentz factor and the hypothesis of superluminal velocities are mind-stretching. The cosmos, in its vast expanse, may hide surprises that challenge our ingrained theories.
Your proposition of different relativities based on maximum velocities is intriguing, urging us to step outside our comfort zone. Your suggestion hints at the reality that the map we hold is not the territory, and our comprehension of this territory is in a state of perpetual evolution.
Closing my response, I am reminded of the sentiment that the tranquility between our scientific theories and the universe's phenomena is born from understanding. Our quest is to deepen this understanding, and your insightful contributions are a cornerstone of this journey.
Eager to continue this enlightening exchange,
Alessandro
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Raphael Neelamkavil added a reply
15 hours ago
Thanks, Alessandro. Giusto adesso ho visto che sei italiano! Just 2 days ago I finished a work in English and in Italian: Cosmic Causality Code and Artificial Intelligence: Analytic Philosophy of Physics, Mind, and Virtual Worlds, circa 200 pp., and its self-made Italian version (corrected by native speakers): Il Codice di Causalità Cosmica e l’Intelligenza Artificiale: Filosofia Analitica di Fisica, Mente, e Mondi Virtuali, circa 220 pp.
Source of Major Flaws in Cosmological Theories: Mathematics-to-Physics Application Discrepency
https://www.researchgate.net/post/Source_of_Major_Flaws_in_Cosmological_Theories_Mathematics-to-Physics_Application_Discrepency
Application of Mathesis to causal phenomena does not mean that Mathesis itself is causal ..............
See this conversation:
Wolfgang Konle added a reply
22 minutes ago
Raphael Neelamkavil "Gravitational waves are..."
Gravitational waves are oscillations of a cosmic medium of gravitational nature. This medium overcompensates the negative energy density E of gravitiational fields. (E= -g²/(8πG)). It is omnipresent with a pressure, which equals E and a mass density which equals E/c². According to wave theory this medium supports compressional waves with a propagation velocity c.
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Raphael Neelamkavil added a reply
4 minutes ago
The negative energy you speak of in theory is not an energy that has a negative effect on matter-energy. It is negative due to the math involved. The notion of omnipresence should now be clarified and the reason for gravitation being an omnipresent God should be given. If not so omnipresent, but here less and there more, then the reason should not be just a theoretical need, but instead, a real existence of gravitation (as gravitons) here less and there more!
I feel that you are trying to cover up the non-commitment to gravitation's extra-theoretical and existence. Covering it up perhaps in the theoretical necessities in the form of a negative substitute for some missing form of energy?
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
Infinite-Eternal Multiverse?
https://www.researchgate.net/post/Infinite-Eternal_Multiverse
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
If we are referring to ourselves as "we," { within Infinite-Eternal Multiverses } it implies that we are sentient beings capable of communication. However, if one claims that we are Infinite-Eternal , it contradicts the understanding of our existence as three-dimensional beings. In the physical world, humans and most objects have three dimensions: length, width, and height.
If one is speaking metaphorically or hypothetically or metonymically , please provide more context so I can better understand what you mean by "a single Infinite-Eternal Multiverse" (( non-plural))
I don't know if I used anywhere "single" with respect to the Infinite-Eternal Multiverse. If I have used it, I meant only a denotative manner of referring to the whole Infinite-Eternal Multiverse together as one cosmos. But as far as I remember, I used to specifically say that an infinite-eternal multiverse consists of infinite number of finite-content universes.
But I never claimed that we (humans) are infinite-eternal. Our discussions have always been about the cosmos, characteristics of the cosmos, and our knowledge of it. Note this: even here I spoke of the cosmos, and what I meant is whatever it is (and in that sense, denotatively as one cosmos), i.e., maybe a finite-content universe or an infinite-content multiverse. Whether it is eternal is a matter to be attempted to derive from the various possibilities given of gravitational coalescence formations within the cosmos.
Raphael Neelamkavil
You are certainly a TRUE philosopher , sir ..............
REZA
I try to develop something philosophically strong and general about the physical sciences. That is all. Thanks.
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
If anyone wants to read about a fantastic concept of the existence of consciousness and non-existence of the cosmos, see the comments till today here, by L Kurt Engelhart.......!!! Here you can learn the meaning of solipsism.... and similar to mathematical platonism creating ideas / notions into objects.
https://www.researchgate.net/post/How_to_philosophize_How_to_philosophize_in_the_sciences
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!
https://www.researchgate.net/post/Essential_Reason_in_Physicists_Use_of_Logic_And_in_Other_Sciences_Too
Preprint ESSENTIAL REASON IN PHYSICISTS' USE OF LOGIC: IN OTHER SCIENCES TOO
How Does Physics Know? The Epistemology Presupposed by Physics and Other Sciences
https://www.researchgate.net/post/How_Does_Physics_Know_The_Epistemology_Presupposed_by_Physics_and_Other_Sciences
Preprint MATHEMATICAL SOURCE OF FLAWS IN COSMOLOGICAL THEORIES: MATHE...
Preprint THE EPISTEMOLOGY PRESUPPOSED BY PHYSICS AND OTHER SCIENCES R...
PHYSICAL-PROCESSUAL REPRESENTATION OF IRRATIONAL NUMBERS
https://www.researchgate.net/post/Physical-Processual_Representation_of_Irrational_Numbers
THE ONTOLOGY BEHIND PHYSICS
3.1. Traditional Physical Categories
https://www.researchgate.net/post/The_Ontology_behind_Physics
https://www.researchgate.net/post/Grounded_Physical-Ontological_Categories_behind_Physics
Grounded (New) Physical-Ontological Categories behind Physics
Preprint THE ONTOLOGY BEHIND PHYSICS: CRITIQUE OF TRADITIONAL PHYSICA...
A SIMPLE GAME-CHANGER CAUSALITY FOR PHYSICS: Beyond the Two Millennia
https://www.researchgate.net/post/A_SIMPLE_GAME-CHANGER_CAUSALITY_FOR_PHYSICS_Beyond_the_Two_Millennia
https://www.researchgate.net/post/DEFINITION_OF_THE_ONTOLOGY_BEHIND_PHYSICS_5_Paragraphs
DEFINITION OF THE ONTOLOGY BEHIND PHYSICS (5 Paragraphs)
THE ANOMALY IN MATHEMATICAL / THEORETICAL PHYSICS (Short Text)
https://www.researchgate.net/post/THE_ANOMALY_IN_MATHEMATICAL_THEORETICAL_PHYSICS_Short_Text
Here a serious and somewhat complex matter to discuss:
NON-FOUNDATIONS OF ‘WAVICLES’ IN EINSTEIN-PODOLSKY-ROSEN PARADOX: Bases for Quantum Physics to Evolve (Maybe a physical-ontological Breakthrough)
https://www.researchgate.net/post/NON-FOUNDATIONS_OF_WAVICLES_IN_EINSTEIN-PODOLSKY-ROSEN_PARADOX_Bases_for_Quantum_Physics_to_Evolve_Maybe_a_physical-ontological_Breakthrough
Preprint A SIMPLE GAME-CHANGER CAUSALITY FOR PHYSICS Beyond the Two Millennia
AGAINST COSMIC ISOTROPY, CONFORMAL CYCLIC COSMOS, ETERNAL INFLATION, etc.: A Critique of Identity, Simultaneity, Cosmic Repetition / Recycling, etc.
https://www.researchgate.net/post/AGAINST_COSMIC_ISOTROPY_CONFORMAL_CYCLIC_COSMOS_ETERNAL_INFLATION_etc_A_Critique_of_Identity_Simultaneity_Cosmic_Repetition_Recycling_etc
Preprint ESSENTIAL LOGIC, EPISTEMOLOGY, AND ONTOLOGY BEHIND PHYSICS, ...
WHAT IS THE MYSTERIOUS STUFF OF INFORMATION? A Short but Clear Definition
https://www.researchgate.net/post/WHAT_IS_THE_MYSTERIOUS_STUFF_OF_INFORMATION_A_Short_but_Clear_Definition
Preprint COSMIC ISOTROPY, CONFORMAL CYCLIC COSMOS, ETERNAL INFLATION:...
THE PLANCK ERA / QUANTUM ERA and “DISAPPEARANCE” OF PHYSICAL CAUSALITY: “OMNIPOTENCE” OF MATHEMATICS
https://www.researchgate.net/post/THE_PLANCK_ERA_QUANTUM_ERA_and_DISAPPEARANCE_OF_PHYSICAL_CAUSALITY_OMNIPOTENCE_OF_MATHEMATICS
Can electromagnetic and gravitational "quanta" form an ether-like background for the material part of the cosmos? Can there be interaction between the ether and the cosmos? If there is interaction between them, then every parts of them should interact, since the material part of the cosmos is within the so-called ether part. Then:
Are there consistent physical theories which exclude causality completely from the cosmos? Or, do they exclude causality from some portions of the cosmos and permit it in some other portions of it? In that case, how do they permit any realistic physical connection between the causal portions and non-causal portions of the cosmos?
Now, can the electromagnetic and gravitational "ether" be considered as a mere information, virtual information, etc.? Or, are these really existent energy which, of course, carry information for and from the causal formation of all that they causally affect?
Preprint PLANCK ERA or QUANTUM ERA,and ”DISAPPEARANCE” OF CAUSALITY. ...
Preprint CAUSAL HORIZONAL RESEARCH: A METHODOLOGY IN PHYSICS Raphael ...
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