Science topic
Rationality - Science topic
Explore the latest questions and answers in Rationality, and find Rationality experts.
Questions related to Rationality
The economic man is assumed to be an individual who seeks to achieve the greatest utility at the lowest possible cost. Can we then discuss the concept of the "economy of love" (an economy that encourages individuals to consider human and emotional aspects in their economic behavior) as a pursuit of long-term benefits, such as psychological comfort and self-satisfaction? Or is it a departure from economic rationality by accepting additional costs for intangible and non-material benefits in the short term?
Artificial intelligence (AI) has rightfully found its place and significance in the 21st century. Research has advanced significantly, enabling developing nations to present innovative ideas and establish standards for research assistance and doubt resolution. AI has metaphorically opened Pandora's box, granting researchers access to high-quality insights and support that were once confined to theses and academic discourse. It has become a wiser and more pragmatic tool for obtaining clarification and ultimately securing human validation, which remains essential for legitimizing research.
Nevertheless, the question of its practical acceptance urges us to look forward and ask: What comes next? While the future is inherently uncertain, the emergence of superior and more refined products seems not only possible but rational. So, what lies ahead?
Human consciousness includes cognitive patterns, logical notions, as well as rational and emotional elements. The complex process of thinking can be categorized as logical or factual (rational), and emotional. In your perspective, why is rational thinking important?
How can we rationally utilize biological resources to meet the needs of human development while protecting the natural ecological environment?
Prior to drafting, I was given the chance to use either a quantitative or mixed methods approach. Due to me consulting with teachers and a former panelist before. However, as I am writing my undergraduate study it becomes apparent that I could not utilize a theory due to the limitations of my study (i.e., learning curve of learning a software or a research instrument and determining how reliable it is, financial capacity of the researcher and time frame for a simultaneous course such as mine). Also I would like to add that the 3 theories considered were rejected due to this: the first one had a variable that is beyond the scope of the study; second and third both had unclear definitions and would be a source of uncertainty; plus the third one had math topics that are too hard for me such would only exacerbate the concerns of learning curve and the time frame. Besides that (I am not sure of this) the research question that I had was exploratory in nature so even if I did use one or two theories I am hesitant if it is truly necessary.
So I am wondering if my understanding is correct, does an exploratory research not warrant a theory? If it does, is it acceptable of me not to utilize one given my limitations ?
On another note, given how quantitative study is always about theory testing should I go for a mixed methods approach and state the assumptions of my study as follows:
Qualitative assumptions:
1. The research generates meaning as he or she interacts with the study and its context.
2. Researcher finds pattern when collecting data from or for a specific problem.
3. Theory generation. (Not to be included)
Quantitative assumptions:
1. Theory testing (Not to be included)
2. Knowledge is antifoundational.
3. Data collection, know how and rational considerations create knowledge.
Would it be acceptable for me to use an exploratory sequential mixed method? Is it okay for me not to use either theory generation or testing as I find it difficult to find the middle ground between the two and just present it as a research gap?
I am quite confused at the moment. Inputs would be highly appreciated. Thank you madams and sirs.
Muñoz, Lucio, 2000. Rationality, Responsibility, and Sustainability: When Can Human Behaviour Have a Chance to Be Sustainable?, In: Sustainability Review, Warren Flint/PhD(ed), Issue 20, May, USA
Science approximately derives from philosophy thus, at some point, software is at least subconsciously based on a particular epistemology more than other epistemological schools. How can we base software on critical rationalism?
I did this twice.
I couldn't see any pellets after adding isopropanol the 1st time
The second time, the yield and ratio was really bad.
If Wolfram Language practiced critical rationalism instead of quasi-empiricism, would coding no longer be necessary? Why?
In simpler terms, the more rigorous the software, the easier and simpler the programming language.
Does Wolfram Alpha use critical rationalism?
"Sir Karl Popper’s critical rationalism – a philosophy in the fallibilist tradition of Socrates, Kant and Peirce – is applied systematically to illuminate the values and principles underlying contemporary software development. The two aspects of Popper’s philosophy, the natural and the social, provide a comprehensive and unified philosophical basis for understanding the newly emerged 'agile' methodologies. It is argued in the first four sections of the paper – Philosophy of Science, Evolutionary Theory of Knowledge, Metaphysics, and The Open Society – that the agile approach to software development is strongly endorsed by Popper’s philosophy of critical rationalism. In the final section, the relevance of Christopher Alexander’s ideas to agile methodologies and their similarity to Popper’s philosophy is demonstrated"( https://link.springer.com/chapter/10.1007/11787181_26#citeas ).
Northover, M., Boake, A., Kourie, D.G. (2006). Karl Popper’s Critical Rationalism in Agile Software Development. In: Schärfe, H., Hitzler, P., Øhrstrøm, P. (eds) Conceptual Structures: Inspiration and Application. ICCS 2006. Lecture Notes in Computer Science(), vol 4068. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11787181_26
Please prove me right or wrong.
I have recently published a paper [1] in which I conclusively prove that the Stoney Mass invented by George Stoney in 1881 and covered by the shroud of mystery for over 140 years does not represent any physical mass, but has a one-to-one correspondence with the electron charge. The rationale of this rather unusual claim, is the effect of the deliberate choice in establishing SI base units of mass (kg) and the electric charge derived unit (coulomb: C = As). They are inherently incommensurable in the SI, as well as in CGS units.
The commensurability of physical quantities may however depends on the definition of base units in a given system. The experimental “Rationalized Metric System (RMS) developed in [1] eliminates the SI mass and charge units (kg and As, respectively), which both become derived units with dimensions of [m3 s-2]. The RMS ratio of the electron charge to the electron mass became non-dimensional and equal to 2.04098×1021, that is the square root of the electric to gravitational force ratio for the electron.
As much as the proof is quite simple and straightforward I start meeting persons disagreeing with my claim but they cannot come up with a rational argument.
I would like your opinion and arguments pro or against. This could be a rewarding scientific discussion given the importance of this claim for the history of science and beyond.
The short proof is in the attached pdf and the full context in my paper
====================================================
As a results of discussions and critical analysis, I have summarised my position a few answers below, but I have decided to consolidate the most recent here as a supplement to the attached pdf.
I intended to improve my arguments that would increase the level of complexity. However, I found a shorter proof that Stoney Mass has no independent physical existence.
Assumptions:
- Stoney defined the mass as an expression based on pure dimensional analysis relationship, without any implied or explicit ontological status claims.
- Based on Buckingham assertions physical laws do not depend on the choice of base units.
- The system of units [m s] (RMS) can validly replace the system: [kg m s As] as described in [1]
By examining the different systems of units and their corresponding expressions of the Stoney mass, we can shed light on its physical existence. When we consider the CGS and SI systems, we find that both express the Stoney mass in their respective base units of mass (grams or kilograms). However, if we were to use a different system of units, such as the Rationalized Metric System (RMS)[1], we find that there is no equivalent RMS dimensional constants as in the SI Stoney formula to combine with the electron charge to produce a mass value. Stoney Mass expression cannot be constructed in RMS.
In simpler terms, the Stoney mass is a consequence of the chosen arbitrary base units for mass and Current (consequently charge), leading to what is known as the incommensurability of units. This demonstrates that the Stoney mass is not observable or experimentally meaningful outside of the chosen context of CGS or SI units.
Thus it is evident that the Stoney mass lacks a physical manifestation beyond its theoretical formulation in specific unit systems. It exists as somewhat of an artifact caused by the incommensurability between base units of mass and charge. Note that in contrast, the Planck mass SI/CGS expresion does not vanish under the conversion to RMS units, and a dimensional expression is still retained albeit simpler.
When we dig deeper into the fundamental interactions and physical laws, we find no empirical evidence or measurable effects associated with the Stoney mass, reinforcing the understanding that it holds no substantial physical connotation.
The meaning of stoney mass in SI or CGS refers to the mass equivalent of the fundamental unit of electron charge in terms of SM rest energy and (possibly) the equivalent finite electric field energy of the electron.
Why does information theory explain aging, evolution vs creationism, critical rationalism, computer programming and much more?
Perhaps information has a very open definition thus, is very robust.
Yes because critical rationalism recognizes substance, parsimony and identity(adjusts premises upon contradiction), while skeptical empiricism believes all results from impressions. Skeptical empiricism also believes the self is an illusion.
Relativity is used when speed is high enough. Quantum mechanics is used at subatomic scales. Thus, relativity and quantum mechanics are complimentary, depend on different variables, and should follow the law of identity: https://www.researchgate.net/publication/381469939_Critical_Rationalist_Physics
Britannica, The Editors of Encyclopaedia. "Karl Popper". Encyclopedia Britannica, 14 May. 2024, https://www.britannica.com/biography/Karl-Popper. Accessed 23 June 2024.
Meinwald, Constance C.. "Plato". Encyclopedia Britannica, 5 May. 2024, https://www.britannica.com/biography/Plato. Accessed 23 June 2024.
Kenny, Anthony J.P. and Amadio, Anselm H.. "Aristotle". Encyclopedia Britannica, 25 May. 2024, https://www.britannica.com/biography/Aristotle. Accessed 23 June 2024.
Critical rationalism respects the law of identity. https://www.researchgate.net/publication/381469939_Critical_Rationalist_Physics
Either history does NOT EXACTLY repeat or the future is too unpredictable to risk such rationalism. https://www.researchgate.net/publication/377663987_Respectfully_and_Unfortunately_The_Improbability_of_and_Danger_in_Believing_in_Reincarnation
Modern physics because afterlife prediction is new. More specifically, exact and concrete quantum mechanics.
The afterlife is so unpredictable, empiricism is more accurate than rationalism. https://www.researchgate.net/publication/381108355_Quantum_mechanicsmore_exact_would_predict_the_afterlife_more_accurately_than_relativity_more_theoretical
Quantum mechanics focuses more on probability and specific units which seems more empirical. Whereas relativity is more theoretical and thus rationalist.
The diagonal method is built assuming that, if two figure sequences like r = 0.a₁a₂a₃... and t = 0.b₁b₂b₃..., for some n satisfy the inequality aₙ ≠ bₙ, then r ≠ t. However, this is only true under the discrete topology.
Under the standard one, if r = 0.1000... and t = 0.0999..., then r = t although a₁ ≠ b₁.
There is an infinite set of rational numbers in [0, 1], each member of which can be denoted by two different figure sequences.
EPISTEMOLOGY OF EVER PUSHING THE DEFINITIONS
OF SYSTEMIC CATEGORIES AND AXIOMS
Raphael Neelamkavil, Ph.D., Dr. phil.
We discuss here the continuous and never-ending dimensionality of truth in philosophy, science, philosophical cosmology etc. (in my context, also in Gravitational Coalescence Cosmology – CCG). The present work on a new philosophical cosmology is based on general-ontologically validated epistemological truth-probabilism, which spells out the human tendency to articulate general- and physical-ontological foundations (axiomatic Categorial Laws of metaphysics) that will never be fixed forever, will be ever-better defined, and are therefore clearly and continuously dimensional concepts in the inexhaustible continuation of the very dimension of each of the notions and principles under consideration.
Theoretical foundations that can follow such continuous dimensionality, together, in their implications, indicate not our possession of any truth in its alleged correspondence to the totality of all processes (Reality-in-total) ontologically committed to. They clearly indicate that progress is being made in adequately capturing, or corresponding to, the ideal continuous dimension of what are being sought in human intellectual, technological, and cultural accomplishments – thanks to the logical, epistemological, and ontological implications of Kurt Gödel’s mathematical and logical achievements. [For the achievements of Gödel, see Torkel Franzén 2004: 1-11; see also Richard Tieszen 2011. For a detailed cosmological, epistemological, and ontological treatment of it, see my book, Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 2015, and Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 2018.][1]
Progress is being made not merely in the sciences, the arts, human institutions, etc. Progress is concretely taking place in philosophy too. The cumulative effect of progress in philosophy is not so easily visible as in the case of many other disciplines, because philosophy is to some extent philosopher-based and system-based.
The problem of Gödel’s incompleteness theorem stems from the incompleteness of systems that build themselves up with consistency from primitive notions and axioms: “So every formal system of arithmetic cannot derive the assertion of its own consistency, provided that it is consistent.” [Joseph Vidal-Rosset 2006: 56] But the reason for the innate inconsistency is the natural rigidity in the definitions of the primitive notions (Categories) and axioms. Such rigidity stems from the finitely symbolic nature of representations derived from the denotative function of denotatively defined universals / concepts.
Here the system does not sufficiently recognize connotative universals in consciousness, which are the ideal reflections of the ontological universalities / commonalities in the processes being studied. In that case, the issue stems from still deeper realms: the ever-abiding dubitability of any sort of denotative definitions of primitive notions and axioms from which systems start off. This is true of all sciences. That is, we need great flexibility in the definitions of primitive notions and axioms. This flexibility is what I have called “pushing categories and axioms”. In which case, why not consider all sciences philosophies as part of one generalized science facilitating flexibility?
I do not suggest that the general patterns in human thought or philosophy hold within themselves realizations merely of the implications of Gödel’s theorems [Torkel Franzén 2005: 77ff, 137ff] without the possibility of betterment of theories and systems. Truth can be conceived and defined in any rigorous axiomatic system, where foundational incompleteness will be systemically built in clearly from the possibility, after Gödel, of improvement of completeness if the system can follow the method of indefinitely pushing back the ontological and logical limits of definitions of both (1) axioms and sub-axioms as such into more fundamental ones or more adequate definitions of the same axioms, and (2) primitive notions’ meanings by reason of their definitions. I shall call this solution the method of “pushing Categories and axioms” into more fundamental realms in their definitions. This is the epistemological-methodological foundation of systemic science, namely, the science of all sciences.
This manner of procedure is the most fundamental epistemological ingredient of progress in systems, and this is what happens in history when systems are overhauled or overwhelmed in parts or as wholes. Without such pushing the definitional limits of the basic Categories (primitive notions, metaphysical Laws) and the axioms already created in any system, there is no foundation-building in systems of any kind, especially after we have proofs for this necessity in the logical, epistemological, and ontological implications of the work of Gödel.
This fact will (1) positively relativize the concept of philosophical, mathematical, and scientific truth and (2) negatively highlight human intellectual, technological, cultural, political, and religious institutions’ tendency to fossilize truths. Not relativistic truth-probabilism but clear, adequate, and applicable systemism with ever higher truth-probabilities is to be the foundation of all human thought including mathematics and logic. This is the justification for the creation of the systemic, axiomatic foundations of the sciences of all sciences. This would also satisfy postmodern philosophies with their Socratic effect upon philosophies and sciences and permit philosophy to find surer but ever more flexible paths.
[1] I define: Logic is the science of the best intersubjectively rational consequence of ever higher truth-probability in statements. Epistemology is the science of justifications for the fact and manner of achieving rationally explicable consequence, in a spirally broadening and deepening manner, serving to achieve ever better approximations of the epistemological ideal of Reality-in-general. (Einaic) Ontology is the rationally consequent science of the totality of existents, its parts, and their sine qua nons in terms of the To Be (Einai) of Reality-in-total and/or the to be (einai) of its parts (reality-in-particular), serving to achieve ever better approximations of the epistemological ideal of Reality-in-total.
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.
PHYSICAL AND EXACT SCIENCES AND AXIOMATIC PHILOSOPHY:
INTODUCING GROUNDING
Raphael Neelamkavil, Ph.D., Dr. phil.
1. WHY SHOULD PHYSICS AND COSMOLOGY BE GROUNDED?
I get surprised each time when some physicists tell me that either the electromagnetic (EM) or the gravitational (G) or both the forms of energy do not exist – that EM and G are, are "existent" neither like nor unlike material bodies – but that EM and G are to be treated or expressed as mathematical waves or particles propagated from material objects that of course exist for all sciences.
Some of them put in all their energies to show that both EM and G are mere mathematical objects, fields, etc., and not physically existent objects or fields of energy emissions that then become propagations from material bodies. If propagation from material bodies, then their nature too would have to be similar to that of material bodies!!! This is something that the mathematical realists of theoretical physics and cosmology cannot bear!!!
This is similar in effect to Newton and his followers thinking honestly and religiously that at least gravitation and perhaps also other energies are just miraculously non-bodily actions at a distance without any propagation particles / wavicles. But I admit that I explained certain things in the first paragraph above as if I myself were a Newtonian. This has been on purpose.
Even in the 21st century, we must be sharply aware that from the past more than 120 years the General Theory of Relativity with its various versions and especially its merely mathematical interpretations have succeeded in casting and maintaining the power of a terrifying veil of mathematical miracles on the minds of many scientists – miracles such as the mere spacetime curvature being the meaning of gravitation and all other sorts of fields. The mathematics did not need existence, and hence gravitation did not exist! But the same persons did not create a theory whereby the mathematics does not need the existence of the material world and hence the material world does not exist!!
A similar veil has been installed by quantum physics on the minds of many physicists and their audience too. We do not discuss it here. Hence, I have constructed in four published books a systemic manner of understanding these problems in cosmology and quantum physics. I do not claim perfection in any of my attempts. Hence, I keep perfecting my efforts in the course of time, and hope to achieve some improvement. The following is a very short attempt to summarize in this effort one important point in physics, cosmology, and the philosophy of physics and of cosmology.
There exists the tradition of lapping up whatever physicists may say about their observable and unobservable constructs, based on their own manner of using mathematics. The mathematics used are never transparent. Hence, the reader or the audience may not have the ability to makes judgements based on the minimum physical ontology expected of physicists. I believe that this should stop forever at least in the minds of physicists. Moreover, physicists are not to behave like magicians. Their readers and audience should not practice religious faithfulness to them. Nor should physicists expect it from them.
2. ONTOLOGICALLY QUALITATIVE NATURE OF INVARIANTS
When the search is for the foundations of any science, it is in fact for the invariant aspects of all the realities of that science, and not merely for the invariant aspects of some parts of the realities (object-set/s), methods, conclusions, etc. This does not suffice for science for maximizing success. This is because, any exclusive search for the foundations of the specific object-set or of the discourse of the specific object-set will further require foundations upon the totality of all specific object-sets and their discourse.
We find ourselves in a tradition that believes that proportionality quantities are to be taken as the invariables in physics. But I used to reduce into universal qualities the quantitative-structural aspect of all sciences, that are represented in mathematics as the ontological quantities dealt with in science. The real invariants of physics are not the ontological quantities or proportionalities of certain quantities being treated in physics.
The latter, being only the constant quantities, are one kind of ontological qualities, namely, (1) the quantitatively expressible qualities of processes, e.g., ‘quantity’, ‘one’, ‘addition’, etc. are explicable, respectively, as the qualities: ‘being a specific quantity’, ‘being a unity’, ‘togetherness of two or more units’, etc. The other kind is (2) the ontological qualities of processes in general (say, malleability, toughness, colour, redness, etc.) which cannot directly be expressed as ontological quantities of processes. This shows that pure ontological qualities are a more general notion than ontological quantities and includes the latter.
Explaining ontological qualities in terms of physical quantities cannot be done directly by fundamental physical quantities, but by physical properties that involve fundamental physical quantities. Properties are a mix mainly of ontological qualities and of course includes ontological quantities, of which some are the fundamental physical quantities. Hence, the invariants must be qualities that are generative of and apply to both quantities and non-quantities. These invariants then are fully qualitative.
If the invariants apply to all physical processes, these invariants are qualities ontologically universal to all of them in the specified group. Out of them are constructed properties by mixing many qualitative and quantitatively qualitative universals. Clearly, universals applying to all existents are the real invariants of all Reality – which is a matter to be discussed later.
Since universals are all qualitative and some of them are quantitative as qualities, ontological qualities are broader than mathematical in scope, because, the moment mathematics uses quantities, the use is not of quantities devoid of qualities, but instead, of the quantitative variety of general / universal qualities.
Qualities can also behave as some of the primitive notions that underlie all of physics and other sciences – but this will not exhaust the most necessary foundations of physics and other sciences, because these sciences require the general qualities of all existents, and not merely those of mathematics. These are the axiomatically formulable Categorial notions of philosophy, which latter is thus a general science.
In short, quantitative proportionalities as invariants are very partial with respect to existent processes and their totality. Naturally, philosophy too needs general qualities and not merely quantitative qualities to base the discipline.
3. DIFFERENCES IN FOUNDATIONS: EXACT AND NATURAL SCIENCES AND PHILOSOPHY
We see many theories in physics, mathematics, etc. becoming extremely axiomatic and rigorous. They call themselves or attempt to be as quantitative as possible. But are adequate comparisons between mathematics, physical sciences, biological sciences, human sciences, and philosophy, and adequate adaptation of the axiomatic method possible by creating a system of all exact, physical, and human sciences that depend only on the quantitively qualitative proportionalities and call them invariables?
They cannot do well enough to explain Reality-in-total, because Reality-in-total primarily involves all sorts of ontological universals that are purely qualitative, and some of them are the most fundamental, proportionality-type, quantitative invariables of all physical existents in their specificity and totality in their natural kinds. But as the inquiry comes to Reality-in-total, ontological qualitative universals must come into the picture. Hence, merely quantitative (mathematical) explanations do not exhaust the explanation of Reality-in-total.
Existence as individuals and existence in groups are not differentiable and systematizable in terms of quantitatively qualitative universals alone. Both qualitative and quantitatively qualitative universals are necessary for this. Both together are general qualities pertaining to existents in their processual aspect, not merely in their separation from each other. Therefore, the primitive notions (called traditionally as Categories) of Reality-in-total must be ontological qualitative universals involving both the qualitative and quantitative aspects. The most basic of universals that pertain properly to Reality-in-total are now to be found.
Can the primitive notions (Categories) and axioms of the said sciences converge so that the axioms of a system of Reality take shape from a set of the highest possible ontological Categories as simple sentential formulations of the Categories which directly imply existents? This must be deemed necessary for philosophy, natural sciences, and human sciences, because these deal with existents, unlike the formal sciences that deal only with the qualitatively quantitative form of arguments.
Thus, in the case of mathematics and logic there can be various sorts of quantitative and qualitative primitive notions (categories) and then axioms that use the primitive notions in a manner that adds some essential, pre-defined, operations. But the sciences and philosophy need also the existence of their object-processes. For this reason, the primitive axioms can be simple sentential formulations involving the Categories and nothing else. This is in order to avoid indirect existence statements and to involve existence in terms exclusively of the Categories.
Further, the sciences together could possess just one set of sufficiently common primitive notions of all knowledge, from which also the respective primitive notions and axioms of mathematics, logic, physical and human sciences, and philosophy may be derived. I support this view because the physical-ontological Categories involving the existence of Reality and realities, in my opinion, must be most general and fully exhaustive of the notion of To Be (existence) in a qualitatively universal manner that is applicable to all existents in their individual processual and total processual senses.
Today the nexus or the interface of the sciences and philosophies is in a crisis of dichotomy between truth versus reality. Most scientists, philosophers, and common people rush after “truths”. But who, in scientific and philosophical practice, wants to draw unto the possible limits the consequences of the fact that we can at the most have ever better truths, and not final truths as such?
Finalized truths as such may be concluded to in cases where there is natural and inevitable availability of an absolute right to use the logical Laws of Identity, Contradiction, and Excluded Middle, especially in order to decide between concepts related to the existence and non-existence of anything out there.
Practically very few may be seen generalizing upon and extrapolating from this metaphysical and logical state of affairs beyond its epistemological consequences. In the name of practicality, ever less academicians want today to connect ever broader truths compatible to Reality-in-total by drawing from the available and imaginable commonalities of both.
The only thinkable way to accentuate the process of access to ever broader truths compatible to Reality-in-total is to look for the truest possible of all truths with foundations on existence (nominal) / existing (gerund) / To Be (verbal). The truest are those propositions where the Laws of Identity, Contradiction, and Excluded Middle can be applied best. The truest are not generalizable and extendable merely epistemologically, but also metaphysically, physical-ontologically, mathematically, biologically, human-scientifically, etc.
The agents that permit generalization and extrapolation are the axioms that are the tautologically sentential formulations of the most fundamental of all notions (Categories) and imply nothing but the Categories of all that exist – that too with respect to the existence of Reality-in-total. These purely physical-ontological implications of existence are what I analyze further in the present work. One may wonder how these purely metaphysical, physical-ontological axioms and their Categories can be applicable to sciences other than physics and philosophy.
My justification is as follows: Take for example the case of the commonality of foundations of mathematics, logic, the sciences, philosophy, and language. The notions that may be taken as the primitive notions of mathematics were born not from a non-existent virtual world but instead from the human capacity of spatial, temporal, quantitatively qualitative, and purely qualitative imagination.
I have already been working so as to show qualitative (having to do with the ontological universals of existents, expressed in terms of adjectives) quantitativeness (notions based on spatial and temporal imagination, where, it should be kept in mind, that space-time are epistemically measuremental) may be seen to be present in their elements in mathematics, logic, the sciences, philosophy, and language.
The agents I use for this are: ‘ontological universals’, ‘connotative universals’, and ‘denotative universals’. In my opinion, the physical-ontological basis of these must and can be established in terms merely of the Categories of Extension-Change, which you find being discussed briefly here.
Pitiably, most scientists and philosophers forget that following the exhaustively physical-ontological implications of To Be in the foundations of science and philosophy is the best way to approach Reality well enough in order to derive the best possible of truths and their probable derivatives. Most of them forget that we need to rush after Reality, not merely after truths and truths about specific processes.
4. SYSTEMIC FOUNDATIONS VS. EXISTENCE/TS, NON-EXISTENCE/TS
4.1. Basis of Axiomatizing Science and Philosophy
The problem of axiomatizing philosophy, and/or philosophy of science, and/or all the sciences together is that we need to somehow bring in the elemental aspects of existence and existents, and absorb the elemental aspects of non-existence and non-existent objects that pertain to existents. Here it should be mentioned that axiomatizing mathematics and logic does not serve the axiomatization of philosophy, and/or philosophy of science, and/or all the sciences together. So far in the history of philosophy and science we have done just this, plus attempts to axiomatize the sciences separately or together by ignoring the elemental aspects of non-existence and non-existent objects that pertain to existents.
Existence (To Be) is not a condition for the possibility of existence of Reality-in-total or specific processual objects, but instead, To Be is the primary condition for all thought, feeling, sensation, dreaming, etc. All other conditions are secondary to this. If To Be is necessary as the condition for the possibility of any philosophy and science as discourse, we need to be axiomatic in philosophy and science about (1) existence (To Be, which is of all that exist) and/or (2) the direct and exhaustive implications of existence.
It is impossible to define existence without using words that involve existence. But it is possible to discover the exhaustive implications of To Be in order to use them in all discourse. Therefore, towards the end of this short document, I shall name what could be the inevitable primitive notions that are exhaustive of To Be and that may be used to create axioms for both philosophy and science together.
To put it differently, I attempt here to base all philosophy and science on the concept of existence of Reality-in-total as whatever it is, by deriving from the concept of the existence of all that exist the only possible (i.e., the exhaustive) implications of To Be.
Of course, the basic logical notions of identity and contradiction will have to be used here without as much danger as when we use them in statements on other less fundamental notions. I would justify their use here as the rational inevitabilities in the foundations – not as inevitabilities in the details that issue later. The inevitabilities in the later details need never to be realized as inevitabilities, because To Be implies some fundamental notions which will take case of this.
That is, the various ways in which the principles of identity and contradiction should be seen as inexact and inappropriate may be discovered in the in fields of derivation beyond the provinces of the fundamental Categorial implications of To Be. This latter part of the claims is not to be discussed here, because it involves much more than logic – in fact, a new conception of logic, which I would term as systemic logic.
Let me come to the matter that I promise in the name of the foundations of ‘Axiomatic Philosophy and Science’. First of all, to exist is not to be merely nothing. In this statement I have taken access to the Laws of Identity, Non-Contradiction, and Excluded Middle at one go in that whatever is, must be whatever it is, and not its opposite which is nothing but nothing, nor a middle point between the two extremes.
Therefore, existence must always be non-vacuous. That is, the primary logical implication of To Be is the non-non-being of whatever exists. But such a logical implication is insufficient for the sciences and philosophy, because we deal there with existents. Hence, let us ignore the logical implication as a truism. The existential implications of To Be are what we need.
I have so far not found any philosopher or scientist who derived these implications. But let us try, even if the result that obtained may be claimed by many ancients and others as theirs. In fact, theirs were not metaphysical / physical-ontological versions. Their epistemic versions of the same have been very useful, but have served a lot to misguide both philosophy and science into give “truth/s” undue importance in place of “Reality”. My claim about the exhaustive physical(-ontological) implications of To Be that I derive here is that they do not incur this fallacy.
To Be is not a thing. It is, as agreed at the start, the very condition for the possibility of discourse: philosophy, science, literature, art … and, in general, of experience. The To Be of existents is thus not a pre-condition for To Be – instead, it is itself the source of all conditions of discourse, not of existence.
4.2. Extension, Change, Universal Causality
If To Be is non-vacuous, it means that all existents are something non-vacuously real. Something-s need not be what we stipulate them to be, both by name and qualifications. But the purely general implication is that existents are something-s. This is already part of philosophical activity, but not of the sciences. We need to concretize this implication at the first tire of concrete implications. Only thereafter are sciences possible.
To be something is to be non-vacuous, i.e., to be in non-vacuous extendedness. However much you may attempt to show that Extension does not follow from the notions of To Be, something, etc., the more will be extent of your failure. You will go on using the Laws of Identity, Contradiction, and Excluded Middle, and never reach any conclusion useful for the sciences. Then you will have to keep your mouth and mind shut. I prefer for myself meaningful discourse in science and philosophy – when I meditate I shall attempt to keep my mind and lips as “shut” as possible.
As said above, Extension is one of the primary physical-ontological implications of To Be. Nothing exists without being extended, without being in Extension. Extended something-s are not just there in Extension. If in Extension, everything has parts. Thus, having parts is one of the primary implications of being something in existence. I term it alternatively also as Compositionality.
It is the very implication of being something that something-s are in Change. The deepest and most inevitable form of implication of Change is this: nothing that is in existence with parts can have the status of being something existent without the parts impacting at least a few others. This is the meaning of Change: impact-formation by extended parts. Any existent has parts existing in the state of impact formation in other parts and in themselves.
Hence, Change is the only other implication of To Be, not second to but equally important as Extension. I call it differently also as Impact-Formation. The notion of motion or mobility does not carry the full weight of the meaning of Change.
There cannot be any other implication equally directly derivable from To Be as Extension and Change can be. In other words, all other implications can be found to be sub-implications of Extension-Change, i.e., involving only Extension-Change. Showing them as involving only Extension-Change would suffice to show their sub-implications status with respect to Extension-Change.
Existence in Extension-Change belongs to anything existent, hence ubiquitous – to be met with in any existent. This is nothing but existence in the ubiquitously (to be met with in any existent) extended form of continuance in ubiquitous (to be met with in any existent) impact formation. What else is this but Universal Causality?
If you say that causation is a mere principle of science – as most philosophers and scientists have so far thought – I reject this view. From the above paragraphs I conclude that Causation is metaphysically (physical-ontologically) secondary only to existence. Everybody admits today that we and the universe exist. But we all admit that every part of our body-mind and every existent in the world must be causal because we are non-vacuously existent in Extension-Change.
This means that something has been fundamentally wrong about Causality in philosophy and science. We need to begin doing philosophy and science based fully on To Be and its implications, namely, Extension-Change-wise continuance, which is nothing but being in Universal Causation. It is universal because everything is existent. Universal Causality is the combined shape of Extension-Change. Causation the process of happening of Extension-Change-wise continuance in existence. Causality is the state of being in Extension-Change-wise continuance in existence.
4.3. Now, What Are Space and Time?
Note that what we measurementally and thus epistemically call as space is metaphysically to be termed as Extension. Space is the measuremental aspect of the primary quality of all existents, namely, of Extension. That is, space is the quantity of measurement of Extension, of measurements of the extended nature of existents. In this sense, space is an epistemic quality.
Further, note also that what we call time is the measuremental aspect of the primary quality of all existents, namely, of Change. If there is no impact-formation by parts of existents, there is no measurement called time. Hence, time is the epistemic quality of measurements of Change, which is the impact-formation tendency of all existents.
Immanuel Kant termed space as the condition for the possibility of sensibility, and Edmund Husserl called it as one of the fundamental essences of thought. Space and time in Kant are epistemic since they are just epistemic conditions of possibility; and essences in Husserl are epistemic, clearly as they are based on the continuous act of epochḗ.
Nothing can exist in epistemic space-time. That is, language and mind tend to falsely convert space and time into something that together condition existents. Thus, humans tend to believe that our measuremental concepts and derivative results are all really and exactly very essential to existent something-s, and not merely to our manner of knowing, feeling, sensing, etc.
This is the source of scientific and philosophical misconceptions that have resulted in the reification of the conclusions and concepts of thought and feeling. Thus, this is also the source of conceptual insufficiencies in philosophical and scientific theories. Scientism and scientific and mathematical instrumentalism justify these human tendencies in the name of pragmatism about science and thought.
Reification of certain statistical conclusions as probabilities and the metaphysicization of probable events as the only possible events are not merely due to the above sort of reification. It is also by reason of the equivocation of probability with possibility and the reification of our scientific and statistical conclusions of probabilities as real possibilities. Humans tend to forget that a certain amount of probability is exactly and properly the measure of the extent of human capacity (and by implication, of human incapacity), at a given instance and at a given measuremental moment of history, to use instruments to get at all the existents that are the causes of a given process.
As we know, To Be is not a Category / Quality. It is the very condition that is the same as the existence of something-s as whatever they are. This is a tautology: To Be is To Be. If To Be is a metaphysical notion, the physical-ontologically and scientifically relevant metaphysical implications of To Be are Extension-Change. These are the highest and only highest Categories of all philosophy and science. Universal Causality is the notion of combination of Extension-Change. It is not an indirectly derived notion.
If scientists tend to relegate such notions as philosophical, they are trying to be practical in a silly manner. Even scientific results need the hand of proper and best possible formulations of notions and theoretical principles. Theoretical principles (say, of causation, conservation, gravitation, matter, mass, energy, etc., which may clearly be formulated in terms of Extension-Change-wise existence and existents) must be formulated in the most systemic manner possible.
I would call Extension, Change, and the combination-term Universal Causality not merely as the highest metaphysical Categories. They are the very primitive terms in addition to terms like ‘existent’, ‘matter-energy’, etc., which are necessary for an axiomatic formulation of the foundations of the sciences. Hence, we need to formulate axiomatically both philosophy and science.
Universal Causality may hereafter also be taken as an axiom in philosophy and the sciences. An axiom is a formulated basic principle. In that case, why not formulate also the primitive notions (Categories) of Extension and Change as axioms? In short, the difference between mathematical-logical axiomatic foundations and physical-philosophical axiomatic foundations is that in the former set primitive notions are not axioms, and in the latter primitive notions may be formulated as axioms.
In the light of the above discussion, it becomes clear that Einstein’s postulation of gravitation and matter-energy as space-time curvatures is at the most a formulation of these notions in terms of the mathematical necessity to use space-time (epistemic) measurements and theorize based on them in theoretical physics.
Einstein was immersed in the neo-positivism and logical positivism of his time. Hence, he could not reason beyond the use, by mathematics, of quantitative notions as concrete measurements. Scientists and philosophers who still follow Einstein on this sort of a misguided reification of epistemic space and time are taking refuge not on Einstein but on his theoretical frailties. Even today most scientists and philosophers are unaware that quantities are in fact quantitatively characterized pure qualities – and not properties that are combinations of qualitative and quantitatively qualitative notions.
Minkowski formulated the mathematics of space-time and thus reduced space-time into a sort of ether in which physical processes take place gravitationally. Einstein put gravitation into this language and mistook this language (the language of mathematical space-time) to be the very matter-energy processes that curve according to gravitational processes. For the mathematics this is no too great error, because it worked. This is why some physicists even today consider gravitation and/or all energy forms as ether, as if without this stuff in the background material bodies would not be able to move around in the cosmos! A part of the cosmos is thus being converted into a background conditioner!
Only formal functioning has so far been found necessary in mathematics. Derivation from the metaphysical sources of existents and non-existents has not so far been found necessary in mathematics. But, note here also this: for more than 100 years physicists and philosophers of physics lapped up this substitution of the language of mathematics for the actual, physically existent, processes, which otherwise should have been treated also metaphysically, and if possible, in a manner that is systemically comprehensive of the sources of all sciences.
The implications of existence, non-existence, existents, and non-existents too can help to make the mathematical adaptations work pragmatically. Hence, clearly it does not suffice that only the mathematical formalism attained so far be used in physics and the sciences. The project of science, philosophy, mathematics, and logic must grow out of their limits and become parts of a systemic science with foundations in the implications of existence, non-existence, existents, and non-existents.
I have been attempting to explain in these pages a limited realm of what I otherwise have been attempting to realize. I show only that there are two physical-ontological Categories and some derived axioms (out of these many axioms, only one is discussed here, i.e., Universal Causality), using which we need to formulate not merely philosophy but also physics and other sciences.
But I suggest also that the existence-related and non-existents-related mathematical objects too must be formulated using some primitive terms and axioms that are compatible with the philosophical and physical primitive terms and axioms that may facilitate a systemic approach to all sciences.
4.4. Why Then Is Science Successful?
The awarding of the Nobel Prize 2023 for quantum informatics to Alain Aspect, John F. Clauser, and Anton Zeilinger does not, therefore, mean that all of quantum physics and their assumptions and results are ‘the realities’ behind the ‘truths’ formulated. Instead, it means only that the truths they have formulated are relatively more technology-productive within the context of the other truths and technologies that surround them in physics. Quantum informatics works at a level of effects where we involve only those movements and processes that result in the resulting discoveries, general truths, and the derivative technology.
Similarly, the successes of engineering, informatics, medical processing technology, and the medical science that (as of today) are based on these need not be a proof for the alleged “absolute truth status” of the theories based on Newtonian physics, of molecular and atomic level chemistry and biology, etc. These sciences use only certain contextual levels of interaction in the physical world.
Recollect here the ways in which occidental philosophers dating at least from Parmenides and Heraclitus and extending up until today have been mistaking space and time as (1) two metaphysical categories, or (2) as mere existents, or (3) as illusions.
Oriental philosophies, especially Hindu and Buddhist, have been the best examples of rejecting space-time as metaphysical and as equivalent to permanent substances in a manner that made some Occidental thinkers to look down on them or to reject all of them. In the course of conceptualization that is typical of humans, having to create further theoretical impasses is necessarily to be avoided as best as we can. Such an ideal requires the help of Extension, Change, and Universal Causality.
In the foregoing paragraphs I have only hinted at the necessity of axiomatic philosophy and science. I have only suggested some basic notions in this systemic science. I do also use these notions and some axioms developed from them to formulate a new philosophy of mathematics. I have already published some books based on these and have been developing other such works. I hope to get feedbacks from earnest minds that do not avoid directly facing the questions and the risk of attempting a reply to the questions themselves.
Bibliography
(1) Gravitational Coalescence Paradox and Cosmogenetic Causality in Quantum Astrophysical Cosmology, 647 pp., Berlin, 2018.
(2) Physics without Metaphysics? Categories of Second Generation Scientific Ontology, 386 pp., Frankfurt, 2015.
(3) Causal Ubiquity in Quantum Physics: A Superluminal and Local-Causal Physical Ontology, 361 pp., Frankfurt, 2014.
(4) Essential Cosmology and Philosophy for All: Gravitational Coalescence Cosmology, 92 pp., KDP Amazon, 2022, 2nd Edition.
(5) Essenzielle Kosmologie und Philosophie für alle: Gravitational-Koaleszenz-Kosmologie, 104 pp., KDP Amazon, 2022, 1st Edition.
Dear Researchers, having received some comments on the fact of using only two values to determine the rational parameter that allows my proof of Fermat's Last Theorem in the article "On the Nature of Some Euler's Double Equations Equivalent to Fermat's Last Theorem, in Mathematics, 10-23, (2022), pp. 1-12.
Free access https//www.mdpi.com/2227-7390/10/23/4471. "
I have prepared this document which definitively closes the discussion on the validity of my elementary proof.
Best Regards
Andrea Ossicini
I am struggling to get my work on Fermat's last theorem peer reviewed as it appears to be too simplistic/ not relevant to the mathematical journals I have so far contacted. However, being biased I think it's at least worthy of logical consideration and would appreciate any advice to this end.
For reference:
Abstract
This investigation assumed Fermat’s conjecture to be incorrect, i.e. that his equation has a whole number solution to enable consideration of the rationality of the equation’s terms by constructing a 1st triangle with sides representing the whole number, i.e. rational digits, a, b and c, with perpendicular divisors, h1, h2 andh3, and a 2nd, ‘similar triangle’, (with identical angles) but two sides representing divisors h1, and h2. Logical analysis then showed that the perpendicular divisors are also rational digits. Hence the two right angle triangles formed by the divisor, h1, in the 1st triangle can be analysed as Pythagorean Triples since all 3 sides of each triangle being rational can be represented as a fraction p/q of two integers, as long as the denominator q is not equal to zero. Thus, by appropriate multiplication of a combination of all their denominators the sides of the two right angled triangles can be transformed into integers of a larger, scaled triangle, with the same mathematical properties as the original.
This was further interrogated by the use of a Mathcad computer program to determine a Difference Ratio, DR, based on variations between the trigonometric functions calculated as per Fermat’s equation and those as Pythagorean Triples. It was seen, as expected, that both sets of calculations gave identical results unless the integrity of the latter was maintained by limiting certain internal ratios to a given number of decimal points thereby ensuring their sides rationality. The Fermat’s set should automatically give a rational number solution if his conjecture is incorrect as per this supposition and the DR value should at some point equate to zero. However, graphical representation of these calculations shows that DR actually diverges away from zero, for any given set of analysis, with increases in both the Fermat index, n, and the number of decimal points. Hence, it is concluded that this investigation demonstrates, at least to engineering standards, that Fermat’s last theorem is correct, but also that this methodology could be a possible pathway to Fermat’s claimed ‘marvelous’ proof.
Because of people's engagement in digital platforms and watching customized advertisement it may be possible to impact the rationality of customers.
Customer Rationality
The concept of rational consumer describes the individual acting out of self-interest with the main aim of maximising their private benefits through consumption
My new article proves by using a Dirichlet theorem that Theta-3 Functions give only irrational outputs when the inputs are rationals. The proof is all calculus and Analysis without any Algebra. However, in my previous article I proved that if all the outputs of Theta-3 Functions are irrational then this will contradict the continuity of these functions.
Can you exploit these results otherwise?
I wait for your collaboration. Here is the link:
No one has the mental capacity to know all languages. Additionally, the more languages one is fluent in, the more likely that individual will mix up words. Thus, knowing enough languages for survival is optimal while artificial intelligence could and potentially will bridge language barriers. Of course knowing three languages or more is somewhat of an advantage.
Hi everyone,
I have expressed 6x histidine tagged protein(35kDa) and purified using Ni-NTA agarose (Qiagen). The elution buffer contain 20mM of Sodium phosphate, 500mM NaCl and 250mM Imidazole. I concentrated the eluted protein using amicon ultra centrifuge filter. 8 tubes of 500uL of eluted protein was concentrated and washed 5 times with 1xPBS pH 7.4 (500uL each). I measure the concentration of protein, the 260/280 ration was high which was 1.05 and 1.86. I used the purified protein to run ELISA and there was no signal at all (same as blank).
Any suggestions to improve the purity of protein (260/280) because I concern that imidazole is still there and effect the ELISA results.
I have the conception which allows the development of artificial universal rational autonomous subjects (AURAS) and looking for partners in the development.
Preferred partner should have a team proficient in the development of humanoids.
With my participation we are will be able to develop an artificial autonomous subject in 3 years.
WhatsApp number is +1 917 816-4477
Michael Zeldich
What is the difference between critical rationalism and skeptical empiricism?
Can reason and rational questions be carried beyond Physics and Cosmology, where reason and rational questions are perhaps based on and by generalization of existing results in Physics and Cosmology?
As is well known physicists rarely take philoso0hers arguments and positions about science seriously. There are 3 rationales:
1. Agnostisism.
Physicists laugh off serious philosophical arguments naively seeing them as no brainers because they cannot break off their prejudices about the entities they deal of off positivistic thinking to more logical non empirical syllogism
2. Extreme Superiority as sector/discilline leaders.
This happens in every sector. Accomplished and higher in hierarchy individuals believe "we are the best sector/field" or others are inferior. Physicists take to the extreme and polarizevwith philoso0hers because its easy to ground their superiority because of pilsr opposite criteria of success yet similar domain
3. Some rationality
Physicists strive to get strictly assessed results, are tested in the applicability of their funds while philosophers argue in an Abstract context. Thus physicists find that dismissing philosophy's attack is a rational justified stance.
Also physicists believe philosophers have simply a negative (destructive) agenda towards physics, which has some weight
I have a research study on rationalizing energy consumption in Saudi Arabian society; how can I develop a good questionnaire? The questionnaire must have all types of questions you studied in the branches, e.g., dichotomous (yes/no), multichotomous (MCQ), checklist, ranking and rating scale, and open-ended questions. A minimum of 20 questions.
Thank you
Following a short discussion in another forum, in which reference was made to AI having a Theory of Mind (ToM), I am interested in other opinions from RG members who have an active interest in an Ethics of AI.
In a sense, one of the critical emergent capabilities (in my thinking: limitations) is the idea that AI may possess a ToM. This presents an argument that any AI with a ToM exhibits a form of imagination, since it can attribute mental states to human subjects. However, the very act of such attribution is, to my mind, problematic in the least.
I have written, elsewhere, that “…through subjectification, [a] ToM assumes a rationality of action that may be irrationally violated by an ‘Other’. We are shaken when an absurd action is taken by an ‘Other’ that appears to us as irrational, or wrong, or immoral, or illegal; we question mental states we have ascribed to that ‘Other’, and whether they are an ‘other’ at all. Thus …the axiomatic variability of an individual’s mental state ensures there can be no level of universal access to reality…”
Allowing AI to (imaginatively) attribute mental states as part of its outputs raises ethical concerns we perhaps have not yet begun to grasp. Is the real problem here that, perhaps ironically, generative AI is more human-like in its processing (flaws and all) than we might have anticipated.
Interested in other perspectives...
Which of the two graphical presentations of religiosity can be considered to be appropriate to use:
> imagined by the author – DAWKINS’ LINEAR SCALE OF RELIGIOSITY, including five categories of Religious Agnosticism
or
> founded on rational argumentation – CANI’S COMPLEX PLANE OF RELIGIOSITY, embracing CANI’s Intermedialism?
*****
Definition of CANI’s Intermedialism and Huxley’s Agnosticism as well as the answer to the above-asked question based on argumentum ad rem you’ll find in my video lecture on YouTube at:
Should we learn from past mistakes and correct them in the present? Or should we smart enough to think rationally so that we don't need to follow adaptive expectations?
Alternatively speaking should we belong to Cagan School of thought or Rational Expectations school of thought?
Irrational numbers are uncountable while rational numbers are countable. Archimedes theorem says: there exsist a rational number between any two irrational numbers, so there must be rational numbers as much as irrational numbers.So rational numbers must be uncountable like the irrational numbers. Or irrational numbers must be countable like rational numbers.
In practice all science is a mix of empiricism and rationalism. What do you think?
Since multiplication is defined in matrices and division is also defined, how to simplify and expand rational matrices?
Suicide and Death Penalty, fatal and tragic acts, leave no one indifferent. These touch on the sacredness of life and therefore on the deepest convictions and beliefs. Philosophical reflection has been prolific on the subject dealing with the rationality and morality of and Death Penalty. The question also covers a societal component in relation to the debate on the "right to die within dignity"
All contributions on the topic are welcome.
Picture: Staged seppuku with ritual attire and kaishaku, 1897 https://en.wikipedia.org/wiki/Seppuku

how far can Artificial Intelligence simulate and replicate human capabilities? Can it extend to the human abilities such as discovery and Inspiration?
Is scientific approach capable of answering this question at present or should we employ a rational reasoning approach? what would be that rational reasoning approach then?
Is it ethical to question the credibility and plausibility of a persons experience, if they are diagnosed with a severe mental illness such as paranoid schizophrenia? To what extent does one draw the line between rational and irrational when appraising a persons experience of distress and is it wise to rely solely on a rationalist empiricist framework to attempt to derive meaning from the persons experience?
What are the available and possible tools to face this thrust the world is witnessing today? Is it satisfying to merely describe and study the details and their accumulation? Or is it that reality imposes several facts that are in the same direction of the new ones. The era of rationality that humanity has first dedicated since the 17th century and according to Toynbee, was principally based upon (thinking power). ( Richard Paul, 2007, p 137) , According to Toynbee, the British historian, man should be keen on developing it, and promoting it through programs and plans that enable it to be part of the societal and cultural system, not merely a slogan, that advocates an emerging idea or trend.
The congruent number problem has been a fascinating topic in number theory for centuries, and it continues to inspire research and exploration today. The problem asks whether a given positive integer can be the area of a right-angled triangle with rational sides. While this problem has been extensively studied, it is not yet fully understood, and mathematicians continue to search for new insights and solutions.
In recent years, there has been increasing interest in generalizing the congruent number problem to other mathematical objects. Some examples of such generalizations include the elliptic curve congruent number problem, which asks for the existence of rational points on certain elliptic curves related to congruent numbers, and the theta-congruent number problem as a variant, which considers the possibility of finding fixed-angled triangles with rational sides.
However, it is worth noting that not all generalizations of the congruent number problem are equally fruitful or meaningful. For example, one might consider generalizing the problem to arbitrary objects, but such a generalization would likely be too broad to be useful in practice.
Therefore, the natural question arises: what is the most fruitful and meaningful generalization of the congruent number problem to other mathematical objects? Any ideas are welcome.
here some articles
M. Fujiwara, θ-congruent numbers, in: Number Theory, Eger, 1996, de Gruyter, Berlin, 1998,pp. 235–241.
New generalizations of congruent numbers
Tsubasa Ochiai
DOI:10.1016/j.jnt.2018.05.003
A GENERALIZATION OF THE CONGRUENT NUMBER PROBLEM
LARRY ROLEN
Is the Arabic book about the congruent number problem cited correctly in the references? If anyone has any idea where I can find the Arabic version, it will be helpful. The link to the book is https://www.qdl.qa/العربية/archive/81055/vdc_100025652531.0x000005.
EDIT1:
I will present a family of elliptic curves in the same spirit as the congruent number elliptic curves.
This family exhibits similar patterns as the congruent number elliptic curves, including the property that the integer is still "congruent" if we take its square-free part, and there is evidence for a connection between congruence and positive rank (as seen in the congruent cases of $n=5,6,7$).
Our answer is certain: YES. See
It is common to affirm that "One can never perform any measurement whose result is an irrational number."
This is equivalent to say the contrapositive, that anything that can be measured or produced is a rational number.
But the irrational number √2 can be produced to infinite length in finite steps, as 2×sin(45 degrees). It also exists like that in nature, as the diagonal of a unit square.
There is no logical mystery in these two apparently opposing views. Nature is not Boolean, a new logic is needed.
In this new logic, the statements 'p' and 'not p' can coexist. In the US, Pierce already said it. In Russia, Setun used it.
This opens quantum mechanics to be logical, and sheds new light into quantum computation.
One can no longer expect that a mythical quantum "analog computer" will magically solve things by annealing. Nature is also solving problems algebraically, where there is no such limitation.
Gödel’s undecidability is Boolean, and does not apply. The LEM (Law of the Excluded Middle) falls.
What is your qualified opinion?
Our answer has been YES. Gödel's uncertainty is valid for the B set. The LEM is also valid in the B set. In the B set, numbers are either 0 or 1. And 0^n=0, while 1^n=1, so arithmetic is fast and easy. Digital computers only use the B set, and yet can calculate everything. Gödel's uncertainty is valid.
We, humans, can use the Q* set for fast and easy mental calculations. A negative times a negative is a positive. Gödel's uncertainty is not valid.
Quantum computing uses the set Q, to allow calculus with discontinuous functions--as functions must be in the digital world. We see that world in the XXI century. Gödel's uncertainty is not valid.
By the Curry-Howard relationship, this deprecates Gödel's uncertainties.
So must be finally accepted, under experiments -- not theory or opinions.
No longer individually distinguishable, the digits in each prime number is a "lump" and belong together, in a collective effect beyond digits or names. Peter Shor said this first, in 1994. This is important for quantum computing.
What is your qualified opinion?
(We are not attempting to define nature or evolution. We are just pointing out an illusion. Mathematical results can be absolutely exact.)
Our answer is NO. Think of it: Pythagorean Triples would NOT exist if numbers are arbitrary as values. Given a and b, c is fixed or it doesn't exist.
Given 2 and 3, what is c?
Prime numbers seem not arbitrary either. Some people consider prime numbers as just some feature of Z, which does not exist for composite numbers. And, they think, there are no primes or coprimes in Z_p, p-adic numbers, except for some numbers, which end by 0; there are no negative and positive numbers; there are not even or odd numbers (I e., they may point to the number 19 underscore 31, is it even or odd?).
Instead, let's be humble and observe nature. A prime number in any place of the universe must be a prime number. Here on Earth and in the star Betelgeuse. It is not a feature defined by a human.
Dedekind (1888) was incorrect, and mathematical real-numbers an illusion, that cannot be calculated (Gisin, Gerck).
That is why a number is a semiotic quantity. Numbers can be thought of as a 1:1 mapping between a symbol and a value. Digits become a “name”, a reference, and it is clear that one can use different “names” for the same number as a value.
So, the number 1 can have a name as "1", "2/2", "3/3" and infinitely many more, but is always 1 in value.
Equality of rational numbers does not have to have the same name for each other, as "2/3=2/3".
They can also obey the rule that their cross product is equal in value, so that "2/3=4/6".
That way, equivalence extends equality in a consistent way, even though the numbers are neither equal nor divisible. This is possible because numbers are semiotic quantities, and is essential to understand quantum computing.
Numbers are not arbitrary as values, which can allow us to calculate prime numbers using periodicity.
What is your qualified opinion?
explain the rational of a code of conduct/ethics of an organisation
At the moment, antibiotics are the most effective tools against infectious infections. Yet, the spread of antimicrobial resistance and the lack of recently produced antimicrobial medications pose a serious threat to both human and animal health (Cheng et al., 2016). The most effective methods for combating antimicrobial resistance involve the rational use of antibiotics.
Antimicrobial Activity and Resistance: Influencing Factors - PMC. (2017, June 13). NCBI. Retrieved February 24, 2023, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5468421/
- Is the construction of the Cantor set on the segment [0, 1], on the segment [2, 7] and on the segment [0, π] equivalent?
- How do the points of the Cantor set on the number line relate to natural (in particular, prime), rational, irrational, transcendental and, finally, hyperreal numbers?
Could any expert try to examine the new interesting methodology for multi-objective optimization?
A brand new conception of preferable probability and its evaluation were created, the book was entitled "Probability - based multi - objective optimization for material selection", and published by Springer, which opens a new way for multi-objective orthogonal experimental design, uniform experimental design, respose surface design, and robust design, etc.
It is a rational approch without personal or other subjective coefficients, and available at https://link.springer.com/book/9789811933509,
DOI: 10.1007/978-981-19-3351-6.
Best regards.
Yours
M. Zheng
My article asks if the image of the Line of Real positive numbers, which is bigger than the origine 2 , by the function f(B) related to Theta Function 3 is only a set of irrationals. Hence the function would be not continuous at all as demonstrated in the article. And this would be a contradiction.
Here is the link to the article :
Rationalism distinguishes between empirical knowledge, i.e., knowledge that arises through experience, and a priori knowledge, i.e., knowledge that is prior to experience and that arises through reason. Empirical knowledge depends upon our senses, senses that, the rationalist wastes no time to demonstrate, are unreliable. Here the rationalist appeals to common sense deceptions and perceptual illusions.
Empiricism denies the rationalist distinction between empirical and a priori knowledge. All knowledge, the empiricist argues, arises through, and is reducible to, sense perception. Thus, there is no knowledge that arises through reason alone. Thus, empiricism credo is that where there is (or can be) no experience there is (and can be) no knowledge.
Thanks in advance.
Our answer is YES. Irrationals, since the ancient Greeks, have had a "murky" reputation. We cannot measure physically any irrational, as one would require infinite precision, and time. One would soon exhaust all the atoms in the universe, and still not be able to count one irrational.
The set of all irrationals does not even have a name, because there seems to be no test that could indicate if a member belongs to the set or not. All we seem to know is it is not a rational number -- but what is it?
The situation is clarified in our book Quickest Calculus, available at lowest price in paper, for class use. See https://www.amazon.com/dp/B0BHMPMMTY/
There, Instead of going into complicated values of elliptic curves, and infinite irrationals, algebra allows us to talk about "x".
No approximating rational numbers need to be used, nor Hurwitz Theorem.
Thus, one can "tame" irrationals by algebra, with 0 (zero) error. For example, we know the value of pi. It is 2×arcsin(1) exactly, and we can calculate it using Hurwitz Theorem, approximately.
GENERALIZATION: Any irrational number is some function f(x), where x belongs to the sets Z, or Q -- well-defined, isolated, and surrounded by a region of "nothingness". The set of all such numbers we call "E", for Exact. It is an infinite set.
What is your qualified opinion?
The realistic definition of transition probability in physics is well defined and constrains the probability to rational numbers. The abstract definition of probability in mathematics is also well defined, but it allows probability to be an arbitrary real number element of [0,1], whether rational or irrational. The difference is enormous and the conclusions diverge widely. The question is who do we track and when?
: We can provide two specific published examples among many others,
a-Numerical resolution of the 3D PDE of heat diffusion as a function of time in its most general case using the physical definition of probability.
b-Solve the statistical numerical integration for an arbitrary number of free nodes using the physical definition of probability. The trapezoidal ruler and the FDM-based sympson ruler would be just a special case.
Can we call a smart robot as Rational Artificial Being (RAB)? Can robots be considered as Rational Beings? Smart Robots are designed and programmed as intelligent artificial agents (or beings) that have the capacity to make certain decisions alike human beings. Human beings are the only entities who are considered as rationally intelligent, having a unique blend of sense of conscience, emotions, and feelings, and so are deemed as rational agents.
But it is also true that there has been enough progress in the field of Artificial Intelligence over the past few decades. Robots are now designed and programmed as highly intelligent entities that often outsmart their human counterparts in some selected activities.
Now whether it would be rational for us to call robots "rational beings" or rational artificial beings could be a question of interest, for they function on software programmed to mimic largely human behaviors which are considered as rational.
i am passaging my bacterial strain (DH5 alpha) without the selection marker and it has been post 12 passages but unknowingly it is still holding onto the plasmid and doesnt loose it, which it should have if talking rationally. Any suggestions?
I am searching for the main theories or frameworks that could help to explain consumer behaviours when they face sustainability constraints in their choices. It is fact that rational choices play a central role in decision making on consumption, but what theories or frameworks would help to raise broader awareness on the danger of pure rational choices in consumption? What strategies other than research-action could make consumers change their minds when perceiving the collective and individual effects of their behaviours?
I was told that Gary Becker's rational choice theory was NOT the basis for the theories in environmental criminology & situational crime prevention. Is that correct?
If not, which rational choice theory was the reference?