Three-dimensional material models of molecules were used throughout the 19th century, either functioning as a mere representation or opening new epistemic horizons. In this paper, two case studies are examined: the 1875 models of van ‘t Hoff and the 1890 models of Sachse. What is unique in these two case studies is that both models were not only folded, but were also conceptualized mathematically. When viewed in light of the chemical research of that period not only were both of these (...) aspects, considered in their singularity, exceptional, but also taken together may be thought of as a subversion of the way molecules were chemically investigated in the 19th century. Concentrating on this unique shared characteristic in the models of van ‘t Hoff and the models of Sachse, this paper deals with the shifts and displacements between their operational methods and existence: between their technical and epistemological aspects and the fact that they were folded, which was forgotten or simply ignored in the subsequent development of chemistry. (shrink)

● Any given placement (e.g. Sun in Taurus; Mars in Capricorn; Mercury in the third house) is necessarily common to tens of thousands of people. Saturn in the ninth house, for example, will not behave the same or produce the same effects in the twenty or one hundred charts in which we find it there. In each case Saturn will behave in accordance with the rest of the astrographic/chart composition (as if we stayed in the same hotel in different epochs (...) or different people contracted the same disease; our stay will be different each time, according to the epoch, and each person’s symptoms will too, be different, according to their individual biochemistry; not to mention that each chart or astrography, like each genetic code or sequence, is unrepeatable). Certainly, “no planet can produce, on its own, what only the combined or concerted action of all can” (BUSTAMANTE, 2023, SPICA magazine, pp. 93-111). Hence the synergistic nature of the interpretative exercise (i.e., the whole is greater than all its parts). The fundamental component of the mathematical expression of the interpretive exercise is: astrological triangulation, the functional denomination for what we know as synthesis (WEISS, 1946; LEO, 1983, HAND, 1981). In order to demonstrate its usefulness, as well as the convenience of its mathematical expression, we have chosen two individuals (JEFFREY DAHMER, STEVEN SPIELBERG) whose astrographies do not—according to the community—explain their lives. The rest of the astrographies correspond to those of serial killers JOHN WAYNE GACY, DAVID CARPENTER, and TED BUNDY. ● We explain, by means of algebraic notations, the synthesis and the functional values that make up the synthesis. ● We take the Moon and Neptune as relevant bodies for the purpose of diagnosing or studying endocrine or neurohormonal issues, and Mars, Pluto, and Saturn as relevant planets for the purpose of inferring violence or sinister behaviour, upon the case, and quadratures or oppositions—and conjunctions—between Venus and the Moon, the Moon and Neptune, and the Sun or Venus and Neptune or Uranus as indicators of neurohormonal disorders and/or sexual deviance (APA definition) . ● We consider quadratures (90º) or oppositions (180º)—and conjunctions—between Mercury or the Moon and Saturn, or between Mars or the Moon and Saturn, Uranus, Neptune, and/or Pluto as powerful indications of violence or mental disorders, upon the case. ● We have also regarded Sagittarius as a sign as expansive and abundant as its ruler, Jupiter, according to the best of its characterisations (or as an exceptionally swift and wild sign, according to other characterisations), and the fifth region of a natal chart as one closely related to fortune in a broad sense (material and immaterial). ● Because we advocate the idea that orbs should be predicated of the planet (size, speed), not the aspect itself, the gas giants (Jupiter, Saturn, Uranus, and Neptune) and the Sun have been granted up to 10º of orb (or 12º, in the case of broad influence ). We understand aspectual relationships as angular relationships held between two or more celestial bodies placed in signs with at least one property in common (according to our molecular theory of the ecliptic, compatible with the optical theory of the aspects from the Hellenistic tradition). (shrink)

Science and mathematics continually change in their tools, methods, and concepts. Many of these changes are not just modifications but progress---steps to be admired. But what constitutes progress? This dissertation addresses one central source of intellectual advancement in both disciplines: reformulating a problem-solving plan into a new, logically compatible one. For short, I call these cases of compatible problem-solving plans "reformulations." Two aspects of reformulations are puzzling. First, reformulating is often unnecessary. Given that we could already solve a problem using (...) an older formulation, what do we gain by reformulating? Second, some reformulations are genuinely trivial or insignificant. Merely replacing one symbol with another does not lead to intellectual progress. What distinguishes significant reformulations from trivial ones? According to what I call "conceptualism" (or "conceptual empiricism"), reformulations are intellectually significant when they provide a different plan for solving problems. Significant reformulations provide inferentially different routes to the same solution. In contrast, trivial reformulations provide exactly the same problem-solving plans, and hence they do not change our understanding. This answers the second question about what distinguishes trivial from significant reformulations. However, the first question remains: what makes a new way of solving an old problem valuable? Here, a bevy of practical considerations come to mind: one formulation might be faster, less complicated, or use more familiar concepts. According to "instrumentalism," these practical benefits are all there is to reformulating. Some reformulations are simply more instrumentally valuable for meeting the aims of science than others. At another extreme, "fundamentalism" contends that a reformulation is valuable when it provides a more fundamental description of reality. According to this view, some reformulations directly contribute to the metaphysical aim of carving reality at its joints. Conceptualism develops a middle ground between instrumentalism and fundamentalism, preserving their benefits without their costs. I argue that the epistemic value of significant reformulations does not reduce to either practical or metaphysical value. Reformulations are valuable because they are a constitutive part of problem-solving. Both science and mathematics aim at solving all possible problems within their respective domains. Meeting this aim requires being able to plan for any possible problem-solving context, and this requires reformulating. By reformulating, we clarify what we need to know to solve problems. Still, one might wonder whether the value of reformulations requires underlying differences in explanatory power. According to "explanationism," a reformulation is valuable only when it provides a better explanation. Explanationism stands as a rival middle ground position to my own. However, it faces numerous counterexamples. In many cases, two reformulations provide the same explanation while nonetheless providing different ways of understanding a phenomenon. Hence, reformulating can be valuable even when neither formulation is more explanatory. Methodologically, I draw on a variety of case studies to support my account of reformulation. These range from classical mechanics to quantum chemistry, along with examples from mathematics. Symmetry arguments provide a paradigmatic example: the mathematics of symmetry groups radically recasts quantum mechanics and quantum chemistry. Nevertheless, elementary approaches exist that eschew this additional mathematical apparatus, solving problems in a more tedious but less mathematically-demanding manner. Further examples include reformulations of quantum field theory, Arabic vs. Roman numerals, and Fermat's little theorem in number theory. In each case, my account identifies how reformulations change and improve our understanding of science and mathematics. (shrink)

Suppose one has a system, the infinite set of positive integers, P, and one wants to study the characteristics of a subset (or subsystem) of that system, the infinite subset of odd positives, O, relative to the overall system. In mathematics, this is done by pairing off each odd with a positive, using a function such as O=2P+1. This puts the odds in a one-to-one correspondence with the positives, thereby, showing that the subset of odds and the original set of (...) positives are the same size, or have the same cardinality. This counter-intuitive result ignores the “natural” relationship of one odd for every two positives in the sequence of positive integers, which would suggest that O is one-half the size of P. However, in the set of axioms that constitute mathematics, it is considered valid. Fair enough. In the physical universe (i.e., the starting system), though, relationships between entities matter. In biochemistry, if you start with an organism, say a rat, and you want to study its heart, you can do this by removing some heart cells and studying them in isolation in a cell culture system. But, the results often differ compared to what occurs in the intact animal because studying the isolated cultured cells ignores the relationships in the intact body between the cells, the rest of the heart tissue and the rest of the rat. In chemistry, if a copper atom were studied in isolation, it would never be known that copper atoms in bulk can conduct electricity because the atoms share their electrons. In physics, the relationships between inertial reference frames in relativity, and observer and observed in quantum physics can't be ignored. Relationships matter in the physical world, but the mathematics of infinite sets is still used to describe it. Does this matter? It seems to, at least in physics. Infinities cause numerous problems in theoretical physics such as non-renormalizability and problems in unifying quantum mehanics and general relativity . This suggests that the pairing off method and the mathematics of infinite sets based on it are analogous to a cell culture system or studying a copper atom in isolation if they are used in studying the physical universe because they ignore the inherent relationships between entities. In the real, physical world, the natural, inherent, relationships between entities can't be ignored. Said another way, the set of axioms that constitute abstract mathematics may be similar but not identical to the set of physical axioms by which the real, physical universe runs. This suggests that the results from abstract mathematics about infinities may not apply to or should be modified for use in physics. (shrink)

When philosophers discuss the possibility of machines making scientific discoveries, they typically focus on discoveries in physics, biology, chemistry and mathematics. Observing the rapid increase of computer-use in science, however, it becomes natural to ask whether there are any scientific domains out of reach for machine discovery. For example, could machines also make discoveries in qualitative social science? Is there something about humans that makes us uniquely suited to studying humans? Is there something about machines that would bar them (...) from such activity? A close look at the methodology of interpretive social science reveals several abilities necessary to make a social scientific discovery, and one capacity necessary to possess any of them is imagination. For machines to make discoveries in social science, therefore, they must possess imagination algorithms. (shrink)

The picture of synthetic biology as a kind of engineering science has largely created the public understanding of this novel field, covering both its promises and risks. In this paper, we will argue that the actual situation is more nuanced and complex. Synthetic biology is a highly interdisciplinary field of research located at the interface of physics, chemistry, biology, and computational science. All of these fields provide concepts, metaphors, mathematical tools, and models, which are typically utilized by synthetic biologists (...) by drawing analogies between the different fields of inquiry. We will study analogical reasoning in synthetic biology through the emergence of the functional meaning of noise, which marks an important shift in how engineering concepts are employed in this field. The notion of noise serves also to highlight the differences between the two branches of synthetic biology: the basic science-oriented branch and the engineering-oriented branch, which differ from each other in the way they draw analogies to various other fields of study. Moreover, we show that fixing the mapping between a source domain and the target domain seems not to be the goal of analogical reasoning in actual scientific practice. (shrink)

In this dissertation I achieve the following: (1) I present motivating criteria for a general comprehensive theory of scientific explanation. I review historical approaches to modeling explanation in light of these criteria. (2) I present New Mechanist Explanation ("NME") as the leading candidate for a contemporary, complete theory of scientific explanation. (3) I present constraints on the applicability of New Mechanism in modeling biology, chemistry, and physics. I argue for the unsuitability of NME as a candidate for a general (...) theory of explanation due to its significant omissions of explanatory content and subsequent incompleteness. (4) I present arguments for the indispensable explanatory power of mathematics in science, noting that much of NME's failures are owed to its poor integration of mathematical explanation as applied to science. (5) I propose a Rational-Relational theory of explanation(“RRE”). I present RRE in detail and demonstrate it as a true working general theory of explanation which best meets the motivating criteria presented in (1). I disambiguate RRE from structural explanation ("SE"). I show that historical models of explanation, including the deductive nomological (DNE) model, statistical relevance ("SRE") model, structural model (SE) and unification model ("UE") may be successfully treated as sub-classes of explanation within the scope of RRE. I provide a rubric for selecting amongst sub-theories of explanation under RRE in the purpose of highlighting particular features of relational explanations. (6) In conclusion, I argue that philosophers of science should move forward using RRE as a general model of scientific explanation as a working alternative to the incomplete model of NME. (shrink)

Invited review of the anthology of new papers _Philosophy of Chemistry: Growth of a New Discipline_.

The entry of resonance into chemistry, or the reception of the theory of resonance in the chemical community, has drawn considerable attention from historians of science. In particular, they have noted Pauling's ¯amboyant yet effective style of exposition, which became a factor in the early popularity of the resonance theory in comparison to the molecular orbital theory, another way of applying quantum mechanics to chemical problems.$ To be sure, the non-mathematical presentation of the resonance theory by Pauling and his (...) collaborator, George Wheland, helped to facilitate the reception ; but this presentation was vulnerable to the confusion that arose among chemists owing to the similarity between resonance and tautomerism, or between foreign and indigenous concepts. The reception occurred at the expense of serious misunderstandings about resonance. This paper investigates the ways in which Pauling and Wheland taught, and taught about, the theory of resonance, especially their ways of coping with the difficulties of translating a quantum-mechanical concept into chemical language. Their different strategies for teaching resonance theory deserve a thorough examination, not only because the strategies had to do with their solutions of the philosophical question whether resonance is a real phenomenon or not, and whether the theory of resonance is a chemical theory or a mathematical method of approximation, but also because this examination will illuminate the role of chemical translators in the transmission of knowledge across disciplinary boundaries. (shrink)

Arthur Clark and Michael Kube–McDowell (“The Triger”, 2000) suggested the sci-fi idea about the direct transformation from a chemical substance to another by the action of a newly physical, “Trigger” field. Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”; according to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of (...) matter-energy.” Dr Horton, his collaborator in the novel replies: “If the universe consists of energy and information, then the Trigger somehow alters the information envelope of certain substances –“. “Alters it, scrambles it, overwhelms it, destabilizes it” Brohier adds. There is a scientific debate whether or how far chemistry is fundamentally reducible to quantum mechanics. Nevertheless, the fact that many essential chemical properties and reactions are at least partly representable in terms of quantum mechanics is doubtless. For the quantum mechanics itself has been reformulated as a theory of a special kind of information, quantum information, chemistry might be in turn interpreted in the same terms. Wave function, the fundamental concept of quantum mechanics, can be equivalently defined as a series of qubits, eventually infinite. A qubit, being defined as the normed superposition of the two orthogonal subspaces of the complex Hilbert space, can be interpreted as a generalization of the standard bit of information as to infinite sets or series. All “forces” in the Standard model, which are furthermore essential for chemical transformations, are groups [U(1),SU(2),SU(3)] of the transformations of the complex Hilbert space and thus, of series of qubits. One can suggest that any chemical substances and changes are fundamentally representable as quantum information and its transformations. If entanglement is interpreted as a physical field, though any group above seems to be unattachable to it, it might be identified as the “Triger field”. It might cause a direct transformation of any chemical substance by from a remote distance. Is this possible in principle? (shrink)

The INBIOSA project brings together a group of experts across many disciplines who believe that science requires a revolutionary transformative step in order to address many of the vexing challenges presented by the world. It is INBIOSA’s purpose to enable the focused collaboration of an interdisciplinary community of original thinkers. This paper sets out the case for support for this effort. The focus of the transformative research program proposal is biology-centric. We admit that biology to date has been more fact-oriented (...) and less theoretical than physics. However, the key leverageable idea is that careful extension of the science of living systems can be more effectively applied to some of our most vexing modern problems than the prevailing scheme, derived from abstractions in physics. While these have some universal application and demonstrate computational advantages, they are not theoretically mandated for the living. A new set of mathematical abstractions derived from biology can now be similarly extended. This is made possible by leveraging new formal tools to understand abstraction and enable computability. [The latter has a much expanded meaning in our context from the one known and used in computer science and biology today, that is "by rote algorithmic means", since it is not known if a living system is computable in this sense (Mossio et al., 2009).] Two major challenges constitute the effort. The first challenge is to design an original general system of abstractions within the biological domain. The initial issue is descriptive leading to the explanatory. There has not yet been a serious formal examination of the abstractions of the biological domain. What is used today is an amalgam; much is inherited from physics (via the bridging abstractions of chemistry) and there are many new abstractions from advances in mathematics (incentivized by the need for more capable computational analyses). Interspersed are abstractions, concepts and underlying assumptions “native” to biology and distinct from the mechanical language of physics and computation as we know them. A pressing agenda should be to single out the most concrete and at the same time the most fundamental process-units in biology and to recruit them into the descriptive domain. Therefore, the first challenge is to build a coherent formal system of abstractions and operations that is truly native to living systems. Nothing will be thrown away, but many common methods will be philosophically recast, just as in physics relativity subsumed and reinterpreted Newtonian mechanics. -/- This step is required because we need a comprehensible, formal system to apply in many domains. Emphasis should be placed on the distinction between multi-perspective analysis and synthesis and on what could be the basic terms or tools needed. The second challenge is relatively simple: the actual application of this set of biology-centric ways and means to cross-disciplinary problems. In its early stages, this will seem to be a “new science”. This White Paper sets out the case of continuing support of Information and Communication Technology (ICT) for transformative research in biology and information processing centered on paradigm changes in the epistemological, ontological, mathematical and computational bases of the science of living systems. Today, curiously, living systems cannot be said to be anything more than dissipative structures organized internally by genetic information. There is not anything substantially different from abiotic systems other than the empirical nature of their robustness. We believe that there are other new and unique properties and patterns comprehensible at this bio-logical level. The report lays out a fundamental set of approaches to articulate these properties and patterns, and is composed as follows. -/- Sections 1 through 4 (preamble, introduction, motivation and major biomathematical problems) are incipient. Section 5 describes the issues affecting Integral Biomathics and Section 6 -- the aspects of the Grand Challenge we face with this project. Section 7 contemplates the effort to formalize a General Theory of Living Systems (GTLS) from what we have today. The goal is to have a formal system, equivalent to that which exists in the physics community. Here we define how to perceive the role of time in biology. Section 8 describes the initial efforts to apply this general theory of living systems in many domains, with special emphasis on crossdisciplinary problems and multiple domains spanning both “hard” and “soft” sciences. The expected result is a coherent collection of integrated mathematical techniques. Section 9 discusses the first two test cases, project proposals, of our approach. They are designed to demonstrate the ability of our approach to address “wicked problems” which span across physics, chemistry, biology, societies and societal dynamics. The solutions require integrated measurable results at multiple levels known as “grand challenges” to existing methods. Finally, Section 10 adheres to an appeal for action, advocating the necessity for further long-term support of the INBIOSA program. -/- The report is concluded with preliminary non-exclusive list of challenging research themes to address, as well as required administrative actions. The efforts described in the ten sections of this White Paper will proceed concurrently. Collectively, they describe a program that can be managed and measured as it progresses. (shrink)

الكيمياء علمٌ تجريبي بطبيعته، يشتغل معمليًا بالجواهر تحليلاً وتركيبًا، ويُقيم بناءاته النسقية استرشادًا بقواعد محددة تحكم إجراءات البحث التجريبي ونتائجه. وكشأن أي نشاط علمي آخر، تستلزم الممارسة الكيميائية لغة جزئية خاصة تصف بناءاتها التجريبية وتُنمّط أشكالها. وما دام التحليل والتركيب – كإجراءين تجريبيين – هما عمادا البحث الكيميائي وجوهره، فمن الضروري أن تحوي لغة الكيمياء تمثيلات صورية توصف بدورها بأنها صيغٌ أو عبارات تحليلية وتركيبية. يمكننا إذن الزعم بأن ثمة علاقة اعتماد متبادلة بين لغة الكيمياء وممارساتها المعملية؛ فاللغة تؤثر مباشرة (...) – وبأكثر من طريقة – على مجرى البحث الكيميائي وتطوره, ومن خلالها يمكن تحديد مدى قوته أو ضعفه ... تقدمه أو تخلفه ... شرعية تنبؤاته أو افتقادها لسمة الشرعية المنطقية؛ كما أن سُبل البحث المعملي للكيمياء تنعكس بالضرورة على قواعد الصياغة الصورية لهذه اللغة ومدى إمكانية تطويرها وتنقيتها من شوائب اللغة العادية التي اشتُقت منها. ويعني ذلك – بعبارة أخرى – أن اللغة والتجريب شقان مُكملان لبعضهما البعض؛ وجهان لعملة واحدة تحمل اسم الممارسة العلمية. فهل تختلف اللغة الكيميائية عن غيرها من لغات العلم الخاصة؟ وكيف يستخدم الكيميائيون لغتهم؟ ما هي القواعد الحاكمة لهذه اللغة؟, وما هي نتائج استخدامها بالنسبة للكيمياء ككل؟. (shrink)

This eighth book of the author on gambling math presents in accessible terms the cold mathematics behind the sparkling slot machines, either physical or virtual. It contains all the mathematical facts grounding the configuration, functionality, outcome, and profits of the slot games. Therefore, it is not a so-called how-to-win book, but a complete, rigorous mathematical guide for the slot player and also for game producers, being unique in this respect. As it is primarily addressed to the slot player, its goal (...) is to present practical applications of the mathematical models of slot games, in order to provide numerical results that a player can use as criteria for gaming decisions or just as information for any slot game and any predicted winning event. These results are focused on probability and expected value, these being the most important parameters for decisional criteria in slots. The book is packed with plenty of figures, tables, and formulas. The content is organized so that readers can skip the theoretical parts and go picking the practical results (numerical, in tables of values where possible, or ready-to-compute formulas) for the desired situation. The practical results are gathered in the last chapter, titled "Practical Applications and Numerical Results," the largest part of the book, for the most popular categories of slot machines, namely with 3, 5, 9, and 16 reels. Any other category of slot games is covered in the theoretical part of the book, where the general formulas apply not only to existing slot games, but also to possible future slot games of any design and configuration. The author does not just throw the slot mathematics to the audience and run away, but offers an ultimate practical contribution with the chapter "How to estimate the number of stops and the symbol distribution on a reel", a surprise for both players and producers, where one can see that mathematics provides players with some statistical methods as well as methods based on physical measurements for retrieving these missing data. Having these data along with the mathematical results of this book, anyone can generate the PAR sheet of any slot machine. In the last decade, mathematics has been taken more and more seriously into account in gaming, as being the essence that governs the games of chance and the only rigorous tool providing information on optimal play, where possible. For the popular game of slots, mathematics already fulfilled its duty by providing all the data that it can provide and that cannot be found on the display of the slot machines - it is all here in this book. (shrink)

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By applying these data, (...) one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind. (shrink)

This collection of articles was written over the last 10 years and edited to bring them up to date (2019). All the articles are about human behavior (as are all articles by anyone about anything), and so about the limitations of having a recent monkey ancestry (8 million years or much less depending on viewpoint) and manifest words and deeds within the framework of our innate psychology as presented in the table of intentionality. As famous evolutionist Richard Leakey says, it (...) is critical to keep in mind not that we evolved from apes, but that in every important way, we are apes. If everyone was given a real understanding of this (i.e., of human ecology and psychology to actually give them some control over themselves), maybe civilization would have a chance. As things are however the leaders of society have no more grasp of things than their constituents and so collapse into anarchy is inevitable. -/- The first group of articles attempt to give some insight into how we behave that is reasonably free of theoretical delusions. In the next three groups, I comment on three of the principal delusions preventing a sustainable world— technology, religion and politics (cooperative groups). People believe that society can be saved by them, so I provide some suggestions in the rest of the book as to why this is unlikely via short articles and reviews of recent books by well-known writers. -/- It is critical to understand why we behave as we do and so the first section presents articles that try to describe (not explain as Wittgenstein insisted) behavior. I start with a brief review of the logical structure of rationality, which provides some heuristics for the description of language (mind, rationality, personality) and gives some suggestions as to how this relates to the evolution of social behavior. This centers around the two writers I have found the most important in this regard, Ludwig Wittgenstein and John Searle, whose ideas I combine and extend within the dual system (two systems of thought) framework that has proven so useful in recent thinking and reasoning research. As I note, there is in my view essentially complete overlap between philosophy, in the strict sense of the enduring questions that concern the academic discipline, and the descriptive psychology of higher order thought (behavior). Once one has grasped Wittgenstein’s insight that there is only the issue of how the language game is to be played, one determines the Conditions of Satisfaction (what makes a statement true or satisfied etc.) and that is the end of the discussion. No neurophysiology, no metaphysics, no postmodernism, no theology. -/- It is my contention that the table of intentionality (rationality, mind, thought, language, personality etc.) that features prominently here describes more or less accurately, or at least serves as an heuristic for, how we think and behave, and so it encompasses not merely philosophy and psychology, but everything else (history, literature, mathematics, politics etc.). Note especially that intentionality and rationality as I (along with Searle, Wittgenstein and others) view it, includes both conscious deliberative System 2 and unconscious automated System 1 actions or reflexes. -/- The next section describes the digital delusions, which confuse the language games of System 2 with the automatisms of System one, and so cannot distinguish biological machines (i.e., people) from other kinds of machines (i.e., computers). The ‘reductionist’ claim is that one can ‘explain’ behavior at a ‘lower’ level, but what actually happens is that one does not explain human behavior but a ‘stand in’ for it. Hence the title of Searle’s classic review of Dennett’s book (“Consciousness Explained”)— “Consciousness Explained Away”. In most contexts ‘reduction’ of higher level emergent behavior to brain functions, biochemistry, or physics is incoherent. Even for ‘reduction’ of chemistry or physics, the path is blocked by chaos and uncertainty. Anything can be ‘represented’ by equations, but when they ‘represent’ higher order behavior, it is not clear (and cannot be made clear) what the ‘results’ mean. Reductionist metaphysics is a joke, but most scientists and philosophers lack the appropriate sense of humor. -/- The last section describes The One Big Happy Family Delusion, i.e., that we are selected for cooperation with everyone, and that the euphonious ideals of Democracy, Diversity and Equality will lead us into utopia, if we just manage things correctly (the possibility of politics). Again, the No Free Lunch Principle ought to warn us it cannot be true, and we see throughout history and all over the contemporary world, that without strict controls, selfishness and stupidity gain the upper hand and soon destroy any nation that embraces these delusions. In addition, the monkey mind steeply discounts the future, and so we cooperate in selling our descendant’s heritage for temporary comforts, greatly exacerbating the problems. The only major change in this edition is the addition in the last article of a short discussion of China, a threat to peace and freedom as great as overpopulation and climate change and one to which even most professional scholars and politicians are oblivious so I regarded it as sufficiently important to warrant a new edition. -/- I describe versions of this delusion (i.e., that we are basically ‘friendly’ if just given a chance) as it appears in some recent books on sociology/biology/economics. Even Sapolsky’s otherwise excellent “Behave”(2017) embraces leftist politics and group selection and gives space to a discussion of whether humans are innately violent. I end with an essay on the great tragedy playing out in America and the world, which can be seen as a direct result of our evolved psychology manifested as the inexorable machinations of System 1. Our psychology, eminently adaptive and eugenic on the plains of Africa from ca. 6 million years ago, when we split from chimpanzees, to ca. 50,000 years ago, when many of our ancestors left Africa (i.e., in the EEA or Environment of Evolutionary Adaptation), is now maladaptive and dysgenic and the source of our Suicidal Utopian Delusions. So, like all discussions of behavior (philosophy, psychology, sociology, biology, anthropology, politics, law, literature, history, economics, soccer strategies, business meetings, etc.), this book is about evolutionary strategies, selfish genes and inclusive fitness (kin selection, natural selection). -/- The great mystic Osho said that the separation of God and Heaven from Earth and Humankind was the most evil idea that ever entered the Human mind. In the 20th century an even more evil notion arose, or at least became popular with leftists—that humans are born with rights, rather than having to earn privileges. The idea of human rights is an evil fantasy created by leftists to draw attention away from the merciless destruction of the earth by unrestrained 3rd world motherhood. Thus, every day the population increases by 200,000, who must be provided with resources to grow and space to live, and who soon produce another 200,000 etc. And one almost never hears it noted that what they receive must be taken from those already alive, and their descendants. Their lives diminish those already here in both major obvious and countless subtle ways. Every new baby destroys the earth from the moment of conception. In a horrifically overcrowded world with vanishing resources, there cannot be human rights without destroying the earth and our descendant’s futures. It could not be more obvious, but it is rarely mentioned in a clear and direct way, and one will never see the streets full of protesters against motherhood. -/- The most basic facts, almost never mentioned, are that there are not enough resources in America or the world to lift a significant percentage of the poor out of poverty and keep them there. Even the attempt to do this is already bankrupting America and destroying the world. The earth’s capacity to produce food decreases daily, as does our genetic quality. And now, as always, by far the greatest enemy of the poor is other poor and not the rich. -/- America and the world are in the process of collapse from excessive population growth, most of it for the last century, and now all of it, due to 3rd world people. Consumption of resources and the addition of 4 billion more ca. 2100 will collapse industrial civilization and bring about starvation, disease, violence and war on a staggering scale. The earth loses about 2% of its topsoil every year, so as it nears 2100, most of its food growing capacity will be gone. Billions will die and nuclear war is all but certain. In America, this is being hugely accelerated by massive immigration and immigrant reproduction, combined with abuses made possible by democracy. Depraved human nature inexorably turns the dream of democracy and diversity into a nightmare of crime and poverty. China will continue to overwhelm America and the world, as long as it maintains the dictatorship which limits selfishness. The root cause of collapse is the inability of our innate psychology to adapt to the modern world, which leads people to treat unrelated persons as though they had common interests (which I suggest may be regarded as an unrecognized -- but the commonest and most serious-- psychological problem -- Inclusive Fitness Disorder). This, plus ignorance of basic biology and psychology, leads to the social engineering delusions of the partially educated who control democratic societies. Few understand that if you help one person you harm someone else—there is no free lunch and every single item anyone consumes destroys the earth beyond repair. Consequently, social policies everywhere are unsustainable and one by one all societies without stringent controls on selfishness will collapse into anarchy or dictatorship. Without dramatic and immediate changes, there is no hope for preventing the collapse of America, or any country that follows a democratic system. Hence my concluding essay “Suicide by Democracy”. -/- Those wishing to read my other writings may see Talking Monkeys 2nd ed (2019), The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle 2nd ed (2019), Suicide by Democracy 3rd ed (2019), The Logical Stucture of Human Behavior (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019) . (shrink)

Since 2004, it has been mandated by law that all Danish undergraduate university programmes have to include a compulsory course on the philosophy of science for that particular program. At the Faculty of Science and Technology, Aarhus University, the responsibility for designing and running such courses were given to the Centre for Science Studies, where a series of courses were developed aiming at the various bachelor educations of the Faculty. Since 2005, the Centre has been running a dozen different courses (...) ranging from mathematics, computer science, physics, chemistry over medical chemistry, biology, molecular biology to sports science, geology, molecular medicine, nano science, and engineering. -/- We have adopted a teaching philosophy of using historical and contemporary case studies to anchor broader philosophical discussions in the particular subject discipline under consideration. Thus, the courses are tailored to the interests of the students of the particular programme whilst aiming for broader and important philosophical themes as well as addressing the specific mandated requirements to integrate philosophy, some introductory ethics, and some institutional history. These are multiple and diverse purposes which cannot be met except by compromise. -/- In this short presentation, we discuss our ambitions for using case studies to discuss philosophical issues and the relation between the specific philosophical discussions in the disciplines and the broader themes of philosophy of science. We give examples of the cases chosen to discuss various issues of scientific knowledge, the role of experiments, the relations between mathematics and science, and the issues of responsibility and trust in scientific results. Finally, we address the issue of how and why science students can be interested in and benefit from mandatory courses in the philosophy of their subject. (shrink)

Many students consider mathematics as the most dreaded subject in their curriculum, so much so that the term “math phobia” or “math anxiety” is practically a part of clinical psychological literature. This symptom is widespread and students suffer mental disturbances when facing mathematical activity because understanding mathematics is a great task for them. This paper described the students’ cognitive skills performance in Basic Mathematics based on the following logical operations: Classification, Seriation, Logical Multiplication, Compensation, Ratio and Proportional Thinking, Probability Thinking (...) and Correlation Thinking as it serves a critical element of teaching and learning, that is determining the current position of the learners’ mathematical capacity. Its implications for mathematics education were also revealed. A descriptive quantitative design was used in this study. The study included 1011 first-year college students from six state universities in the Philippines who were enrolled in the Bachelor of Science of Secondary Education Program during the first semester of the Academic Year 2019-2020. This study made use of the teacher-made test called the Test on Logical Operations. Findings revealed that the cognitive skills achievement of the first year BSE students from different state universities in the Philippines falls under the category of late concrete operational stage. As a result, students are unable to perform the logical operational skills expected of their age. At their age level, they are expected to be under the formal operational stage based on Piaget’s stages of cognitive development. These findings revealed a weak mathematical education foundation among students which requires immediate attention. This reality should be recognized by educational planners and implementers when making curricular and other instructional decisions. (shrink)

The term philosophy of chemistry is here construed broadly to include some publications from the history of chemistry and chemical education. Of course this initial selection of material has inevitably been biased by the interests of the author. This bibliography supersedes that of van Brakel and Vermeeren (1981), although no attempt has been made to include every single one of their entries, especially in languages other than English. Also, readers interested particularly in articles in German may wish to (...) consult the bibliography by Dittus and Mayer which also contains some material not included here (Dittus and Mayer, 1992). The aim is to maintain an up-to-date version of this bibliography and to publish a revised version in due course. Suggestions for further inclusions should be sent to the author. (shrink)

Building upon Nancy Cartwright's discussion of models in How the Laws of Physics Lie, this paper addresses solid state research in transition metal oxides. Historical analysis reveals that in this domain models function both as the culmination of phenomenology and the commencement of theoretical explanation. Those solid state chemists who concentrate on the description of phenomena pertinent to specific elements or compounds assess models according to different standards than those who seek explanation grounded in approximate applications of the Schroedinger equation. (...) Accurate accounts of scientific debate in this field must include both perspectives. (shrink)

Francis Ysidro Edgeworth’s unduly neglected monograph New and Old Methods of Ethics (1877) advances a highly sophisticated and mathematized account of social well-being in the utilitarian tradition of his 19th-century contemporaries. This article illustrates how his usage of the ‘calculus of variations’ was combined with findings from empirical psychology and economic theory to construct a consequentialist axiological framework. A conclusion is drawn that Edgeworth is a methodological predecessor to several important methods, ideas, and issues that continue to be discussed in (...) contemporary social well-being studies. (shrink)

This study determined the cognitive skills achievement in mathematics of elementary pre-service teachers as a basis for improving problem-solving and critical thinking which was analyzed using Piaget's seven logical operations namely: classification, seriation, logical multiplication, compensation, ratio and proportional thinking, probability thinking, and correlational thinking. This study utilized an adopted Test on Logical Operations (TLO) and descriptive research design to describe the cognitive skills achievement and to determine the affecting factors. Overall, elementary pre-service teachers performed with sufficient understanding in dealing (...) with the TLO. However, in each logical operation, students were found to have insufficient understanding of probability thinking and correlational thinking. These insufficiencies in other logical operations were attributed to their misconceptions on some mathematical terms, misinterpretation of the problems, poor comprehension skills, poor problem-solving skills, and poor performance in mathematics in general. (shrink)

The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...) states is the partition join operation at the set level that prefigures at the quantum level projective measurement as well as the formation of maximally-definite state descriptions by Dirac’s Complete Sets of Commuting Operators. This development is measured quantitatively by logical entropy at the set level and by quantum logical entropy at the quantum level. This follow-the-math approach supports the Literal Interpretation of QM—as advocated by Abner Shimony among others which sees a reality of objective indefiniteness that is quite different from the common sense and classical view of reality as being “definite all the way down”. (shrink)

Since the 1980's, the influence of context-based curricula has been growing in curricula and has been taking place in advance of improving the image of chemistry. This article argues that chemical societies should focus on a better understanding of the negative image of chemistry, by supporting historical and philosophical research. Based on that, chemistry curricula should change.

Book Review Mathematics of casino carnival games by Mark Bollman, New York: CRC Press 2021, 318 pp., GBP 48.99 (hardback), ISBN 9780367348656.

Information Theory, Evolution and The Origin ofLife: The Origin and Evolution of Life as a Digital Message: How Life Resembles a Computer, Second Edition. Hu- bert P. Yockey, 2005, Cambridge University Press, Cambridge: 400 pages, index; hardcover, US $60.00; ISBN: 0-521-80293-8. The reason that there are principles of biology that cannot be derived from the laws of physics and chemistry lies simply in the fact that the genetic information content of the genome for constructing even the simplest organisms is (...) much larger than the information content of these laws. Yockey in his previous book (1992, 335) In this new book, Information Theory, Evolution and The Origin ofLife, Hubert Yockey points out that the digital, segregated, and linear character of the genetic information system has a fundamental significance. If inheritance would blend and not segregate, Darwinian evolution would not occur. If inheritance would be analog, instead of digital, evolution would be also impossible, because it would be impossible to remove the effect of noise. In this way, life is guided by information, and so information is a central concept in molecular biology. The author presents a picture of how the main concepts of the genetic code were developed. He was able to show that despite Francis Crick's belief that the Central Dogma is only a hypothesis, the Central Dogma of Francis Crick is a mathematical consequence of the redundant nature of the genetic code. The redundancy arises from the fact that the DNA and mRNA alphabet is formed by triplets of 4 nucleotides, and so the number of letters (triplets) is 64, whereas the proteome alphabet has only 20 letters (20 amino acids), and so the translation from the larger alphabet to the smaller one is necessarily redundant. Except for Tryptohan and Methionine, all amino acids are coded by more than one triplet, therefore, it is undecidable which source code letter was actually sent from mRNA. This proof has a corollary telling that there are no such mathematical constraints for protein-protein communication. With this clarification, Yockey contributes to diminishing the widespread confusion related to such a central concept like the Central Dogma. Thus the Central Dogma prohibits the origin of life "proteins first." Proteins can not be generated by "self-organization." Understanding this property of the Central Dogma will have a serious impact on research on the origin of life. (shrink)

Longtermists have recently argued that it is overwhelmingly important to do what we can to mitigate existential risks to humanity. I consider three mistakes that are often made in calculating the value of existential risk mitigation. I show how correcting these mistakes pushes the value of existential risk mitigation substantially below leading estimates, potentially low enough to threaten the normative case for existential risk mitigation. I use this discussion to draw four positive lessons for the study of existential risk. -/- (...) . (shrink)

This manuscript is intended to illustrate the existence of a natural ethic as a universal and special case in which the notion of proximity differs from the reflexively perceived physical notion that is both commonly and scientifically employed. In this case actual proximity in nature is proposed to diverge from the physical lines construed to connect points to be a function of relations of the lines of perception as the components of a universal volume that is energetic and active, an (...) active "line of sight" to a single unique surface composed of all lines of sight, in contrast to a common notion of seeing based on connected points, and emerged as a function of past, transparent to witness, processes, in synergy with the more apparent, temporal and physical proximal , and possesses a logic that is based upon the same mathematical means of operations that are commonly known reflexively. This scheme, the nature of the natural ethic postulated precludes genetic manipulation as unethical in that it violates natural inherent, inherited proximities, synergies of past and present as, in name, nature itself as genetic and emerging. (shrink)

The nature of time is variously understood and varied expressions of time available are critically discussed. The nature of time formation, its structure and textures are presented taking examples from natural sciences and Indian spirituality. The physics and mathematics used to evolve the concept of time are chronologically presented. The mathematical allusion and physical illusion associated with the concept of theories of relativity are analyzed. The mathematical conjectures responsible for evolution of theories of relativity are pronounced. The missing physical reality (...) in theories of relativity in relation to appearance of contraction of length and dilation of time is given comparing these mathematical illusions associated; with the optical illusion of appearance of a scale as bent in water in a beaker to stress the point of illusion - mental and physical respectively. The physical and mathematical nature of time, its measurement and passage and the complex mathematical nature of physical and psychological times are presented. (shrink)

Over the past two decades, gamblers have begun taking mathematics into account more seriously than ever before. While probability theory is the only rigorous theory modeling the uncertainty, even though in idealized conditions, numerical probabilities are viewed not only as mere mathematical information, but also as a decision-making criterion, especially in gambling. This book presents the mathematics underlying the major games of chance and provides a precise account of the odds associated with all gaming events. It begins by explaining in (...) simple terms the meaning of the concept of probability for the layman and goes on to become an enlightening journey through the mathematics of chance, randomness and risk. It then continues with the basics of discrete probability, combinatorics and counting arguments for those interested in the supporting mathematics. These mathematic sections may be skipped by readers who do not have a minimal background in mathematics; these readers can skip directly to the Guide to Numerical Results to pick the odds and recommendations they need for the desired gaming situation. Doing so is possible due to the organization of that chapter, in which the results are listed at the end of each section, mostly in the form of tables. The chapter titled The Mathematics of Games of Chance presents these games not only as a good application field for probability theory, but also in terms of human actions where probability-based strategies can be tried to achieve favorable results. Through suggestive examples, the reader can see what are the experiments, events and probability fields in games of chance and how probability calculus works there. The main portion of this work is a collection of probability results for each type of game. Each game s section is packed with formulas and tables. Each section also contains a description of the game, a classification of the gaming events and the applicable probability calculations. The primary goal of this work is to allow the reader to quickly find the odds for a specific gaming situation, in order to improve his or her betting/gaming decisions. Every type of gaming event is tabulated in a logical, consistent and comprehensive manner. The complete methodology and complete or partial calculations are shown to teach players how to calculate probability for any situation, for every stage of the game for any game. Here, readers can find the real odds, returned by precise mathematical formulas and not by partial simulations that most software uses. Collections of odds are presented, as well as strategic recommendations based on those odds, where necessary, for each type of gaming situation. The book contains much new and original material that has not been published previously and provides great coverage of probabilities for the following games of chance: Dice, Slots, Roulette, Baccarat, Blackjack, Texas Hold em Poker, Lottery and Sport Bets. Most of games of chance are predisposed to probability-based decisions. This is why the approach is not an exclusively statistical one, but analytical: every gaming event is taken as an individual applied probability problem to solve. A special chapter defines the probability-based strategy and mathematically shows why such strategy is theoretically optimal.". (shrink)

Continuing his series of books on the mathematics of gambling, the author shows how a simple-rule game such as roulette is suited to a complex mathematical model whose applications generate improved betting systems that take into account a player's personal playing criteria. The book is both practical and theoretical, but is mainly devoted to the application of theory. About two-thirds of the content is lists of categories and sub-categories of improved betting systems, along with all the parameters that might stand (...) as the main objective criteria in a personal strategy - odds, profits and losses. The work contains new and original material not published before. The mathematical chapter describes complex bets, the profit function, the equivalence between bets and all their properties. All theoretical results are accompanied by suggestive concrete examples and can be followed by anyone with a minimal mathematical background because they involve only basic algebraic skills and set theory basics. The reader may also choose to skip the math and go directly to the sections containing applications, where he or she can pick desired numerical results from tables. The book offers no new so-called winning strategies, although it discusses them from a mathematical point of view. It does, however, offer improved betting systems and helps to organize a player's choices in roulette betting, according to mathematical facts and personal strategies. It is a must-have roulette handbook to be studied before placing your bets on the turn of either a European or American roulette wheel. (shrink)

The success of a few theories in statistical thermodynamics can be correlated with their selectivity to reality. These are the theories of Boltzmann, Gibbs, end Einstein. The starting point is Carnot’s theory, which defines implicitly the general selection of reality relevant to thermodynamics. The three other theories share this selection, but specify it further in detail. Each of them separates a few main aspects within the scope of the implicit thermodynamic reality. Their success grounds on that selection. Those aspects can (...) be represented by corresponding oppositions. These are: macroscopic – microscopic; elements – states; relational – non-relational; and observable – theoretical. They can be interpreted as axes of independent qualities constituting a common qualitative reference frame shared by those theories. Each of them can be situated in this reference frame occupying a different place. This reference frame can be interpreted as an additional selection of reality within Carnot’s initial selection describable as macroscopic and both observable and theoretical. The deduced reference frame refers implicitly to many scientific theories independent of their subject therefore defining a general and common space or subspace for scientific theories (not for all). The immediate conclusion is: The examples of a few statistical thermodynamic theories demonstrate that the concept of “reality” is changed or generalized, or even exemplified (i.e. “de-generalized”) from a theory to another. Still a few more general suggestions referring the scientific realism debate can be added: One can admit that reality in scientific theories is some partially shared common qualitative space or subspace describable by relevant oppositions and rather independent of their subject quite different in general. Many or maybe all theories can be situated in that space of reality, which should develop adding new dimensions in it for still newer and newer theories. Its division of independent subspaces can represent the many-realities conception. The subject of a theory determines some relevant subspace of reality. This represents a selection within reality, relevant to the theory in question. The success of that theory correlates essentially with the selection within reality, relevant to its subject. (shrink)

A basic thesis of Neokantian epistemology and philosophy of science contends that the knowing subject and the object to be known are only abstractions. What really exists, is the relation between both. For the elucidation of this “knowledge relation ("Erkenntnisrelation") the Neokantians of the Marburg school used a variety of mathematical metaphors. In this con-tribution I reconsider some of these metaphors proposed by Paul Natorp, who was one of the leading members of the Marburg school. It is shown that Natorp's (...) metaphors are not unrelated to those used in some currents of contemporary epistemology and philosophy of science. (shrink)

We show how removing faith-based beliefs in current philosophies of classical and constructive mathematics admits formal, evidence-based, definitions of constructive mathematics; of a constructively well-defined logic of a formal mathematical language; and of a constructively well-defined model of such a language. -/- We argue that, from an evidence-based perspective, classical approaches which follow Hilbert's formal definitions of quantification can be labelled `theistic'; whilst constructive approaches based on Brouwer's philosophy of Intuitionism can be labelled `atheistic'. -/- We then adopt what may (...) be labelled a finitary, evidence-based, `agnostic' perspective and argue that Brouwerian atheism is merely a restricted perspective within the finitary agnostic perspective, whilst Hilbertian theism contradicts the finitary agnostic perspective. -/- We then consider the argument that Tarski's classic definitions permit an intelligence---whether human or mechanistic---to admit finitary, evidence-based, definitions of the satisfaction and truth of the atomic formulas of the first-order Peano Arithmetic PA over the domain N of the natural numbers in two, hitherto unsuspected and essentially different, ways. -/- We show that the two definitions correspond to two distinctly different---not necessarily evidence-based but complementary---assignments of satisfaction and truth to the compound formulas of PA over N. -/- We further show that the PA axioms are true over N, and that the PA rules of inference preserve truth over N, under both the complementary interpretations; and conclude some unsuspected constructive consequences of such complementarity for the foundations of mathematics, logic, philosophy, and the physical sciences. -/- . (shrink)

Book Review Luck, logic, and white lies: the mathematics of games, second edition by Jörg Bewersdorff, New York, Taylor & Francis, CRC Press, 2021, 568 pp., GBP 42.99 (paperback), ISBN 9780367548414, Number of chapters 51.

Important achievements were obtained in the fields of mathematics, medicine, chemistry, astronomy, physics, optics, mechanics, zoology, botanic, mineralogy, geography and etc. in the Turkish-Islamic world between the ninth and thirteenth centuries. According to the leading historians of science, scholars living in different parts of the TurkishIslamic world not only surpassed their Greek and Byzantine predecessors. They also paved the way for development of these fields of science for following centuries. It is possible to mention many physicians that left non-erasable (...) marks in the medicine history among these distinguished scholars. One of these names is an Andalusian surgeon-physician called Abul-Qāsim alZahrāwī. He is known for his solid and unique contributions to the surgical world and regarded as the founder of surgery in the TurkishIslamic world. al-Zahrāwī wrote many books. One of these books, called al-Taṣrīf (The Method of Medicine) regarded as a medical encyclopedia has reached until today. The book attracted more attention in the European countries than in the Turkish-Islamic world and had an impact on Europe. Different chapters from the book were translated into languages such as Hebrew, French, English and especially Latin. al-Zahrāwī’s scientific heritage has also been discussed with all its aspects in Russia where scientists in the Turkish-Islamic world have especially been studied. Even though it was translated at a later period than Avicenna’s al-Qānūn fī al-Ṭibb (The Canon of Medicine), al-Taṣrīf was translated into Russian. The aim of this study is to identify Russian studies on Zahrawi and his main work, al-Taṣrīf -within the framework of available opportunitiesand to present prominent ones among these. In conclusion, this article also aims to contribute to the Turkish literature on al-Zahrāwī and al-Taṣrīf. Therefore, the author wishes to assist the relevant ongoing studies and the ones to be conducted in the future in terms of bibliography and material index. (shrink)

Some have argued for a division of epistemic labor in which mathematicians supply truths and philosophers supply their necessity. We argue that this is wrong: mathematics is committed to its own necessity. Counterfactuals play a starring role.

The broad range of emotional factors that affect learning on the sudden change of the learning modality in Mathematics led to this study. This study aimed to compare the level of support factors that greatly affect the students’ learning in mathematics in a blended learning approach. Sex, age, and relationship status were considered grouping variables on the individual, motivational, and social support factors towards learning mathematics in the blended learning mode of thirty education students at the tertiary level. This study (...) used a quantitative approach, particularly descriptive-comparative design. It utilized descriptive statistics such as means, standard deviations, and frequency and percent to describe the level of support factors. T-test for independent samples/ Mann Whitney U test was used to compare the level of support factors when grouped by the profile variables. Repeated Measures Analysis of Variance was used to compare the three support factors. The results revealed that the students’ level of support factors is high. Moreover, the level of support factors towards learning the subject in the blended learning mode of delivery of the students is the same regardless of their sex, age, and relationship status except in individual factors. Older students are influenced by their self-esteem or study habits more than younger students in learning mathematics in a blended approach. The students are eager to learn Mathematics in a blended learning approach because they are more motivated or are supported by their peers or their self-esteem. (shrink)

MethodologyA new hypothesis on the basic features characterizing the Foundations of Mathematics is suggested.Application of the methodBy means of it, the several proposals, launched around the year 1900, for discovering the FoM are characterized. It is well known that the historical evolution of these proposals was marked by some notorious failures and conflicts. Particular attention is given to Cantor's programme and its improvements. Its merits and insufficiencies are characterized in the light of the new conception of the FoM. After the (...) failures of Frege's and Cantor's programmes owing to the discoveries of an antinomy and internal contradictions, respectively, the two remaining, more radical programmes, i.e. Hilbert's and Brouwer's, generated a great debate; the explanation given here is their mutual incommensurability, defined by means of the differences in their foundational features.ResultsThe ignorance of this phenomenon explains the inconclusiveness of a century-long debate between the advocates of these two proposals. Which however have been so greatly improved as to closely approach or even recognize some basic features of the FoM.Discussion on the resultsYet, no proposal has recognized the alternative basic feature to Hilbert's main one, the deductive organization of a theory, although already half a century before the births of all the programmes this alternative was substantially instantiated by Lobachevsky's theory on parallel lines. Some conclusive considerations of a historical and philosophical nature are offered. In particular, the conclusive birth of a pluralism in the FoM is stressed. (shrink)

The Simulation Hypothesis proposes that all of reality is in fact an artificial simulation, analogous to a computer simulation. Outlined here is a method for programming relativistic mass, space and time at the Planck level as applicable for use in Planck Universe-as-a-Simulation Hypothesis. For the virtual universe the model uses a 4-axis hyper-sphere that expands in incremental steps (the simulation clock-rate). Virtual particles that oscillate between an electric wave-state and a mass point-state are mapped within this hyper-sphere, the oscillation driven (...) by this expansion. Particles are assigned an N-S axis which determines the direction in which they are pulled along by the expansion, thus an independent particle motion may be dispensed with. Only in the mass point-state do particles have fixed hyper-sphere co-ordinates. The rate of expansion translates to the speed of light and so in terms of the hyper-sphere co-ordinates all particles (and objects) travel at the speed of light, time (as the clock-rate) and velocity (as the rate of expansion) are therefore constant, however photons, as the means of information exchange, are restricted to lateral movement across the hyper-sphere thus giving the appearance of a 3-D space. Lorentz formulas are used to translate between this 3-D space and the hyper-sphere co-ordinates, relativity resembling the mathematics of perspective. (shrink)

This is a review of Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena, written by Jon Barwise and Lawrence Moss and published by CSLI Publications in 1996.

The Polish philosophy of mathematics in the 19th century is not a well-researched topic. For this period, only five philosophers are usually mentioned, namely Jan Śniadecki, Józef Maria Hoene-Wroński, Henryk Struve, Samuel Dickstein, and Edward Stamm. This limited and incomplete perspective does not allow us to develop a well-balanced picture of the Polish philosophy of mathematics and gauge its influence on 19th- and 20th-century Polish philosophy in general. To somewhat complete our picture of the history of the Polish philosophy of (...) mathematics in those times, we here present the profiles of some lesser-known Polish Romantic philosophers of the 19th century, namely Karol Libelt, Bronisław Trentowski, and Józef Kremer. We discuss their contributions to the philosophy of mathematics and their metaphysical perspectives, and we also show how their metaphysical ideas have found some continuity in the studies of some Catholic philosophers. (shrink)

In light of the observations and research design presented in the previous reports, the current technical report is focused on the relationship between the quality and specificity of the content of the gambling sites and the site’s SEO and marketing policy. This relationship is dependent upon the category of the gambling site and the difference in content quality, and the degree to which the mathematical dimension of gambling is reflected in this content is explained by this dependence.

Games of chance are developed in their physical consumer-ready form on the basis of mathematical models, which stand as the premises of their existence and represent their physical processes. There is a prevalence of statistical and probabilistic models in the interest of all parties involved in the study of gambling – researchers, game producers and operators, and players – while functional models are of interest more to math-inclined players than problem-gambling researchers. In this paper I present a structural analysis of (...) the knowledge attached to mathematical models of games of chance and the act of modeling, arguing that such knowledge holds potential in the prevention and cognitive treatment of excessive gambling, and I propose further research in this direction. (shrink)

Microlearning-based lessons are still new in the field of education because it primarily focuses on corporate training and adult learning. Hence, limited research was conducted in basic education even in higher education. Microlearning-based lessons are designed and delivered in the form of small, bite-sized information which allows students to achieve a certain learning objective. The main purpose of this research is to determine the effectiveness of Microlearning-based Lessons in Chemistry in the level of academic performance of 18 Grade 9 (...) students under the online learning modality. Moreover, the research instrument used was a researcher-made pretest-posttest based on the learning competencies of the Most Essential Learning Competency (MELC) consisting of 25 multiple choice items along the topics in Grade 9 Chemistry during the Second Quarter of the school year 2020-2021. Mean and paired t-tests were used as tools for analysis. Findings reveal that students’ exposure to Microlearning-based Lessons in Teaching Grade 9 Chemistry improved their level of academic performance in Chemistry. This implies that students perform better when they use microlearning-based lessons in learning Chemistry. Thus, it can be concluded that the level of performance in Chemistry of Grade 9 students greatly improved after exposure to microlearning-based lessons. Furthermore, this shows the effectiveness of the intervention material in improving their level of academic performance, thus the microlearning-based lessons be adopted in teaching Chemistry is recommended. (shrink)

Semantic analysis in early analytic philosophy belongs to a long tradition of adopting geometrical methodologies to the solution of philosophical problems. In particular, it adapts Descartes’ development of formalization as a mechanism of analytic representation, for its application in natural language semantics. This article aims to trace the mathematical roots of Frege, Russel and Carnap’s analytic method. Special attention is paid to the formal character of modern analysis introduced by Descartes. The goal is to identify the particular conception of “form” (...) developed by the analytic tradition, from Descartes to early analytic philosophy, and to determine its relation to similar notions, like ‘function’ and ‘syntax’. Finally, I focus on how Frege, Russell and Carnap’s methods of semantic analysis fit the general characterization of formal analysis previously developed. (shrink)

What were the reasons of the Copernican Revolution ? How did modern science (created by a bunch of ambitious intellectuals) manage to force out the old one created by Aristotle and Ptolemy, rooted in millennial traditions and strongly supported by the Church? What deep internal causes and strong social movements took part in the genesis, development and victory of modern science? The author comes to a new picture of Copernican Revolution on the basis of the elaborated model of scientific revolutions (...) that takes into account some recent advances in philosophy, sociology and history of science. The model was initially invented to describe Einstein’s Revolution of the XX century beginning. The model considers the growth of knowledge as interaction, interpenetration and unification of the research programmes, springing out of different cultural traditions. Thus, Copernican Revolution appears as a result of revealation and (partial) resolution of the dualism , of the gap between Ptolemy’s mathematical astronomy and Aristotelian qualitative physics. The works of Copernicus, Galileo, Kepler and Newton were all the stages of mathematics descendance from skies to earth and reciprocal extrapolation of earth physics on skies. The model elaborated enables to reassess the role of some social factors crucial for the scientific revolution. It is argued that initially modern science was a result of the development of Christian Weltanschaugung . Later the main support came from the absolute monarchies. In the long run the creators of modern science appeared to be the “apparatchics” of the “regime of truth” built-in state machine. Natural science became a part of ideological state apparatus providing not only scientific education but the internalization of values crucial for the functioning of state. -/- . (shrink)

The current technical report presents the partial results of the quantitative analysis of the research project, after the review of 247 gambling websites. It is focused on and discusses the usage of the math terms specific to gambling in the reviewed sample. In particular, the fifth technical report discusses the usage of math terms associated with the game of slots, as found in the reviewed sample.

This paper deals with Natorp’s version of the Marburg mathematical philosophy of science characterized by the following three features: The core of Natorp’s mathematical philosophy of science is contained in his “knowledge equation” that may be considered as a mathematical model of the “transcendental method” conceived by Natorp as the essence of the Marburg Neo-Kantianism. For Natorp, the object of knowledge was an infinite task. This can be elucidated in two different ways: Carnap, in the Aufbau, contended that this endeavor (...) can be divided into two distinct parts, namely, a finite “constitution” of the object of knowledge and an infinite incompletable empirical description. In contrast, and more in the original spirit of Cohen and Natorp, the physicist and philosopher Margenau in The Nature of Physical Reality (Margenau. 1950) conceived the infinity of this “Aufgabe” as an infinite dialectical process, in which relative “data” and “conceptual constructs” determine each other. This dialectical process eliminates the dichotomy between Anschauung and Begriff that distinguished the Marburg Neo-Kantianism from Kantian orthodoxy, namely, the abandonment of the difference between intuition and concept. Finally, the paper deals with the non-Archimedean geometrical systems that played a central role in Natorp’s defence of Cohen’s “infinitesimal” metaphysics. (shrink)

An analysis of the counter-intuitive properties of infinity as understood differently in mathematics, classical physics and quantum physics allows the consideration of various paradoxes under a new light (e.g. Zeno’s dichotomy, Torricelli’s trumpet, and the weirdness of quantum physics). It provides strong support for the reality of abstractness and mathematical Platonism, and a plausible reason why there is something rather than nothing in the concrete universe. The conclusions are far reaching for science and philosophy.