We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include (...) a simple proof of this theorem inspired in Ferraioli and Lettieri (Math Logic Q 1:27–43, 2011). (shrink)

In the edited book “Bourdieu and Chinese Education”, a group of scholars in China, Australia, Canada, and the USA engage in a dialogue with Bourdieu and raise persistent questions not only about issues of equity, competition, and change in Chinese education, but also about the value, venture, and violence in using established Western intellectual frameworks for analysing Chinese education. In response to these questions, this special issue analyses and discusses Chinese rural education, teacher education, language education, (...) health and physical education, and transnational education; and proposes a series of new conceptualisations, for example, regression- and network-based field analysis, Bourdieu-Chinese philosophy encounter, field of mediation, localised pedagogical capital, and new Chinese habituses (e.g., contemptuous habitus, diasporic cosmopolitan habitus, habitus (re)structuring). Such collective effort responds to the strident, and sometimes misleading, castigation of Bourdieu for determinism; and also disputes the non-reflexive, celebratory tone that consecrates the French sociologist and his canonical theorem, and hence reproduces the symbolic violence in the doxic academia. In this vein, the special issue is respectful for, but not restricted to, Bourdieu’s sociology, showing no timidity in questioning and contesting the framework of the famed thinker when research problems and findings demand so. (shrink)

This paper critically assesses the claim by Gavin Menzies that Regiomontanus knew about the Chinese Remainder Theorem (CRT) through the Shù shū Jiǔ zhāng (SSJZ) written in 1247. Menzies uses this among many others arguments for his controversial theory that a large fleet of Chinese vessels visited Italy in the first half of the 15th century. We first refute that Regiomontanus used the method from the SSJZ. CRT problems appear in earlier European arithmetic and can be solved (...) by the method of the Sun Zi, as did Fibonacci. Secondly, we pro-vide evidence that remainder problems were treated within the European abbaco tradition independently of the CRT method. Finally, we discuss the role of recreational mathematics for the oral dissemination of sub-scientific knowledge. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Kennedy Institute of Ethics Journal 14.1 (2004) 47-54 [Access article in PDF] Ethical Guidelines for Human Embryonic Stem Cell Research*(A Recommended Manuscript) Adopted on 16 October 2001Revised on 20 August 2002 Ethics Committee of the Chinese National Human Genome Center at Shanghai, Shanghai 201203 Human embryonic stem cell (ES) research is a great project in the frontier of biomedical science for the twenty-first century. Be- cause the research (...) involves the use of human embryos, it triggers serious debate on ethical issues. Opponents consider the embryo to be an early form of human life that should be respected and not destroyed. However, the majority of scientists support embryonic stem cell research, believing that it offers good prospects for the treatment of diseases that have remained incurable until now and so will benefit humankind. The Ethics Committee of the Department of Ethical, Legal, and Social Implications of the Chinese National Human Genome Center at Shanghai seriously discussed the ethical debate initiated by embryonic stem cell research. We concluded that we should support the scientists of our country in actively carrying out human embryonic stem cell research for the noble cause of "medicine being a beneficent art." For the healthy and orderly development of human embryonic stem cell research in our country, we put forward the following recommended Ethical Guidelines for Human Embryonic Stem Cell Research as a reference for leaders, administrative departments, and related scientists. Preface Article 1. Human embryonic stem cells are the primitive cells that play the main role in the growth and development of a human body. These [End Page 47] primitive cells have the potential for infinite proliferation, self-renewal, and multi-directional differentiation. If scientists can discover the mechanism of differentiation of human embryonic stem cells, it will be possible to induce differentiation of human embryonic stem cells to form various types of human cells for clinical cell therapy. If human embryonic stem cell research can be integrated with modern biomedical engineering techniques, it also will be possible to make repair and replacement of human tissues and organs a reality. Article 2. There are two ways to classify human embryonic stem cells. One way is to classify them according to their potential for differentiation. There could be three kinds of stem cells: totipotent stem cells, pluripotent stem cells, and unipotent stem cells.A totipotent stem cell has the potential to develop into a whole individual. It can differentiate into the more than 200 cell types in the whole body, construct any tissue or organ of the body, and finally develop into a whole individual. The fertilized egg and the cleavage cells at the very early stage of embryonic development are totipotent stem cells.A pluripotent stem cell has the potential to differentiate into many cell types derived from the three embryonic layers. However, it has lost the capacity to develop into a complete organism.A unipotent stem cell is derived from the further differentiation of the pluripotent stem cell. It can differentiate only into one cell type such as a hematopoietic stem cell, neural stem cell, and others.The other way is to classify human stem cells according to their source. There could be two kinds of human stem cells: embryonic stem cells and tissue stem cells (also called adult stem cells). The former involves experimentation with embryos, which has serious ethical implications. Ethical issues associated with the latter are mainly expressed in the various opinions regarding the allocation of health resources. Article 3. Human embryonic stem cells are the group of cells called the blastocyst inner cell mass during the early stage of embryonic development. They are the main source of totipotent stem cells, and hence the focal and hot point in stem cell research. Studies on the clinical application of embryonic stem cells probably will involve use of the somatic cell nucleus transfer (SCNT) technique, which destroys the early human embryo. At present, the ethical and moral debate is very serious in human embryonic stem cell research regarding whether the research will develop... (shrink)

James A. Diefenbeck, Wayward Reflections on the History ofPhilosophyThomas R. Flynn Sartre, Foucault and Historical Reason. Volume 1:Toward an Existential Theory of HistoryMark Golden and Peter Toohey Inventing Ancient Culture:Historicism, Periodization and the Ancient WorldZenonas Norkus Istorika: Istorinis IvadasEverett Zimmerman The Boundaries of Fiction: History and theEighteenth‐Century British Novel.

In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to (...) be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas. (shrink)

In this article the central philosophical issues concerning human-level artificial intelligence (AI) are presented. AI largely changed direction in the 1980s and 1990s, concentrating on building domain-specific systems and on sub-goals such as self-organization, self-repair, and reliability. Computer scientists aimed to construct intelligence amplifiers for human beings, rather than imitation humans. Turing based his test on a computer-imitates-human game, describing three versions of this game in 1948, 1950, and 1952. The famous version appears in a 1950 article in Mind, ‘Computing (...) Machinery and Intelligence’ (Turing 1950). The interpretation of Turing's test is that it provides an operational definition of intelligence (or thinking) in machines, in terms of behavior. ‘Intelligent Machinery’ sets out the thesis that whether an entity is intelligent is determined in part by our responses to the entity's behavior. Wittgenstein frequently employed the idea of a human being acting like a reliable machine. A ‘living reading-machine’ is a human being or other creature that is given written signs, for example Chinese characters, arithmetical symbols, logical symbols, or musical notation, and who produces text spoken aloud, solutions to arithmetical problems, and proofs of logical theorems. Wittgenstein mentions that an entity that manipulates symbols genuinely reads only if he or she has a particular history, involving learning and training, and participates in a social environment that includes normative constraints and further uses of the symbols. (shrink)

A notion of delegated causality is introduced here. This subtle kind of causality is dual to interventional causality. Delegated causality elucidates the causal role of dynamical systems at the “edge of chaos”, explicates evident cases of downward causation, and relates emergent phenomena to Gödel’s incompleteness theorem. Apparently rich implications are noticed in biology and Chinese philosophy. The perspective of delegated causality supports cognitive interpretations of self-organization and evolution.

Hao Wang, a prolific philosopher and researcher, was known for his close intellectual friendship with Kurt Gödel, his advocacy for the study of logic at Oxford, and for his path-breaking contributions to logic and automated theorem proving. Yet in a memorial volume published sixteen years after Wang’s passing, the editors Charles Parsons and Montgomery Link noted “rather little has been published on Wang’s considerable body of work or on the man’s personality and unusual personal history.” The goal of this (...) article is to see what light Wang’s logical journey in life sheds on Chinese philosophy and the Western analytic tradition. (shrink)

Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras’s theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes’ method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino (...) tumbling, and find out how slicing cones helped save a city and put a man on the moon. (shrink)

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, (...) chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem.Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, (...) chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises will stretch the more advanced reader. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship – (...) the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (shrink)

Q.E.D. presents some of the most famous mathematical proofs in a charming book that will appeal to nonmathematicians and math experts alike. Grasp in an instant why Pythagoras’s theorem must be correct. Follow the ancient Chinese proof of the volume formula for the frustrating frustum, and Archimedes’ method for finding the volume of a sphere. Discover the secrets of pi and why, contrary to popular belief, squaring the circle really is possible. Study the subtle art of mathematical domino (...) tumbling, and find out how slicing cones helped save a city and put a man on the moon. (shrink)

The thesis aims at analyzing metaphysical implications of the ordinary concept of "cause". The approach is justified through a discussion of Hume's theory of causation, accompanied by discussions about the nature of definition itself. ;Four major metaphysical problems of causation are discussed: The ontological status of cause ; the temporal relation between causes and effects ; the direction of causation ; and causal necessity . ;Through analytical discussions of the existing literatures on those problems, the thesis identifies certain metaphysical assumptions (...) to be responsible for the profound difficulties that the authors encounter, including the assumptions of a sort of Cartesian dualism of beings and activities, Leibniz' law of identity, and the Newtonian mechanical model of causation. A "particle-wave" ontology is introduced as an alternative to these assumptions, and thus provides solutions to the difficulties which otherwise cannot be solved. The dialectical nature of the ontology may not be happily accepted by philosophers of strict analytical tradition, but it finds its predecessors in the Chinese Taoist philosophy, Hegelian philosophy, Whiteheadian philosophy, and the Copenhagen interpretation of quantum physics. The author hopes to convince the readers that there is a paradox in the metaphysics of causation analogous to the paradox in the arithmetics revealed by Godel's theorem: We cannot have a complete metaphysics of causation without inconsistency. (shrink)

This work attempts to respond to Tomas Aquinas' Cosmological Argument in a way that combines Set Theory with the idea of the ‘Book of Change’. The study defines the ith Cause Set on which to operate on, which leads to the ontological commitment of austerity that the ‘First Cause's Compromise with emergence’ cannot be avoided. It is argued in the present paper that the concept that ‘emergence only consists of Synchronic Emergence and Diachronic Emergence’ should be extended to a broader (...) notion of emergence, which is made up of the two discussed elements and a third one ‘No-Boundary Emergence’ (beyond the time dimension). The article defines the concept of No-Boundary Emergence, proves why it is a type of emergence that differs from the traditional two types, and asserts that it underlies the bottom layer of the cosmos. This study describes the common feature of all emergence as communication protocols between layers. The assemblage of all emergences behaves similar to a distributed system that cannot be restricted by Gödel's theorem. The paper provides evidence (in Big Bang Cosmology, Conformal Cyclic Cosmology, Superstring Theory, Quantum Gravity) for this point of view, and notes that emergence (in the context of No-Boundary Emergence) is not only a simple scientific theory but also a progressive scientific research programme that can spontaneously grow from scientific theory based on Platonism at the expense of a degenerating shift to the ontological commitment of austerity. This paper proposes an improved model of Schrödinger Cat that provides a new explanation for quantum measurement and argues that there must be a forbidden zone of thought experiments. The study also introduces the implications of ancient Chinese thoughts (namely, the ‘Book of Change’ and Confucius). The paper comes to the conclusion that emergence (crossing the gap between ‘being’ and ‘nothing’, while ignoring the forbidden zone of thought experiments) relieves ‘cosmological insufficiency’ in the sense of Neo-Aristotelism. (shrink)

The first step of the construction of Nézondet's models of finite arithmetics which are counter-models to Erdös–Woods conjecture is to add to the natural numbers the non-standard numbers generated by one of them, using addition, multiplication and divisions by a natural factor allowed in an ultrapower construction. After a review of some properties of such a structure, we show that the choice of the ultrafilter can be managed, using just the Chinese remainder's theorem, so that a model as (...) desired is obtained as early as at the first time. (shrink)

The first step of the construction of Nézondet's models of finite arithmetics which are counter-models to Erdös–Woods conjecture is to add to the natural numbers the non-standard numbers generated by one of them, using addition, multiplication and divisions by a natural factor allowed in an ultrapower construction. After a review of some properties of such a structure, we show that the choice of the ultrafilter can be managed, using just the Chinese remainder's theorem, so that a model as (...) desired is obtained as early as at the first time. (shrink)

The unified theory of dose and effect, as indicated by the median-effect equation for single and multiple entities and for the first and higher order kinetic/dynamic, has been established by T.C. Chou and it is based on the physical/chemical principle of the massaction law (J. Theor. Biol. 59: 253-276, 1976 (質量作用中效定理) and Pharmacological Rev. 58: 621-681, 2006) (普世中效指數定理). The theory was developed by the principle of mathematical induction and deduction (數學演繹歸納法). Rearrangements of the median-effect equation lead to Michaelis-Menten, Hill, Scatchard, (...) and Henderson-Hasselbalch equations. The “median” serves as the universal reference point and the “common link” for the relationship of all entities and is also the “harmonic mean” of kinetic dissociation constants. Over 300 mechanism-specific equations have been derived and published using the mathematical induction-deduction process. These equations can be deduced into several general equations, including the median-mediated whole/part equation, combination index theorem, isobologram equation, and polygonogram. It is proven that “dose” and “effect” are interchangeable, thus, “substance” and “function” are interchangeable, which leads to “the unity theory” (劑效、心物、知行一元論) in quantitative mathematical philosophy (數學的定量哲學) in functional context. Therefore, a general theory centered on the “median” and based on equilibrium dynamics has evolved. In other words: [「中」的宇宙觀： 以「中」爲基凖的動力學生態平衡]. Based on the median-effect equation of the mass-action law, the fundamental claim is that we can draw “a specific cure” for only two data points, if they are determined accurately. This claim has far reaching consequences since it defies the general held belief that two points can dray only a straight line. Remarkably, the unity theory (一元論) providesscientific/mathematical interpretation in equations and in graphics of Chinese ancient philosophy, including Fu-Si Ba Gua (伏羲八卦), Dao’s Harmony (和諧), the Confucian doctrine of the mean (儒家中庸之道), Chou Dun-Yi’s (周敦頤, 1017-1073) From Wu-ji to Tai-ji and Taiji Tu Sho (無極而太極及太極圖說). The moderntopological analysis for trinity yields an exact correspondence to the Ba-Gua, which was introduced over 4,000 years ago. Furthermore, the median-centered algorithm, promotes modern ecological content (生態學) in the equilibral dynamic state of harmony. It is concluded that Western science and Eastern philosophy are directly linked and complementary to each other. Since the truth in mathematical quantitative philosophy (數學的定量哲學) has no boundaries, East and West philosophies can flourish together for the common goal and ideal in science and in humanity (世界大同). (shrink)

We study the strength (over bounded induction) of axioms expressing particular cases of the Chinese Remainder Theorem with respect to the axiom ∀ x, y∃ z (z = xy).

Whether it was John Searle’s Chinese Room argument (Searle, 1980) or Roger Penrose’s argument of the non-computable nature of a mathematician’s insight – an argument that was based on Gödel’s Incompleteness theorem (Penrose, 1989), we have always had skeptics that questioned the possibility of realizing strong Artificial Intelligence (AI), or what has become known by Artificial General Intelligence (AGI). But this new book by Landgrebe and Smith (henceforth, L&S) is perhaps the strongest argument ever made against strong AI. (...) It is a very extensive review of what building a mind essentially amounts to drawing on insights and results from biology, physics, linguistics, computability, philosophy, and mathematics. (shrink)

Jury theorems are mathematical theorems about the ability of collectives to make correct decisions. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise’: many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans across various disciplines such (...) as economics, political science, philosophy, and computer science. This entry reviews and critically assesses a variety of jury theorems. It first discusses Condorcet's initial jury theorem, and then progressively introduces jury theorems with more appropriate premises and conclusions. It explains the philosophical foundations, and relates jury theorems to diversity, deliberation, shared evidence, shared perspectives, and other phenomena. It finally connects jury theorems to their historical background and to democratic theory, social epistemology, and social choice theory. (shrink)

Computer assisted theorem proving is an increasingly important part of mathematical methodology, as well as a long-standing topic in artificial intelligence (AI) research. However, the current generation of theorem proving software have limited functioning in terms of providing new proofs. Importantly, they are not able to discriminate interesting theorems and proofs from trivial ones. In order for computers to develop further in theorem proving, there would need to be a radical change in how the software functions. Recently, (...) machine learning results in solving mathematical tasks have shown early promise that deep artificial neural networks could learn symbolic mathematical processing. In this paper, I analyze the theoretical prospects of such neural networks in proving mathematical theorems. In particular, I focus on the question how such AI systems could be incorporated in practice to theorem proving and what consequences that could have. In the most optimistic scenario, this includes the possibility of autonomous automated theorem provers (AATP). Here I discuss whether such AI systems could, or should, become accepted as active agents in mathematical communities. (shrink)

Representation theorems are often taken to provide the foundations for decision theory. First, they are taken to characterize degrees of belief and utilities. Second, they are taken to justify two fundamental rules of rationality: that we should have probabilistic degrees of belief and that we should act as expected utility maximizers. We argue that representation theorems cannot serve either of these foundational purposes, and that recent attempts to defend the foundational importance of representation theorems are unsuccessful. As a result, we (...) should reject these claims, and lay the foundations of decision theory on firmer ground. (shrink)

For anyone looking to understand Chinese philosophy, here is the place to start. Introducing this vast and far-reaching tradition, the longest continuous heritage of philosophical reflection in our existence, Ronnie L. Littlejohn tells you everything you need to know about those Chinese thinkers who have made the biggest contributions to the conversation of philosophy. From the Han dynasty to the present, he leads us into the indigenous philosophical traditions of Confucianism, Daoism and the uniquely modified forms of Buddhism (...) in China and introduces: - The six classical schools of Chinese philosophy (Yin-Yang, Ru, Mo, Ming, Fa and Dao-De) - The arrival of Buddhism in China and its distinctive development - The central figures and movements from the end of the Tang dynasty to the introduction into China of Western thought - The impact of Chinese philosophers ranging from Confucius and Laozi to Tu Weiming on their equivalents in the West. Weaving together key subjects, thinkers and texts, we see how Chinese traditions have profoundly shaped the institutions, social practices and psychological character of not only East and Southeast Asia, but the world we are living in. Praised for its completely original and illuminating thematic approach, this new edition includes updated features such as reading lists, a comparative chronology of Western and Chinese philosophers, and additional translated extracts. (shrink)

This chapter contains sections titled: Polarization Light Quanta The Entangled State How Do They Do It? Bell's Theorem(s) Aspect's Experiment What Is Weird About the Quantum Connection? Appendix A: The GHZ Scheme.

Specific Chinese models for theories of knowledge were premised upon a structurally ordered external reality; since natural (or cosmic) order is organic, it naturally follows the 'flow' of structural patterns and operates in accordance with structural principles that regulate every existence. In this worldview, our mind is also structured in accordance with this all-embracing, but open, organic system. The axioms of our recognition and thought are therefore not arbitrary, but follow this rationally designed structure. The compatibility of both the (...) cosmic and mental structures is the basic precondition that enables humans to perceive and recognize external reality. The present study shows that this paradigm of structural epistemology can already be found in the earliest Chinese theories of knowledge. The introduction of Chinese models and their incorporation into Western discourses fills an important theoretical gap in the Western model of structuralism. This book offers an insight into epistemological systems that arose outside the discourses of the Euro-American tradition. It can thus help us to eliminate and supersede certain culturally conditioned prejudices as to the superiority and omnipresence of Western theoretical models, while demonstrating incontrovertibly that the results of Western discourses are by no means the only force driving theoretical innovation at the present time. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. The static agreement (...) result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

We give a review and critique of jury theorems from a social-epistemology perspective, covering Condorcet’s (1785) classic theorem and several later refinements and departures. We assess the plausibility of the conclusions and premises featuring in jury theorems and evaluate the potential of such theorems to serve as formal arguments for the ‘wisdom of crowds’. In particular, we argue (i) that there is a fundamental tension between voters’ independence and voters’ competence, hence between the two premises of most jury theorems; (...) (ii) that the (asymptotic) conclusion that ‘huge groups are infallible’, reached by many jury theorems, is an artifact of unjustified premises; and (iii) that the (nonasymptotic) conclusion that ‘larger groups are more reliable’, also reached by many jury theorems, is not an artifact and should be regarded as the more adequate formal rendition of the ‘wisdom of crowds’. (shrink)

The representation theorems of expected utility theory show that having certain types of preferences is both necessary and sufficient for being representable as having subjective probabilities. However, unless the expected utility framework is simply assumed, such preferences are also consistent with being representable as having degrees of belief that do not obey the laws of probability. This fact shows that being representable as having subjective probabilities is not necessarily the same as having subjective probabilities. Probabilism can be defended on the (...) basis of the representation theorems only if attributions of degrees of belief are understood either antirealistically or purely qualitatively, or if the representation theorems are supplemented by arguments based on other considerations (simplicity, consilience, and so on) that single out the representation of a person as having subjective probabilities as the only true representation of the mental state of any person whose preferences conform to the axioms of expected utility theory. (shrink)

Chinese Philosophy provides a clear, accessible conception of the Chinese philosophical sensibility and its evolution throughout history.

The book begins with an overview that introduces the Theorem and the issues surrounding it, and explores how the essays that follow contribute to our understanding of those issues.

Understanding Chinese philosophy requires knowledge of the referential framework prevailing in Chinese intellectual traditions. But Chinese philosophical texts are frequently approached through the lens of Western paradigms. Analysing the most common misconceptions surrounding Western Sinology, Jana Rošker alerts us to unseen dangers and introduces us to a new more effective way of reading Chinese philosophy. Acknowledging that different cultures produce different reference points, Rošker explains what happens we use rational analysis, a major feature of the European (...) intellectual tradition, to read Chinese philosophy. We rely on impossible comparisons, arrive at prejudiced assumptions and fail to arrive at the truth, the consequence of applying a different methodology to the process of perceiving, understanding and interpreting reality. Instead of transferring concepts and categories from Western sinology onto socio-cultural Chinese contexts, Rošker constructs a new methodology of reading, understanding and interpreting Chinese philosophy. She opens our eyes to the basic problems of Western paradigms, encourages intercultural approaches and allows us to master a more autochthonous understanding of Chinese philosophy. (shrink)

An investigation into the reasons for the inclusion and exclusion of Chinese and Indian philosophical thought in 17th-and-18th-century Europe.

The research examines the features of the Mahayana world of Chinese Buddhism in the system of worlds of Mahayana Buddhism. A definition is given of the concept of “worlds of Mahayana Buddhism” as divergent constructs formed in the areas of distribution of Buddhism, as well as the world of Chinese Mahayana Buddhism. The specific features of Mahayana Buddhism in China, formed as a result of its assimilation on traditional religious and sociocultural grounds, are shown. The factors that prevented (...) the entry of Buddhism into the civilizational space of China and determined its formation there over the course of several centuries are indicated. The role of the Prajnaparamita texts, the Lotus Sutra, the Nirvana Sutra and the Avatamsaka Sutra in the formation of schools of Chinese Buddhism is revealed. The role of the Mahaparinirvana Sutra in the formation of the idea of an instant path to salvation in China is especially emphasized. The importance of the idea of an instant way of salvation for the formation of Chinese schools itself is shown. An analysis is given of the formation of the philosophical and soteriological direction in China, which took a different direction than in India, where the development of Madhyamaka ideas led to an emphasis on the epistemological aspects of the doctrine of emptiness, while in China attention was focused on its ontological aspects. The significance of the problem of truly existing is indicated as one of the main problems of philosophical research of the Tiantai, Chan, Huayan schools of Chinese Buddhism, as well as the idea of instantly achieving Buddhahood, which became the main soteriological guideline of these schools. It is indicated that in Tibet the development of philosophical and soteriological directions was developed in line with Indian Buddhism. The reasons for the Tibetans' choice of the soteriological path of the gradual movement of nirvana, which determined the development of Buddhism in their country, are considered. The role of Atisha in choosing the gradual path to nirvana is revealed. The difference between the worlds of Mahayana Buddhism, formed in China and Tibet, is shown. (shrink)