Here I reexamine Duhem's question of the continuity between medieval dynamics and early modern conservation theories. I concentrate on the heavens. For Aristotle, the motions of the heavens are eternally constant (and thus mathematizable) because an eternally constant divine Reason is their mover. Duhem thought that impetus and conservation theories, by extending sublunar mechanics to the heavens, made a divine renewer of motion redundant. By contrast, I show how Descartes derives his law of conservation by extending Aristotelian celestial dynamics (...) to the earth. Descartes argues that motion is intrinsically linear, not circular. But he agrees that motion is mathematically intelligible only where divine Reason moves bodies in a constant and eternal motion. Descartes strips bodies of active powers, leaving God as the only natural mover; thus both celestial and sublunar motions are constant, and uniformly mathematizable. The law of conservation of the total quantity of motion is an attempt to harmonize the constancy derived a priori with the phenomenal inconstancy of sublunar motions. (shrink)

When we examine the history of astronomy up to the end of the seventeenth century by considering the relation between mathematical astronomy and natural philosophy, it has been argued that there were two groups of philosophers and astronomers: instrumentalists and realists. However, this classification is deficient when we consider attitudes toward the explanatory power of mathematics in determining astronomical theories. I offer the solution of dividing realists into two subcategories—mathematical realists and physical realists. Mathematical realists include those who thought mathematics (...) could provide the real motions of celestial bodies. The physical realists, who include Ibn Rushd (Averroës), believed mathematics could not provide us with the real structure of the heavens. To avoid contradictions between the physical and mathematical models, the physical realists held that a mathematical model of the heavens should be designed by considering physics. I argue, in this article, that Francis Bacon can be considered a physical realist. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Natural Philosophy: On Retrieving a Lost Disciplinary Imaginary by Alister E. McGRATHJack ZupkoMcGRATH, Alister E. Natural Philosophy: On Retrieving a Lost Disciplinary Imaginary. Oxford: Oxford University Press, 2023. viii + 248 pp. Cloth, $39.95This book attempts to retrieve and reimagine the tradition of natural philosophy as an antidote for what the author sees as the fragmented, instrumentalized, and ethically disengaged understanding of the natural world most of us (...) have today. The idea is not to reinstate the older vision of Aristotle and Thomas Aquinas, with its final causes and animated spheres, or even the early modern culmination of natural philosophy in Newton’s universe of mathematically fixed natural laws; rather, the author hopes to engender a newer and deeper understanding of nature that is at once scientific, ethical, and poetic, which he explains in terms of the conceptual framework of Popper’s “Three Worlds”: objective, subjective, and theoretical. What is recovered thereby is said to be a “lost conceptual space” wherein human beings learn both about and from nature, modes of knowing rendered obsolete by disciplinary specialization in the sciences as well as our commitment to objective methods that leave no room for ethical or spiritual approaches to understanding the natural world and our place in it.The author covers quite a bit of ground on the historical side, from the ancient Greeks through the Middle Ages, moving on to the idea of natural philosophy as it was gradually transformed during the early modern period by Copernicus, Kepler, Galileo, Bacon, Boyle, and Newton—a picture finally eclipsed by the objective, empirical concept of natural science familiar to us today. Curiously, the book says very little about the Platonic tradition of natural philosophy that grew up around the Timaeus. Because it was available in Latin (or the first half of it, anyway, in a Latin translation by the Roman Neoplatonist Calcidius, who also wrote an influential commentary on the work), the Timaeus was, for almost a millennium, the authoritative text in natural philosophy in the West, at least until Aristotle’s nonlogical and scientific writings were recovered in the twelfth century. The Timaeus was the subject of many commentaries and philosophical discussions, from Calcidius in the fourth century to Bernardus Silvestris, William of Conches, and Alan of Lille in the twelfth. It fell out of favor among philosophers with the rise of Aristotle’s Physics and Aristotelian natural philosophy, though it continued to shape the popular imagination of nature in other genres, such as art and literature—recall, for example, the well-known image of “God the Geometer” (c. 1230), measuring the cosmos with a compass. If the author’s project is about “retrieving” natural philosophy “as a lost disciplinary imaginary” (the book’s subtitle), then surely the Platonic vision of the universe deserves equal billing with the Aristotelian. [End Page 158]That said, there is much to like in the project sketched here. The author’s diagnosis of the epistemic malaise of modern-day science sounds right to anyone familiar with the history of philosophy and natural science. So, even though we can now correctly describe the velocity constant of earth’s gravity as 9.8 m/s2, among other scientific achievements, we take ourselves to be wearing a different hat when we wax poetic at the beauty of the sky and the stars. Early-and pre-modern authors were more adept at bringing together science and poetry, but that might be because their epistemic position was radically different from our own. Calcidius, for example, finds it easy to draw moral and aesthetic conclusions from the motions of the cosmos because he really believed heavenly bodies are, like us, animated by souls. Even a materialist like Lucretius accepts that the gods exist; his (still) very radical thesis is that they don’t care about us. (And why should they? The Pythagorean theorem is much more beautiful and edifying to consider than the troubles of ignorant and weak-willed mortals.) Enlightened moderns that we are, we no longer believe the heavens are populated by super-intelligent beings; yet we continue to marvel at Van Gogh’s Starry Night and feel it is wrong to cause gratuitous... (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)

Immanuel Kant's Metaphysical Foundations of Natural Science (1786) provides metaphysical foundations for the application of mathematics to empirically given nature. The application that Kant primarily has in mind is that achieved in Isaac Newton's Principia (1687). Thus, Kant's first chapter, the Phoronomy, concerns the mathematization of speed or velocity, and his fourth chapter, the Phenomenology, concerns the empirical application of the Newtonian notions of true or absolute space, time, and motion. This paper concentrates on Kant's second and third chapters—the Dynamics (...) and the Mechanics, respectively—and argues that they are best read as providing a transcendental explanation of the conditions for the possibility of applying the (mathematical) concept of quantity of matter to experience. Kant again has in mind the empirical measures of this quantity that Newton fashions in the Principia, and he aims to make clear, in particular, how Newton achieves a universal measure for all bodies whatsoever by projecting the static quantity of terrestrial weight into the heavens by means of the theory of universal gravitation. Kant is not attempting to prove a priori what Newton has established empirically but, rather, to clarify the character of Newton's mathematization by building Newton's empirical measures into the very concept of matter that is articulated in the Metaphysical Foundations. (shrink)