Search Results (9)

In the Timaeus, Plato explores the topic of cosmology. The demiurge creates a perfect cosmos by imitating the eternal being and using necessity as an auxiliary cause. The unique cosmos not only contains immortal gods, but also mortal living beings. Concerning the academic research on cosmology in Plato’s Timaeus, scholars have explored it through reason, good, and necessity, and they have conducted in-depth analyses of multiple dimensions, such as human organs and diseases. Nonetheless, we should acknowledge the significance of fate, a hidden thread that runs through all of Plato’s cosmology. Whether it is the immortal cosmos created by the demiurge or the mortal humans created by the lesser gods, both demonstrate the significance of fate. This article takes the horizon of divine providence and uses eikos logos as the argument pattern to explore characteristics of determinism contained in the hidden concept of fate in the Timaeus. We cannot ignore the crucial significance of freedom in the thought of fate. Without freedom, the demiurge cannot achieve the overall goodness of the cosmos. Full article

Ancient Near Eastern and Mediterranean cosmologies shared general assumptions about the interconnectivity of heaven and earth. Plato’s Myth of Er, the Book of the Watchers in 1 Enoch, and Cicero’s Dream of Scipio, narrate the travels of Er, Enoch, and Scipio, respectively, into the Beyond, where they each learn astonishing things about the cosmos, and are tasked with imparting a message to humanity. This comparative study argues that cosmic travel is an integral means of constructing a rhetoric of authority designed to recruit its audiences to its socio-political vision. By analysing literary conventions like pseudepigraphy and epiphany in the features that make up cosmic travel, we better understand how each story bridges the gap between the narrated (story) world and the external (real) world. The ability to blend the realities of a story and its audiences stems from the ways in which tropes of legitimacy render spatio-temporal reality malleable, but is also imperative to the very authority these tropes offer. Without arguing for deliberate intertextuality between all these sources, this study compares the use of heavenly voyages as a literary device for legitimising worldview across cultures, times, and places. Full article

In this paper, I approach Hegel’s philosophy under the banner of a “Keplerian Revolution”, the implicit reference being, of course, to Kant’s supposed Copernican philosophical revolution. Kepler had been an early supporter of the Copernican paradigm in astronomy, but went well beyond his predecessor, and so is invoked here in an attempt to capture some of the important ways in which Hegel attempted to go beyond the philosophy of Kant. To make these issues more determinate, however, Hegel’s Keplerian orientation will not be presented in its contrast to Kant’s “Copernicanism” as such, but as contrasted with that of another early follower of Copernicus, Giordano Bruno, and this Brunian orientation will be used to characterize Kant’s philosophy as seen from Hegel’s rival Keplerian point of view. Interpreting Hegel as a philosophical Keplerian will require that we broach those worrisome aspects of Kepler’s astronomy, namely his support for Plato’s cosmology and the tradition of the “music of the spheres”, but this will be shown to have connections to Hegel’s own approach to logic. This in turn will help shed light on the meaning of Hegel’s form of idealism and, in particular, on its usually unacknowledged Platonic dimensions. Full article

This paper presents a historical overview of conceptions about the Sun in Western astronomical and cosmological traditions before the advent of spectroscopy and astrophysics. Rather than studying general cultural ideas, we focus on the concepts developed by astronomers or by natural philosophers impacting astronomy. The ideas we investigate, from the works of Plato and Aristotle to William Herschel and his contemporaries, do not line up into a continuous and integrated narrative, since the nature of the Sun was not a genuine scientific topic before the nineteenth century. However, the question recurringly arose as embedded in cosmological and physical contexts. By outlining this heterogeneous story that spreads from transcendence to materiality, from metaphysics to physics, from divinity to solar inhabitants, we receive insight into some major themes and trends both in the general development of astronomical and cosmological thought and in the prehistory of modern solar science. Full article

Recently, historians have discussed the relevance of the nineteenth-century mathematical discipline of projective geometry for early modern classical logic in relation to possible solutions to semantic problems facing it. In this paper, I consider Hegel’s Science of Logic as an attempt to provide a projective geometrical alternative to the implicit Euclidean underpinnings of Aristotle’s syllogistic logic. While this proceeds via Hegel’s acceptance of the role of the three means of Pythagorean music theory in Plato’s cosmology, the relevance of this can be separated from any fanciful “music of the spheres” approach by the fact that common mathematical structures underpin both music theory and projective geometry, as suggested in the name of projective geometry’s principal invariant, the “harmonic cross-ratio”. Here, I demonstrate this common structure in terms of the phenomenon of “inverse foreshortening”. As with recent suggestions concerning the relevance of projective geometry for logic, Hegel’s modifications of Aristotle respond to semantic problems of his logic. Full article

Philosophical practice is guided by an ideal of autonomous intelligence: to think for oneself. But is a fully autonomous form of intelligence possible? Autonomy in thinking may be thought to be relative or absolute. First, one may imagine an asymptotic social process of self-ruling; in this case, to become philosophically healthy would then mean to become more virtuous and more autonomous cognitively, relative to others or to a previous version of ourselves. But there seems to be a contradiction here, as autonomy seems to imply, by definition, completeness rather than comparison or relativity, the latter being seen as a form of dependence. Hence, a second stance, absolute rather than relative: the idea that some humans can achieve a perfect state of philosophical health, implying full autonomous intelligence. This hypothesis was historically thought to imply a state of autarkia, self-divinization, or autotheosis: being divine by one’s own effort. Many have forgotten that most ancient philosophers, chief among them Epicurus, Plato, and Aristotle, thought this likeness to a god (homoiosis theoi) to be the reward of theoria, a theoretical life. I argue that we can reconcile relative and absolute cognition by understanding autonomous intelligence to be a cosmotheosis: a becoming divine not as an act of singular separation, but by welcoming the multiversal reality that we already are, and partaking in the universal creative worlding process referred to here as “Creal”. In this sense, philosophical practice calls for a pantheistic form of religiosity; a shared cosmology that compossibilizes all intercreative entities. Full article

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying principles through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation. Full article

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a–b, Plato uses Pingala’s Mātrāmeru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the point of identifying the two supreme principles of the Cosmos—the One (1) and the Indefinite Dyad (Φ and1/Φ)—with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = Φ) and the Mātrāmeru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible. Full article

Although Plato states that the perceptible god that he describes in Timaeus is visible to the human eye, the reflection of the Cosmic Soul in the heavens has largely been explained away or forgotten in the Western mind. But Roman texts, early Christian testimony, and Imperial coins illustrate that Plato’s intersection in the heavens played a major role in Hellenistic cosmology and soteriology. Full article