Philosophy and Non-Euclidean Geometry

1919 ◽  
Vol 11 (4) ◽  
pp. 196-198
Author(s):  
F. A. Foraker

Leibnitz and Descartes made remarkable contributions to both mathematics and philosophy. Newton obtains a high rank in the history of the former subject, but only a minor place in the history of philosophy, while Kant, who possessed a well-founded knowledge of the science and mathematics of his time, receives one of the foremost positions in the history of philosophy. Upon the basis of these facts, if we neglect a few of the lesser lights, the statement is often made that there is a relationship between the study of mathematics and the study of philosophy, and that he who studies one of them will also find himself a devotee in the pursuit of the other.

Author(s):  
Thomas Grundmann

What is the epistemic significance of reflecting on a discipline’s past for making progress in that discipline? The author assumes that the answer to this question negatively correlates with that discipline’s degree of progress over time. If and only if a science is progressive, then what people have thought and argued in the past in that discipline ceases to be up to date. This chapter distinguishes different dimensions of disciplinary progress and subsequently argue that veritic progress, that is, collective convergence to truth, is the most important dimension for disciplines with scientific ambitions. It then argues that, on the one hand, veritic progress in philosophy is more significant than many current philosophers believe, but that, on the other hand, it also has severe limitations. The author offers an explanation of these limitations that suggests that the history of philosophy should play some role, though only a minor one, in systematic philosophy.


Space ◽  
2020 ◽  
pp. 1-10
Author(s):  
Andrew Janiak

Space is ubiquitous. So are spatial concepts. Scholars in architecture, art history, mathematics, cosmology, ecology, neuroscience, sculpture, chemistry, and geography employ concepts of space and articulate concepts with spatial components. It would be hopeless to list them all, and equally fruitless to search for patterns among them, or for their common node. One needs a specific focal point. In our case, the history of philosophy—and the ways in which philosophers in different eras have pondered space—is our focus. We will also consider some of the myriad intersections between philosophical discussions of space and treatments in other disciplines and enterprises. Some of these intersections are obvious: philosophers and scientists in the nineteenth century were deeply influenced by and played important roles in articulating the new non-Euclidean geometry developed by mathematicians like Bolyai and Lobachevsky. The intertwining of ...


Author(s):  
Alexander V. Koltsov ◽  

The paper is an attempt to narrow down the notion of spiritual crisis which is now widely applied in research on history of culture of the 19th–20th centuries, with respect to history of German philosophy and observation of modern reli­giosity. The shift from the history of philosophy to the religious context is ful­filled through analysis of texts of two religious thinkers, A. Reinach and S. Frank, whose thought clearly demonstrates strong interconnection between the both fields. Analysis of contemporary studies on history of phenomenological philos­ophy (C. Möckel and W. Gleixner) lets firstly observe ways of application of Koselleck’s notion of crisis to investigations in the history of philosophy. Sec­ondly it discovers two possibilities of philosophical contextualization of the con­cept of spiritual crisis – on the one hand, as a constituent rhetorical element of the philosophical statement (Möckel), on the other hand, as a term which de­scribes the uniqueness of an intellectual situation of the beginning of the 20thcentury (Gleixner). Then these aspects of the rhetoric of crisis are applied to reli­gious philosophy of Reinach and Frank, what leads to interpretation of their works as a particular statement discovering the divine (or the holy) as a new cat­egory of religious consciousness.


Author(s):  
Thomas M. Lennon

Bernier was a minor figure who influenced the history of philosophy out of all proportion to his own strictly philosophical abilities. He was effective as a propagandist in the debates over the analysis of matter, and especially as a popularizer of the views of Pierre Gassendi, whose nominalism he sought to apply with greater consistency.


Author(s):  
Karin de Boer

This chapter examines Hegel’s lectures on the history of modern philosophy in view of the tension between, on the one hand, his ambition to grasp philosophy’s past in a truly philosophical way and, on the other hand, the necessity to account for the actual particularities of a wide range of philosophical systems. Hegel’s lectures are put in relief by comparing their methodological principles to those put forward by his Kantian predecessor Tennemann. After discussing Hegel’s conception of modern philosophy as a whole, the chapter turns to his reading of Locke, Leibniz, and, in particular, Kant. In this context, it also compares Hegel’s assessment of Kant’s achievements to that of Tennemann. The chapter concludes by considering Hegel’s account of the final moment of the history of philosophy.


Nature ◽  
1910 ◽  
Vol 84 (2128) ◽  
pp. 172-172
Author(s):  
D. M. Y. SOMMERVILLE

2016 ◽  
Vol 43 (136) ◽  
pp. 279
Author(s):  
Bento Silva Santos

Resumo: O artigo comenta globalmente algumas anotações da Vorlesung não proferida – “Os Fundamentos Filosóficos da Mística Medieval” (1918-1919) – na tentativa ainda fragmentária de esboçar uma compreensão fenomenológica da experiência mística. Assim, destaco, primeiramente, as duas observações iniciais de Heidegger sobre o sentido ambíguo da formulação “fundamentos filosóficos da mística medieval” ora com base na história da filosofia (1), ora com base na abordagem fenomenológica. Em segundo lugar, optando pela mística medieval como expressão (Ausdruck) da religiosidade cristã, Heidegger estabelece uma dupla distinção: de um lado, a religiosidade se distingue tanto da filosofia da religião como da teologia; de outro lado, a separação entre o problema da teologia e problema da religiosidade cristã (2). Por fim, em função desta oposição problemática entre teologia escolástica e mística medieval, trato brevemente da permanência ambígua do esquema de pensamento da teologia cristã no Denkweg de Heidegger, que pressupõe inegavelmente suas origens católicas (3).Abstract: This article broadly discusses Heidegger’s notes for his undelivered Vorlesung - “The Philosophical Foundations of Medieval Mysticism” (1918-1919) - in a still fragmentary attempt to outline a phenomenological understanding of the mystical experience. In order to do so, I first highlight the two initial observations of Heidegger concerning the meaning of the ambiguous wording “philosophical foundations of medieval mysticism”, sometimes referring to the basis of mysticism in the history of philosophy (1), sometimes to its phenomenological approach. Second, I discuss Heidegger’s option to consider medieval mystic as expression (Ausdruck) of Christian religiousness. Thus, the author establishes a double distinction: on the one hand, religiousness distinguishes itself from both the philosophy of religion and theology, and on the other hand, the problem of theology is separated from that of Christian religiousness (2). Finally, in light of this problematic opposition between scholastic theology and medieval mysticism, I briefly deal with the ambiguous persistence of the model of thinking of the Christian theology in Heidegger’s Denkweg, that unmistakably presupposes his Catholic origins (3).


2015 ◽  
Vol 3 (3) ◽  
pp. 18-23
Author(s):  
Сафиулина ◽  
Yu. Safiulina ◽  
Шмурнов ◽  
V. Shmurnov

The tragedy for the pioneers of non-Euclidean geometry (N. Lobachevsky and J. Boyai) was their quarrel with the scientific tradition. Figuratively speaking, in the judgment of the scientific world they could not provide proof of their views, and substantive law of science was not on their side despite the efforts of such an influential advocate as Karl Friedrich Gauss. They lost the civil process to the scientific layman, who sincerely believed that the earth is flat. Traditionally mathematical logic considers a new idea proven, if it is derived by inference from already proven ones, or recognized as obvious, or recognized without proof (postulates). Yet the founders of non-Euclidean geometry could not imagine such traditional evidence at all desire, because it had not yet been developed, and most importantly respective starting points (axioms, postulates, and theorems) had not been recognized by mathematicians. The paper outlines the original concept of non-Euclidean geometries. Hyperbolic geometry of Lobachevsky is considered based on viewing the sphere as a surface of zero curvature. In this case, the plane will have a real curvature properties of hyperboloid or a pseudosphere depending on the absolute and space anisotropy index, which replaces the concept of curvature of space; i.e. the notion of the curvature of the surface is converted to purely analytical attributes. Parabolic geometry of Euclid with degenerate absolute becomes a special case of geometries with non-degenerate absolute. The geometry of Riemann having the absolute of imaginary surface with negative Gaussian curvature at all points is declared not real but imaginary, since, according to the authors, it is impossible for plotting. References to textbooks of mechanics and mathematics departments of universities.


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