The Reconcilability of Non-Euclidean Geometries with Kant's Philosophy of Mathematics

Download

THE RECONCILABILITY OF NON-EUCLIDEAN GEOMETRIES WITH KANT'S PHILOSOPHY OF MATHEMATICS.pdf

Date

2021-9-27

Author

Çöteli, Can

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

347
views

344
downloads

This thesis examines Kant’s philosophy of geometry, and the possibility of reconciling non-Euclidean geometries with Kant’s philosophy of geometry. Kant believed that the propositions of Euclidean geometry are necessary and universal. In addition to that, he embraced the view that the character of space is Euclidean and he did not give any credence to the possibility of determining the character of space by using another geometrical structure. He also propounded the view that experience plays no positive role in the acquisition of geometrical knowledge. In this thesis, the views of Helmholtz, Poincaré and Reichenbach as to the positive role experience plays in the genesis of geometry are elaborately discussed. In the light of their views, it is shown that different environmental conditions have the potency to compel sentient beings like us to adopt nonEuclidean geometries. These geometries, in turn, has a proper intuitive content in contradistinction to Kant’s claim that they are only possible logically, not intuitively. Under these considerations, this thesis shows that it is not possible to reconcile Kant’s theory of geometry with non-Euclidean geometries even if undergoes appropriate modifications offered by certain philosophers such as Strawson, who tried to reduce the scope of Kant’s theory of geometry to visual space by arguing that visual space cannot be non-Euclidean. For Strawson, the propositions of Euclidean geometry are necessary and universal as was propounded by Kant, but its validity its limited to our visual space. This thesis also shows the possibility of visualizing non-Euclidean geometries by considering the views of abovementioned philosophers in contradistinction to Strawson’s arguments in support of Kant’s theory of geometry.

Subject Keywords

arı görü, görsel uzay, Öklid-dışı geometri, Poincaré, Reichenbach

URI

https://hdl.handle.net/11511/92771

Collections

Graduate School of Social Sciences, Thesis

Suggestions

OpenMETU
Core

The anarchy of justice: Hesiod’s Chaos, Anaximander’s apeiron, and geometric thought Grıffıth, James Edmond Carr (2022-04-01) This article examines Hesiod’s Chaos and Anaximander’s apeiron individually and inrelation to each other through the frame of René Descartes’ notion of natural geometry andthrough bounds and limits in Euclid and Immanuel Kant. Thanks to this frame, it shows that, inhis poetic vision, Hesiod saw in Chaos the act of bounding such that different things can appearwhile, in his speculative vision, Anaximander saw in the apeiron the self-limiting limit ofbounded things, which is to say, time as distinct from the ...
The visual formation of cartesian subject in modern metaphysics : a critique of Cogito philosophy Ganioğlu, Zafer; Akçay, Ali Adnan; Department of Sociology (2006) This thesis scrutinizes modern metaphysics through a specific reading and critique of Cartesian Philosophy. In the study, the concepts of metaphysics, ideology, modernity, subject and modern science are re-examined in their relations among them and in that the peculiarity of modern metaphysics is attempted to be revealed. At the core of the thesis, Descartes’ understanding of subject is inquired to be modern subject, and its role in the transformations happened in Western world with the advent of modern age...
The formation of the self as mental unity and moral agency in hume’s philosophy Neslioğlu, E. Funda; Grünberg, David; Department of Philosophy (2008) This dissertation proposes to analyze the stages in the formation of the idea of self in Hume’s philosophy. According to Hume we have no a simple and individual impression that we can call the self where the self is the totality of conscious life of a person. Nevertheless, we do have an idea of personal identity that must be accounted for. He begins his explanation of this idea by noting that our perceptions are fleeting, and he concludes from this that all we are is a bundle of different perceptions. But ...
THE ONTOLOGY OF CAPITAL: ON THE SHARED METHODOLOGICAL LIMITS OF MODERNIZATION THEORY AND ITS CRITICS Mücen, Barış (2018-06-01) This article argues that critical scholarship in historical studies has not overcome the methodological limits of modernization theory for failing to question the ontological principles that construct its object of analysis. I call these principles the ontology of capital and explicate them through Bourdieu's conceptualization of the field and capital. I argue that this ontology is established according to a distribution model in which social entities come into the analysis with the amount and value of the ...
THE CONCEPT OF AKRASIA IN ANCIENT GREEK PHILOSOPHY: PLATO, ARISTOTLE, AND THE STOICS Akkökler Karatekeli, Büşra; Turan, Şeref Halil; Department of Philosophy (2022-9) This thesis investigates the concept of akrasia, with particular attention given to its sundry interpretations in the philosophies of Plato, Aristotle, and the Stoics. In this inquiry, I argue that these philosophers agree on the lack of knowledge of the akratic person, while they differentiate from each other as to what this missing knowledge is. Irrespective of their rejection or acknowledgement of akrasia due to their conceptions of the soul, I argue that Plato, Aristotle and the Stoics share the common ...

Citation Formats

C. Çöteli, “The Reconcilability of Non-Euclidean Geometries with Kant’s Philosophy of Mathematics,” M.S. - Master of Science, Middle East Technical University, 2021.