A metaphysical foundation for mathematical philosophy

Wójtowicz, Krzysztof; Skowron, Bartłomiej

doi:10.1007/s11229-022-03760-5

Cited by 3 publications

(3 citation statements)

References 66 publications

(32 reference statements)

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“…(Metaphorically speaking, such structures are, we think, something from which philosophical thinking can be struck or shaped, much as model figures are from stone or clay.) Mathematics, then, on our account not only provides a language for use in science and philosophy but also constitutes an invaluable source , thanks to its models, structures, and so forth (Wójtowicz and Skowron 2022).…”

Section: Introductionmentioning

confidence: 99%

“…There are various ways in which one might argue that it is hardly surprising that mathematics works so well in philosophy. Most notably, given a strong metaphysical assumption to the effect that there are ideas similar to those introduced by Plato, it can be argued that there is some overlap between mathematical and philosophical ideas(Wójtowicz and Skowron 2022), and that it is because of this substantial similarity at the level of ideas that mathematics fits so well into philosophical considerations.…”

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confidence: 99%

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Towards a topological philosophy

Skowron,

Kaczmarek,

Wójtowicz

2023

Metaphilosophy

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This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Towards a topological philosophy

Skowron,

Kaczmarek,

Wójtowicz

2023

Metaphilosophy

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“…What the reader may wish to see, however, is more of the author's synthesis for the presented ideas, expanded beyond "Towards general topology of object and its parts" in section 7. One may also follow up on Skowron's ideas in his recently published paper 'A metaphysical foundation for mathematical philosophy" (Wójtowicz and Skowron, 2022).…”

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confidence: 99%

Introduction to topo-philosophy

Krzanowski

2023

ZFN

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In philosophy, it is always refreshing to introduce unconventional ideas. It requires a certain audacity from the author; he or she may face the wall of silence or be shunned by academia, both treatments being undesirable. However, these are more rewarding than gathering laurels for beating the dead philosophical cats like Humes, Leibnitzs, Wittgensteins, Whiteheads, and others, a practice that for many philosophers is their life's opus. Bartłomiej Skowron’s book Part and Whole: Towards Topo-Ontology, published by Oficyna Wydawnicza Politechniki Warszawskiej in 2021, certainly does not fall into this category. Skowron undertakes a discovery trip into an unknown land in his book, exploring new philosophical territories.

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The topology of persons, and surviving to some degree

Skowron,

Kąkol,

Król

2023

Synthese

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Braddon-Mitchell and Miller put forward the claim that the relation of being-the-same-person is gradable: a person can be the same person tomorrow as today, but only half the same. To justify their thesis, they propose a model of persons that is intended to be metaphysically neutral. This article sets out to show that such a model implicitly contains strong metaphysical assumptions that run contrary to the authors’ own statements. Using Roman Ingarden’s phenomenological ontology, we aim to demonstrate that within the model in question persons exist intentionally, where this leads to a caricature rather than an adequate account of persons. In opposition to Braddon-Mitchell and Miller, we argue that the justification presented for the thesis of the gradability of the relation of being-the-same-person in fact makes it reasonable to demand that an adequate model of persons be posited. We present Kurt Lewin’s holistic topological-dynamic model, and show that in this context it is not being-the-same-person that is gradable, but rather the characteristic (of persons) that is dimension. Thus, we reject the thesis of the gradability of the relation of being-the-same-person involved in personal identity.

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A metaphysical foundation for mathematical philosophy

Cited by 3 publications

References 66 publications

Towards a topological philosophy

Towards a topological philosophy

Introduction to topo-philosophy

The topology of persons, and surviving to some degree

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