Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics
This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intui...
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| Format: | Electronic eBook |
| Language: | English |
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Cham :
Springer International Publishing : Imprint: Springer,
2023.
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| Edition: | 1st ed. 2023. |
| Series: | Mathematics in Mind,
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| Subjects: | |
| Online Access: | https://doi.org/10.1007/978-3-031-23245-9 |
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| 100 | 1 | |a Kiryushchenko, Vitaly. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Diagrams, Visual Imagination, and Continuity in Peirce's Philosophy of Mathematics |h [electronic resource] / |c by Vitaly Kiryushchenko. |
| 250 | |a 1st ed. 2023. | ||
| 264 | 1 | |a Cham : |b Springer International Publishing : |b Imprint: Springer, |c 2023. | |
| 300 | |a X, 172 p. 1 illus. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
| 341 | 0 | |b Use of color is not sole means of conveying information |2 onix | |
| 341 | 0 | |b Use of high contrast between text and background color |2 onix | |
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| 341 | 0 | |b All non-decorative content supports reading without sight |2 onix | |
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| 490 | 1 | |a Mathematics in Mind, |x 2522-5413 | |
| 505 | 0 | |a 1. Introduction -- 2. Meritocratism, Errors, and the Community of Inquiry -- 3. Logic and Mathematics -- 4. Peirce's Transcendental Deduction -- 5. Sign Relation. - 6 One, Two, Three -- 7. Iconicity and Novelty -- 8. The General and the Particular -- 9. Diagrams Between Images and Schema -- 10. Existential Graphs -- 11. Iconicity, Similarity, and Habitual Action -- 12. Mapping Philosophy -- 13. L'Image-Mouvement, Mathematically Sublime, and the Perception of Totality -- 14. The Metaphysics of Continuity -- 15. Conclusion. . | |
| 520 | |a This book is about the relationship between necessary reasoning and visual experience in Charles S. Peirce’s mathematical philosophy. It presents mathematics as a science that presupposes a special imaginative connection between our responsiveness to reasons and our most fundamental perceptual intuitions about space and time. Central to this view on the nature of mathematics is Peirce’s idea of diagrammatic reasoning. In practicing this kind of reasoning, one treats diagrams not simply as external auxiliary tools, but rather as immediate visualizations of the very process of the reasoning itself. Thus conceived, one's capacity to diagram their thought reveals a set of characteristics common to ordinary language, visual perception, and necessary mathematical reasoning. The book offers an original synthetic approach that allows tracing the roots of Peirce’s conception of a diagram in certain patterns of interrelation between his semiotics, his pragmaticist philosophy, his logical and mathematical ideas, bits and pieces of his biography, his personal intellectual predispositions, and his scientific practice as an applied mathematician. | ||
| 532 | 8 | |a Accessibility summary: This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 650 | 0 | |a Mathematical logic. | |
| 650 | 0 | |a Mathematics |x Study and teaching . | |
| 650 | 0 | |a Mathematics |x Philosophy. | |
| 650 | 1 | 4 | |a Mathematical Logic and Foundations. |
| 650 | 2 | 4 | |a Mathematics Education. |
| 650 | 2 | 4 | |a Philosophy of Mathematics. |
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| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783031232442 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031232466 |
| 776 | 0 | 8 | |i Printed edition: |z 9783031232473 |
| 830 | 0 | |a Mathematics in Mind, |x 2522-5413 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-031-23245-9 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||