Lie, Nga Sze. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 103-111). / Abstracts in English and Chinese. / Abstract --- p.i / Chapter 1 --- Introduction and Preliminary Discussions --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Overview of the Thesis --- p.2 / Chapter 1.1.2 --- Background --- p.3 / Chapter 1.1.3 --- About Chapter 3: Details of the Theory --- p.4 / Chapter 1.1.4 --- About Chapter 4: Defects of the Theory --- p.7 / Chapter 1.2 --- Preliminary Discussions --- p.12 / Chapter 1.2.1 --- number --- p.12 / Chapter 1.2.2 --- mathematical existence and abstract reality --- p.12 / Chapter 1.2.3 --- finite/infinite --- p.12 / Chapter 1.2.4 --- actually/potentially infinite --- p.13 / Chapter 1.2.5 --- denumerability --- p.13 / Chapter 1.3 --- Concluding Remarks --- p.14 / Chapter 2 --- Mapping Mathematical Philosophies --- p.15 / Chapter 2.1 --- Preview --- p.15 / Chapter 2.1.1 --- Nominalism --- p.16 / Chapter 2.1.2 --- Conceptualism --- p.16 / Chapter 2.1.3 --- Intuitionism --- p.17 / Chapter 2.1.4 --- Realism --- p.18 / Chapter 2.1.5 --- Empiricism --- p.19 / Chapter 2.1.6 --- Logicism --- p.19 / Chapter 2.1.7 --- Neo-logicism --- p.21 / Chapter 2.1.8 --- Formalism --- p.21 / Chapter 2.1.9 --- Practicism --- p.23 / Chapter 2.2 --- Central Problem of Philosophy of Mathematics --- p.23 / Chapter 2.3 --- Metaphysics --- p.24 / Chapter 2.3.1 --- Abstractism --- p.24 / Chapter 2.3.2 --- Abstractist Schools --- p.25 / Chapter 2.3.3 --- Non-abstractism --- p.25 / Chapter 2.3.4 --- Non-abstractist Schools --- p.26 / Chapter 2.4 --- Semantics --- p.26 / Chapter 2.4.1 --- Literalism --- p.26 / Chapter 2.4.2 --- Literalistic schools --- p.27 / Chapter 2.4.3 --- Non-literalism --- p.27 / Chapter 2.4.4 --- Non-literalistic schools --- p.27 / Chapter 2.5 --- Epistemology --- p.28 / Chapter 2.5.1 --- Scepticism --- p.28 / Chapter 2.5.2 --- Scepticist Schools --- p.28 / Chapter 2.5.3 --- Non-scepticism --- p.29 / Chapter 2.5.4 --- Non-scepticist Schools --- p.29 / Chapter 2.6 --- Foundations of Mathematics --- p.30 / Chapter 2.6.1 --- Foundationalism --- p.31 / Chapter 2.6.2 --- Foundationalist Schools --- p.32 / Chapter 2.6.3 --- N on-foundationalism --- p.33 / Chapter 2.6.4 --- Non-foundationalist schools --- p.33 / Chapter 2.7 --- Finitistic Considerations --- p.33 / Chapter 2.7.1 --- Finitism --- p.41 / Chapter 2.7.2 --- Finitist Schools --- p.42 / Chapter 2.7.3 --- Non-finitism --- p.44 / Chapter 2.7.4 --- Non-finitist Schools --- p.44 / Chapter 2.8 --- Finitistic Reconsiderations --- p.44 / Chapter 2.8.1 --- C-finitism --- p.45 / Chapter 2.8.2 --- C-finitist Schools --- p.45 / Chapter 2.8.3 --- Non-C-finitism --- p.46 / Chapter 2.8.4 --- Non-C-finitist Schools --- p.46 / Chapter 2.9 --- Concluding Remarks --- p.47 / Chapter 3 --- Principles of Transfinite Theory --- p.48 / Chapter 3.0.1 --- Historical Notes on Infinity --- p.48 / Chapter 3.0.2 --- Cantor´ةs Proof --- p.49 / Chapter 3.1 --- The Domain Principle --- p.51 / Chapter 3.1.1 --- Variables and Domain --- p.53 / Chapter 3.1.2 --- Attack and Defense --- p.54 / Chapter 3.2 --- The Enumeral Principle --- p.56 / Chapter 3.2.1 --- Cantor´ةs Ordinal Theory of Numbers --- p.58 / Chapter 3.2.2 --- A Well-ordered Set --- p.59 / Chapter 3.2.3 --- An Enumeral --- p.59 / Chapter 3.2.4 --- An Ordinal Number --- p.60 / Chapter 3.2.5 --- Attack and Defense --- p.60 / Chapter 3.3 --- The Abstraction Principle --- p.63 / Chapter 3.3.1 --- Cantor´ةs Cardinal Theory of Numbers --- p.64 / Chapter 3.3.2 --- An Abstract One --- p.65 / Chapter 3.3.3 --- One-one Correspondence --- p.65 / Chapter 3.3.4 --- A Cardinal Number --- p.65 / Chapter 3.3.5 --- Attack and Defense --- p.65 / Chapter 3.4 --- Concluding Remarks --- p.68 / Chapter 4 --- Problems in Transfinite Theory --- p.70 / Chapter 4.1 --- Structure and Procedure --- p.70 / Chapter 4.1.1 --- Free Mathematics --- p.72 / Chapter 4.1.2 --- Non-constructive Proof --- p.75 / Chapter 4.2 --- Number and Numerosity --- p.85 / Chapter 4.2.1 --- Weak Reductionism --- p.85 / Chapter 4.2.2 --- Non-Cantorian Sets --- p.87 / Chapter 4.2.3 --- Intension in an Extensional Theory --- p.89 / Chapter 4.3 --- Conceivability and Comparability --- p.95 / Chapter 4.3.1 --- Tension with Absolute Infinity --- p.95 / Chapter 4.4 --- Conclusion --- p.100 / Bibliography --- p.103
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326324 |
| Date | January 2008 |
| Contributors | Lie, Nga Sze., Chinese University of Hong Kong Graduate School. Division of Philosophy. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, v, 111 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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