How Language Informs Mathematics : Bridging Hegelian Dialectics and Marxian Models.

Intro -- How Language Informs Mathematics: Bridging Hegelian Dialectics and Marxian Models -- Copyright -- Contents -- List of Figures and Tables -- Acknowledgements -- Brief Contents -- Note on the Style of Referencing and the Use of Capitalisation and Emphasis in this Work -- List of Symbols -- Introduction -- 1 On Marx's and Hegel's Dialectical Methods -- Introduction -- 1 The Chronology of Hegel's and Marx's Historical and Systematic Dialectic -- 2 Hegel's Method -- 3 Marx's Comments on Hegel, Their Implications, and Marx's Twist on Hegel's Dialectical Method -- 4 Commentators on and Studies of Marx's Dialectics -- Summary and Conclusions -- Preview -- 2 The Dialectical Foundations of Mathematics -- Introduction -- 1 Previous Literature on Hegel and Mathematics -- 2 Hegel's Determination of the Quantitative -- A Quality -- 2.1 Being -- 2.2 Nothing -- 2.3 Becoming -- 2.4 Presence -- 2.5 Something and Other -- 2.6 One and Many Ones -- 2.7 Attraction and Repulsion -- B Quantity -- 2.8 Quantity -- 2.9 Continuous and Discrete Magnitude -- 2.10 Quantum and Number72 -- 2.11 Unit and Amount -- 2.12 Limit -- 2.13 Intensive and Extensive Magnitude -- C Measure -- 2.14 Measure -- 3 Hegel's Determination of Mathematical Mechanics -- A Space and Time -- 3.1 Space -- 3.2 Spatial Dimensions -- 3.3 The Point -- 3.4 The Line -- 3.5 The Plane -- 3.6 Distinct Space -- 3.7 Time -- 3.8 Temporal Dimensions -- 3.9 Now -- 3.10 Place -- 3.11 Motion -- 3.12 Matter -- Summary and Conclusions How This Dialectic Reflects on Mathematics -- Appendix Comparison of the Determination of the Quantitative in the Wissenschaft and the Encyclopädie -- A1 Being, Nothing, Becoming, Presence, Something and Others -- A2 Qualitative Limit -- A3 Finitude and Infinity -- A4 True Infinite -- A5 Being-for-self.

A6 One, Many Ones, Repulsion, Attraction, Quantity, Continuous and Discrete Magnitude, Quantum, Number, Unit and Amount, Quantitative Limit and Intensive and Extensive Magnitude -- A7 Quantitative Infinity -- A8 Direct Ratio -- A9 Inverse Ratio -- A10 Ratio of Powers -- A11 Measure -- Concluding Remarks -- 3 Marx's Systematic Dialectics and Mathematics -- Introduction -- 1 Marx's Acquaintance with and Ideas on Mathematics -- 2 Marx's Exhibition of Capitalism as a System The Systematic-Dialectical Position -- 3 The Role of Mathematics in Marx's Investigation and Exhibition in Capital the Case of Marx's "Schemes of Reproduction -- Summary and Conclusions on the Role of Mathematics in Systematic-Dialectical Investigation and Exhibition -- 4 A Formal Dynamic Reconstruction of Marx's Schemes of Reproduction along Dialectical Lines -- Introduction -- 1 The Model for Simple Reproduction -- 2 Extensive Growth of Total Social Capital -- 3 The Model for Expanded Reproduction -- Summary and Conclusions -- Appendix Derivations -- A1 Accumulation and Growth Rate for Department c as a Function of Accumulation and Growth in Department p with Extensive Growth (expressions 4.15 and 4.16) -- A2 Constant Capital's Growth Rate for Department c for the Case of Expanded Reproduction (expression 4.19) -- A3 The Condition for Constant Rates of Accumulation in Case of Expanded Reproduction (expression 4.20) -- Summary and General Conclusions -- References -- Author Index -- Subject Index.

In How Language Informs Mathematics Dirk Damsma shows how Hegel's and Marx's dialectics allow us to understand the structure and nature of mathematical and capitalist systems. Knowledge of such systems allows for an innovative approach to economic modelling.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.