{"product_id":"how-language-informs-mathematics-bridging-hegelian-dialectics-and-marxian-models-9789004337305","title":"How Language Informs Mathematics: Bridging Hegelian Dialectics and Marxian Models","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eIn How Language Informs Mathematics Dirk Damsma shows how Hegel’s and Marx’s systematic dialectical analysis of mathematical and economic language helps us understand the structure and nature of mathematical and capitalist systems. More importantly, Damsma shows how knowledge of the latter can inform model assumptions and help improve models.    His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003eList of Figure 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 Number   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   2.1 Sociation   2.2 Dissociation   2.3 Association: The Exchange Relation   2.4 The Commodity, Exchangeability and the Bargain   2.5 Value in Exchange   2.6 The Simple, Expanded and General Commodity Form and the Money Form of Value   2.7 Money as Measure of Value, Means of Circulation and End of Exchange   2.8 Capital   2.9 Constant and Variable Capital   2.10 Accumulation   2.11 The Money Capital, Production Capital and Commodity Capital Circuits   2.12 Fixed and Circulating Capital   2.13 Simple Reproduction, Means of Production, Consumption Goods, Total Social Capital and Expanded Reproduction   2.14 General Rate of Profit, Many Capitals, Competition and Minimum Prices of Production   3 The Role of Mathematics in Marx’s Investigation and Exhibition in Capital: the Case of Marx’s “Schemes of Reproduction”   3.1 Simple Reproduction    3.1.1 The Model    3.1.2 Conclusions   3.2 Expanded Reproduction    3.2.1 The Model    3.2.2 Conclusions   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 (expression 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","brand":"Brill","offers":[{"title":"Default Title","offer_id":53210698973527,"sku":"9789004337305","price":131.2,"currency_code":"GBP","in_stock":false}],"url":"https:\/\/bookcurl.com\/products\/how-language-informs-mathematics-bridging-hegelian-dialectics-and-marxian-models-9789004337305","provider":"Book Curl","version":"1.0","type":"link"}