A course of philosophy and mathematics :: toward a general theory of reality /
"The nature of this book is fourfold: First, it provides comprehensive education in ontology, epistemology, logic, and ethics. From this perspective, it can be treated as a philosophical textbook. Second, it provides comprehensive education in mathematical analysis and analytic geometry, includ...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York :
Nova Science Publishers,
[2021]
|
| Schriftenreihe: | Mathematics research developments series.
World philosophy series. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "The nature of this book is fourfold: First, it provides comprehensive education in ontology, epistemology, logic, and ethics. From this perspective, it can be treated as a philosophical textbook. Second, it provides comprehensive education in mathematical analysis and analytic geometry, including significant aspects of set theory, topology, mathematical logic, number systems, abstract algebra, linear algebra, and the theory of differential equations. From this perspective, it can be treated as a mathematical textbook. Third, it makes a student and a researcher in philosophy and/or mathematics capable of developing a holistic approach to reality, of undertaking interdisciplinary endeavors, of understanding (and possibly contributing to) advances and research projects in different academic disciplines, and of having more sources of inspiration and pleasure. From this perspective, it can be treated as a contribution to pedagogy and as an attempt to refresh and, indeed, revitalize modern philosophy. Fourth, it seeks to defend, refresh, and enrich philosophical and scientific structuralism and dynamical philosophy (known also as dynamism). From this perspective, this book can be treated as a research monograph on structuralism and dynamism, tackling the fundamental problems of reality, truth, and consciousness. In this context, Nicolas Laos expounds and proposes: (i) the concepts of dynamized time and dynamized space; (ii) a theory and method that he calls the "dialectic of rational dynamicity"; and (iii) his attempt to consider the fundamental problems of philosophy and science from the perspective of the dialectic of rational dynamicity. Thus, this book pertains to every field that is controlled by the function of consciousness, namely, being, knowing, and acting. The philosophy of rational dynamicity, as the author explains in this book, is a way of contemplating the laws of motion of nature, history, and spirit"-- |
| Beschreibung: | 1 online resource (xiv, 492 pages) : illustrations. |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 1536196185 9781536196184 |
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| 245 | 1 | 2 | |a A course of philosophy and mathematics : |b toward a general theory of reality / |c Nicolas Laos. |
| 264 | 1 | |a New York : |b Nova Science Publishers, |c [2021] | |
| 300 | |a 1 online resource (xiv, 492 pages) : |b illustrations. | ||
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| 490 | 1 | |a Mathematics research developments | |
| 490 | 1 | |a World philosophy | |
| 504 | |a Includes bibliographical references and index. | ||
| 520 | |a "The nature of this book is fourfold: First, it provides comprehensive education in ontology, epistemology, logic, and ethics. From this perspective, it can be treated as a philosophical textbook. Second, it provides comprehensive education in mathematical analysis and analytic geometry, including significant aspects of set theory, topology, mathematical logic, number systems, abstract algebra, linear algebra, and the theory of differential equations. From this perspective, it can be treated as a mathematical textbook. Third, it makes a student and a researcher in philosophy and/or mathematics capable of developing a holistic approach to reality, of undertaking interdisciplinary endeavors, of understanding (and possibly contributing to) advances and research projects in different academic disciplines, and of having more sources of inspiration and pleasure. From this perspective, it can be treated as a contribution to pedagogy and as an attempt to refresh and, indeed, revitalize modern philosophy. Fourth, it seeks to defend, refresh, and enrich philosophical and scientific structuralism and dynamical philosophy (known also as dynamism). From this perspective, this book can be treated as a research monograph on structuralism and dynamism, tackling the fundamental problems of reality, truth, and consciousness. In this context, Nicolas Laos expounds and proposes: (i) the concepts of dynamized time and dynamized space; (ii) a theory and method that he calls the "dialectic of rational dynamicity"; and (iii) his attempt to consider the fundamental problems of philosophy and science from the perspective of the dialectic of rational dynamicity. Thus, this book pertains to every field that is controlled by the function of consciousness, namely, being, knowing, and acting. The philosophy of rational dynamicity, as the author explains in this book, is a way of contemplating the laws of motion of nature, history, and spirit"-- |c Provided by publisher. | ||
| 588 | |a Description based on online resource; title from digital title page (viewed on June 21, 2021). | ||
| 505 | 0 | |a Intro -- Contents -- Prolegomena by Giuliano di Bernardo -- Preface -- The Scope and the Structure of this Project -- Acknowledgments -- Chapter 1 -- Philosophy, Science, and The Dialectic of Rational Dynamicity -- 1.1. The Meaning of Philosophy and Preliminary Concepts -- 1.2. The Abstract Study of a Being -- 1.2.1. Epistemological Presuppositions -- 1.2.2. The Significance and the Presence of a Being -- 1.2.3. The Knowledge of a Being -- Structuralism in Physics -- Newton's Three Laws of Kinematics -- Newton's Law of Universal Gravitation -- Conservation of Mass and Energy -- Laws of Thermodynamics -- Electrostatic Laws -- Quantum Mechanics -- Structuralism in Biology -- Structuralism in Linguistics -- Philosophical Structuralism and Hermeneutics -- 1.2.4. The Modes of Being -- 1.3. The Dialectic of Rational Dynamicity -- 1.3.1. Dynamized Time -- 1.3.2. Dynamized Space and the Problem of the Extension of the Quantum Formalism -- 1.3.3. Consciousness, the World, and the Dialectic of Rational Dynamicity -- 1.3.4. Matter, Life, and Consciousness -- Chapter 2 -- Foundations of Mathematical Analysis and Analytic Geometry -- 2.1. Sets, Relations, and Groups -- 2.1.2. Basic Operations on Sets -- Applications of Set Theory to Probability Theory -- 2.1.3. Relations -- 2.1.4. Groups -- 2.2. Number Systems, Algebra, and Geometry -- 2.2.1. Axiomatic Number Theory -- The System of Natural Numbers -- Principle of Mathematical Induction -- Recursion -- Properties of the System of Natural Numbers -- Enumeration -- Order in ℕ and Ordinal Numbers -- Division -- 2.2.2. The Set of Integral Numbers -- 2.2.3. The Set of Rational Numbers -- 2.2.4. The Set of Real Numbers -- Dedekind Algebra -- ℝ as a Field -- The Absolute Value of a Real Number -- Exponentiation and Logarithm -- Properties of the System of the Real Numbers. | |
| 505 | 8 | |a 2.2.5. Matrices of Real Numbers and Vectors -- Vectors -- Some Applications of Matrices -- Input-Output Analysis -- Linear Programming -- Game Theory -- 2.2.6. Analytic Geometry and the Abstract Concept of a Distance -- Circle -- Trigonometric Functions -- Ellipse -- Hyperbola -- Parabola -- Analytic Geometry of Space -- The Abstract Concept of a Distance -- 2.3. Topology of Real Numbers -- 2.3.1. Neighborhoods -- 2.3.2. Open Sets -- 2.3.3. Nested Intervals and Cantor's Intersection Theorem -- 2.3.4. Closure Points and Accumulation Points -- 2.3.5. Closed Sets -- 2.3.6. Compactness -- 2.3.7. Relative Topology and Connectedness -- 2.4. Sequences of Real Numbers -- Limit and Convergence of a Sequence -- Cauchy Sequences and the Completeness of the Real Field -- Subsequences -- Monotonic Sequences -- Hilbert Space -- Alphabets and Languages -- 2.5. Infinite Series and Infinite Products -- 2.6. The Limit of a Function -- Preliminary Concepts -- The Limit of a Function -- 2.7. Continuous Functions -- Types of Discontinuity -- 2.8. Complex Numbers -- 2.9. The Birth and the Development of Infinitesimal Calculus -- 2.10. Differential Calculus -- 2.10.1. Derivative -- Drawing a Tangent Line to the Graph of a Function -- The Formal Definition of the Derivative of a Function -- Higher Order Derivatives -- Table of the Derivatives of Elementary Functions -- The Differential of a Function -- A Note about Complex Derivatives -- 2.10.2. The Basic Theorems of Differential Calculus -- 2.10.3. Monotonicity, Critical Points, and Extreme Points of a Function -- 2.10.4. Concave-Up and Concave-Down Functions -- 2.10.5. Asymptotes of a Function -- 2.10.6. Steps for Function Investigation and Curve Sketching -- 2.10.7. Curvature and Radius of Curvature -- 2.10.8. Differentiation of Multivariable Functions. | |
| 505 | 8 | |a Differentiation of Composite Functions, Harmonic Functions, and Homogeneous Functions -- Differentiation of Implicit Functions -- Jacobian (or Functional) Determinant -- Mean Value Theorems -- 2.11. Integral Calculus -- The Definition of the Integral as the Limit of a Sum -- The Physical Significance of the Integral -- Integration of Complex Functions of One Variable -- 2.12. Standard Integration Techniques -- Integration by Substitution -- Integration by Parts -- 2.13. Reduction Formulas -- 2.14. Integration of Rational Functions -- 2.15. Integration of Irrational Functions -- 2.16. Integration of Trigonometric Functions -- 2.17. Integration of Hyperbolic Functions -- 2.18. The Theory of Riemann Integration -- The Riemann Integral -- Criteria of Integrability and Methods of Integration -- Properties of Riemann Integrable Functions -- The Equivalence of the Definitions of the Integral of a Function -- Generalized Integrals -- Riemann Integrability and Sets of Measure Zero -- The Mean Value Theorems of Integral Calculus and the Fundamental Theorem of Infinitesimal Calculus -- 2.19. Numerical Integration -- 2.20. Applications of Integration and Basic Principles of Differential Equations -- 2.20.1. The Calculation of Areas Using Integrals -- 2.20.2. The Calculation of the Area between two Arbitrary Curves -- 2.20.3. The Calculation of the Volume of a Solid of Revolution -- 2.20.4. The Arc Length of a Curve -- 2.20.5. Work -- 2.20.6. Some Basic Applications of Integral Calculus to Economics -- 2.20.7. A Social Utility Model and Optimal Control -- 2.20.8. Integration and Ordinary Differential Equations -- 2.21. Integration of Multivariable Functions -- 2.22. Vector-Valued Functions -- Chapter 3 -- Logic, Epistemology, and the Problem of Truth -- 3.1. Basic Principles of Logic -- 3.2. Predicate Calculus -- 3.3. Axiomatic Model Theory. | |
| 505 | 8 | |a 3.4. Common Sense, Non-Monotonic Logic, and Many-Valued Logic -- 3.5. Crises in the Foundations of Mathematics and Mathematical Philosophy -- 3.5.1. The First Crisis in the Foundations of Mathematics -- 3.5.2. The Second Crisis in the Foundations of Mathematics -- 3.5.3. Logicism -- 3.5.4. Axiomatic Set Theory and Category Theory -- 3.5.5. Intuitionism -- 3.5.6. Formalism -- 3.5.7. Conclusions -- 3.6. The Problem of Empirical Relevance in the Context of Science -- 3.7. Truth as a Discovery and Truth as an Invention -- 3.8. Degrees of Truth -- 3.9. From Logical Values to Moral Values: Ethics and Social Theory from the Perspective of Rational Dynamicity -- References -- About the Author -- Index -- Blank Page -- Blank Page. | |
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| contents | Intro -- Contents -- Prolegomena by Giuliano di Bernardo -- Preface -- The Scope and the Structure of this Project -- Acknowledgments -- Chapter 1 -- Philosophy, Science, and The Dialectic of Rational Dynamicity -- 1.1. The Meaning of Philosophy and Preliminary Concepts -- 1.2. The Abstract Study of a Being -- 1.2.1. Epistemological Presuppositions -- 1.2.2. The Significance and the Presence of a Being -- 1.2.3. The Knowledge of a Being -- Structuralism in Physics -- Newton's Three Laws of Kinematics -- Newton's Law of Universal Gravitation -- Conservation of Mass and Energy -- Laws of Thermodynamics -- Electrostatic Laws -- Quantum Mechanics -- Structuralism in Biology -- Structuralism in Linguistics -- Philosophical Structuralism and Hermeneutics -- 1.2.4. The Modes of Being -- 1.3. The Dialectic of Rational Dynamicity -- 1.3.1. Dynamized Time -- 1.3.2. Dynamized Space and the Problem of the Extension of the Quantum Formalism -- 1.3.3. Consciousness, the World, and the Dialectic of Rational Dynamicity -- 1.3.4. Matter, Life, and Consciousness -- Chapter 2 -- Foundations of Mathematical Analysis and Analytic Geometry -- 2.1. Sets, Relations, and Groups -- 2.1.2. Basic Operations on Sets -- Applications of Set Theory to Probability Theory -- 2.1.3. Relations -- 2.1.4. Groups -- 2.2. Number Systems, Algebra, and Geometry -- 2.2.1. Axiomatic Number Theory -- The System of Natural Numbers -- Principle of Mathematical Induction -- Recursion -- Properties of the System of Natural Numbers -- Enumeration -- Order in ℕ and Ordinal Numbers -- Division -- 2.2.2. The Set of Integral Numbers -- 2.2.3. The Set of Rational Numbers -- 2.2.4. The Set of Real Numbers -- Dedekind Algebra -- ℝ as a Field -- The Absolute Value of a Real Number -- Exponentiation and Logarithm -- Properties of the System of the Real Numbers. 2.2.5. Matrices of Real Numbers and Vectors -- Vectors -- Some Applications of Matrices -- Input-Output Analysis -- Linear Programming -- Game Theory -- 2.2.6. Analytic Geometry and the Abstract Concept of a Distance -- Circle -- Trigonometric Functions -- Ellipse -- Hyperbola -- Parabola -- Analytic Geometry of Space -- The Abstract Concept of a Distance -- 2.3. Topology of Real Numbers -- 2.3.1. Neighborhoods -- 2.3.2. Open Sets -- 2.3.3. Nested Intervals and Cantor's Intersection Theorem -- 2.3.4. Closure Points and Accumulation Points -- 2.3.5. Closed Sets -- 2.3.6. Compactness -- 2.3.7. Relative Topology and Connectedness -- 2.4. Sequences of Real Numbers -- Limit and Convergence of a Sequence -- Cauchy Sequences and the Completeness of the Real Field -- Subsequences -- Monotonic Sequences -- Hilbert Space -- Alphabets and Languages -- 2.5. Infinite Series and Infinite Products -- 2.6. The Limit of a Function -- Preliminary Concepts -- The Limit of a Function -- 2.7. Continuous Functions -- Types of Discontinuity -- 2.8. Complex Numbers -- 2.9. The Birth and the Development of Infinitesimal Calculus -- 2.10. Differential Calculus -- 2.10.1. Derivative -- Drawing a Tangent Line to the Graph of a Function -- The Formal Definition of the Derivative of a Function -- Higher Order Derivatives -- Table of the Derivatives of Elementary Functions -- The Differential of a Function -- A Note about Complex Derivatives -- 2.10.2. The Basic Theorems of Differential Calculus -- 2.10.3. Monotonicity, Critical Points, and Extreme Points of a Function -- 2.10.4. Concave-Up and Concave-Down Functions -- 2.10.5. Asymptotes of a Function -- 2.10.6. Steps for Function Investigation and Curve Sketching -- 2.10.7. Curvature and Radius of Curvature -- 2.10.8. Differentiation of Multivariable Functions. Differentiation of Composite Functions, Harmonic Functions, and Homogeneous Functions -- Differentiation of Implicit Functions -- Jacobian (or Functional) Determinant -- Mean Value Theorems -- 2.11. Integral Calculus -- The Definition of the Integral as the Limit of a Sum -- The Physical Significance of the Integral -- Integration of Complex Functions of One Variable -- 2.12. Standard Integration Techniques -- Integration by Substitution -- Integration by Parts -- 2.13. Reduction Formulas -- 2.14. Integration of Rational Functions -- 2.15. Integration of Irrational Functions -- 2.16. Integration of Trigonometric Functions -- 2.17. Integration of Hyperbolic Functions -- 2.18. The Theory of Riemann Integration -- The Riemann Integral -- Criteria of Integrability and Methods of Integration -- Properties of Riemann Integrable Functions -- The Equivalence of the Definitions of the Integral of a Function -- Generalized Integrals -- Riemann Integrability and Sets of Measure Zero -- The Mean Value Theorems of Integral Calculus and the Fundamental Theorem of Infinitesimal Calculus -- 2.19. Numerical Integration -- 2.20. Applications of Integration and Basic Principles of Differential Equations -- 2.20.1. The Calculation of Areas Using Integrals -- 2.20.2. The Calculation of the Area between two Arbitrary Curves -- 2.20.3. The Calculation of the Volume of a Solid of Revolution -- 2.20.4. The Arc Length of a Curve -- 2.20.5. Work -- 2.20.6. Some Basic Applications of Integral Calculus to Economics -- 2.20.7. A Social Utility Model and Optimal Control -- 2.20.8. Integration and Ordinary Differential Equations -- 2.21. Integration of Multivariable Functions -- 2.22. Vector-Valued Functions -- Chapter 3 -- Logic, Epistemology, and the Problem of Truth -- 3.1. Basic Principles of Logic -- 3.2. Predicate Calculus -- 3.3. Axiomatic Model Theory. 3.4. Common Sense, Non-Monotonic Logic, and Many-Valued Logic -- 3.5. Crises in the Foundations of Mathematics and Mathematical Philosophy -- 3.5.1. The First Crisis in the Foundations of Mathematics -- 3.5.2. The Second Crisis in the Foundations of Mathematics -- 3.5.3. Logicism -- 3.5.4. Axiomatic Set Theory and Category Theory -- 3.5.5. Intuitionism -- 3.5.6. Formalism -- 3.5.7. Conclusions -- 3.6. The Problem of Empirical Relevance in the Context of Science -- 3.7. Truth as a Discovery and Truth as an Invention -- 3.8. Degrees of Truth -- 3.9. From Logical Values to Moral Values: Ethics and Social Theory from the Perspective of Rational Dynamicity -- References -- About the Author -- Index -- Blank Page -- Blank Page. |
| ctrlnum | (OCoLC)1252916836 |
| dewey-full | 510.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| dewey-search | 510.1 |
| dewey-sort | 3510.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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The philosophy of rational dynamicity, as the author explains in this book, is a way of contemplating the laws of motion of nature, history, and spirit"--</subfield><subfield code="c">Provided by publisher.</subfield></datafield><datafield tag="588" ind1=" " ind2=" "><subfield code="a">Description based on online resource; title from digital title page (viewed on June 21, 2021).</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Intro -- Contents -- Prolegomena by Giuliano di Bernardo -- Preface -- The Scope and the Structure of this Project -- Acknowledgments -- Chapter 1 -- Philosophy, Science, and The Dialectic of Rational Dynamicity -- 1.1. The Meaning of Philosophy and Preliminary Concepts -- 1.2. The Abstract Study of a Being -- 1.2.1. Epistemological Presuppositions -- 1.2.2. The Significance and the Presence of a Being -- 1.2.3. The Knowledge of a Being -- Structuralism in Physics -- Newton's Three Laws of Kinematics -- Newton's Law of Universal Gravitation -- Conservation of Mass and Energy -- Laws of Thermodynamics -- Electrostatic Laws -- Quantum Mechanics -- Structuralism in Biology -- Structuralism in Linguistics -- Philosophical Structuralism and Hermeneutics -- 1.2.4. The Modes of Being -- 1.3. The Dialectic of Rational Dynamicity -- 1.3.1. Dynamized Time -- 1.3.2. Dynamized Space and the Problem of the Extension of the Quantum Formalism -- 1.3.3. Consciousness, the World, and the Dialectic of Rational Dynamicity -- 1.3.4. Matter, Life, and Consciousness -- Chapter 2 -- Foundations of Mathematical Analysis and Analytic Geometry -- 2.1. Sets, Relations, and Groups -- 2.1.2. Basic Operations on Sets -- Applications of Set Theory to Probability Theory -- 2.1.3. Relations -- 2.1.4. Groups -- 2.2. Number Systems, Algebra, and Geometry -- 2.2.1. Axiomatic Number Theory -- The System of Natural Numbers -- Principle of Mathematical Induction -- Recursion -- Properties of the System of Natural Numbers -- Enumeration -- Order in ℕ and Ordinal Numbers -- Division -- 2.2.2. The Set of Integral Numbers -- 2.2.3. The Set of Rational Numbers -- 2.2.4. The Set of Real Numbers -- Dedekind Algebra -- ℝ as a Field -- The Absolute Value of a Real Number -- Exponentiation and Logarithm -- Properties of the System of the Real Numbers.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">2.2.5. Matrices of Real Numbers and Vectors -- Vectors -- Some Applications of Matrices -- Input-Output Analysis -- Linear Programming -- Game Theory -- 2.2.6. Analytic Geometry and the Abstract Concept of a Distance -- Circle -- Trigonometric Functions -- Ellipse -- Hyperbola -- Parabola -- Analytic Geometry of Space -- The Abstract Concept of a Distance -- 2.3. Topology of Real Numbers -- 2.3.1. Neighborhoods -- 2.3.2. Open Sets -- 2.3.3. Nested Intervals and Cantor's Intersection Theorem -- 2.3.4. Closure Points and Accumulation Points -- 2.3.5. Closed Sets -- 2.3.6. Compactness -- 2.3.7. Relative Topology and Connectedness -- 2.4. Sequences of Real Numbers -- Limit and Convergence of a Sequence -- Cauchy Sequences and the Completeness of the Real Field -- Subsequences -- Monotonic Sequences -- Hilbert Space -- Alphabets and Languages -- 2.5. Infinite Series and Infinite Products -- 2.6. The Limit of a Function -- Preliminary Concepts -- The Limit of a Function -- 2.7. Continuous Functions -- Types of Discontinuity -- 2.8. Complex Numbers -- 2.9. The Birth and the Development of Infinitesimal Calculus -- 2.10. Differential Calculus -- 2.10.1. Derivative -- Drawing a Tangent Line to the Graph of a Function -- The Formal Definition of the Derivative of a Function -- Higher Order Derivatives -- Table of the Derivatives of Elementary Functions -- The Differential of a Function -- A Note about Complex Derivatives -- 2.10.2. The Basic Theorems of Differential Calculus -- 2.10.3. Monotonicity, Critical Points, and Extreme Points of a Function -- 2.10.4. Concave-Up and Concave-Down Functions -- 2.10.5. Asymptotes of a Function -- 2.10.6. Steps for Function Investigation and Curve Sketching -- 2.10.7. Curvature and Radius of Curvature -- 2.10.8. Differentiation of Multivariable Functions.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Differentiation of Composite Functions, Harmonic Functions, and Homogeneous Functions -- Differentiation of Implicit Functions -- Jacobian (or Functional) Determinant -- Mean Value Theorems -- 2.11. Integral Calculus -- The Definition of the Integral as the Limit of a Sum -- The Physical Significance of the Integral -- Integration of Complex Functions of One Variable -- 2.12. Standard Integration Techniques -- Integration by Substitution -- Integration by Parts -- 2.13. Reduction Formulas -- 2.14. Integration of Rational Functions -- 2.15. Integration of Irrational Functions -- 2.16. Integration of Trigonometric Functions -- 2.17. Integration of Hyperbolic Functions -- 2.18. The Theory of Riemann Integration -- The Riemann Integral -- Criteria of Integrability and Methods of Integration -- Properties of Riemann Integrable Functions -- The Equivalence of the Definitions of the Integral of a Function -- Generalized Integrals -- Riemann Integrability and Sets of Measure Zero -- The Mean Value Theorems of Integral Calculus and the Fundamental Theorem of Infinitesimal Calculus -- 2.19. Numerical Integration -- 2.20. Applications of Integration and Basic Principles of Differential Equations -- 2.20.1. The Calculation of Areas Using Integrals -- 2.20.2. The Calculation of the Area between two Arbitrary Curves -- 2.20.3. The Calculation of the Volume of a Solid of Revolution -- 2.20.4. The Arc Length of a Curve -- 2.20.5. Work -- 2.20.6. Some Basic Applications of Integral Calculus to Economics -- 2.20.7. A Social Utility Model and Optimal Control -- 2.20.8. Integration and Ordinary Differential Equations -- 2.21. Integration of Multivariable Functions -- 2.22. Vector-Valued Functions -- Chapter 3 -- Logic, Epistemology, and the Problem of Truth -- 3.1. Basic Principles of Logic -- 3.2. Predicate Calculus -- 3.3. Axiomatic Model Theory.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">3.4. Common Sense, Non-Monotonic Logic, and Many-Valued Logic -- 3.5. Crises in the Foundations of Mathematics and Mathematical Philosophy -- 3.5.1. The First Crisis in the Foundations of Mathematics -- 3.5.2. The Second Crisis in the Foundations of Mathematics -- 3.5.3. Logicism -- 3.5.4. Axiomatic Set Theory and Category Theory -- 3.5.5. Intuitionism -- 3.5.6. Formalism -- 3.5.7. Conclusions -- 3.6. The Problem of Empirical Relevance in the Context of Science -- 3.7. Truth as a Discovery and Truth as an Invention -- 3.8. Degrees of Truth -- 3.9. 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| id | ZDB-4-EBA-on1252916836 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:30:18Z |
| institution | BVB |
| isbn | 1536196185 9781536196184 |
| language | English |
| lccn | 2021018516 |
| oclc_num | 1252916836 |
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| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiv, 492 pages) : illustrations. |
| psigel | ZDB-4-EBA |
| publishDate | 2021 |
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| publishDateSort | 2021 |
| publisher | Nova Science Publishers, |
| record_format | marc |
| series | Mathematics research developments series. World philosophy series. |
| series2 | Mathematics research developments World philosophy |
| spelling | Laos, Nicolas K., 1974- author. http://id.loc.gov/authorities/names/n97121654 A course of philosophy and mathematics : toward a general theory of reality / Nicolas Laos. New York : Nova Science Publishers, [2021] 1 online resource (xiv, 492 pages) : illustrations. text txt rdacontent computer c rdamedia online resource cr rdacarrier Mathematics research developments World philosophy Includes bibliographical references and index. "The nature of this book is fourfold: First, it provides comprehensive education in ontology, epistemology, logic, and ethics. From this perspective, it can be treated as a philosophical textbook. Second, it provides comprehensive education in mathematical analysis and analytic geometry, including significant aspects of set theory, topology, mathematical logic, number systems, abstract algebra, linear algebra, and the theory of differential equations. From this perspective, it can be treated as a mathematical textbook. Third, it makes a student and a researcher in philosophy and/or mathematics capable of developing a holistic approach to reality, of undertaking interdisciplinary endeavors, of understanding (and possibly contributing to) advances and research projects in different academic disciplines, and of having more sources of inspiration and pleasure. From this perspective, it can be treated as a contribution to pedagogy and as an attempt to refresh and, indeed, revitalize modern philosophy. Fourth, it seeks to defend, refresh, and enrich philosophical and scientific structuralism and dynamical philosophy (known also as dynamism). From this perspective, this book can be treated as a research monograph on structuralism and dynamism, tackling the fundamental problems of reality, truth, and consciousness. In this context, Nicolas Laos expounds and proposes: (i) the concepts of dynamized time and dynamized space; (ii) a theory and method that he calls the "dialectic of rational dynamicity"; and (iii) his attempt to consider the fundamental problems of philosophy and science from the perspective of the dialectic of rational dynamicity. Thus, this book pertains to every field that is controlled by the function of consciousness, namely, being, knowing, and acting. The philosophy of rational dynamicity, as the author explains in this book, is a way of contemplating the laws of motion of nature, history, and spirit"-- Provided by publisher. Description based on online resource; title from digital title page (viewed on June 21, 2021). Intro -- Contents -- Prolegomena by Giuliano di Bernardo -- Preface -- The Scope and the Structure of this Project -- Acknowledgments -- Chapter 1 -- Philosophy, Science, and The Dialectic of Rational Dynamicity -- 1.1. The Meaning of Philosophy and Preliminary Concepts -- 1.2. The Abstract Study of a Being -- 1.2.1. Epistemological Presuppositions -- 1.2.2. The Significance and the Presence of a Being -- 1.2.3. The Knowledge of a Being -- Structuralism in Physics -- Newton's Three Laws of Kinematics -- Newton's Law of Universal Gravitation -- Conservation of Mass and Energy -- Laws of Thermodynamics -- Electrostatic Laws -- Quantum Mechanics -- Structuralism in Biology -- Structuralism in Linguistics -- Philosophical Structuralism and Hermeneutics -- 1.2.4. The Modes of Being -- 1.3. The Dialectic of Rational Dynamicity -- 1.3.1. Dynamized Time -- 1.3.2. Dynamized Space and the Problem of the Extension of the Quantum Formalism -- 1.3.3. Consciousness, the World, and the Dialectic of Rational Dynamicity -- 1.3.4. Matter, Life, and Consciousness -- Chapter 2 -- Foundations of Mathematical Analysis and Analytic Geometry -- 2.1. Sets, Relations, and Groups -- 2.1.2. Basic Operations on Sets -- Applications of Set Theory to Probability Theory -- 2.1.3. Relations -- 2.1.4. Groups -- 2.2. Number Systems, Algebra, and Geometry -- 2.2.1. Axiomatic Number Theory -- The System of Natural Numbers -- Principle of Mathematical Induction -- Recursion -- Properties of the System of Natural Numbers -- Enumeration -- Order in ℕ and Ordinal Numbers -- Division -- 2.2.2. The Set of Integral Numbers -- 2.2.3. The Set of Rational Numbers -- 2.2.4. The Set of Real Numbers -- Dedekind Algebra -- ℝ as a Field -- The Absolute Value of a Real Number -- Exponentiation and Logarithm -- Properties of the System of the Real Numbers. 2.2.5. Matrices of Real Numbers and Vectors -- Vectors -- Some Applications of Matrices -- Input-Output Analysis -- Linear Programming -- Game Theory -- 2.2.6. Analytic Geometry and the Abstract Concept of a Distance -- Circle -- Trigonometric Functions -- Ellipse -- Hyperbola -- Parabola -- Analytic Geometry of Space -- The Abstract Concept of a Distance -- 2.3. Topology of Real Numbers -- 2.3.1. Neighborhoods -- 2.3.2. Open Sets -- 2.3.3. Nested Intervals and Cantor's Intersection Theorem -- 2.3.4. Closure Points and Accumulation Points -- 2.3.5. Closed Sets -- 2.3.6. Compactness -- 2.3.7. Relative Topology and Connectedness -- 2.4. Sequences of Real Numbers -- Limit and Convergence of a Sequence -- Cauchy Sequences and the Completeness of the Real Field -- Subsequences -- Monotonic Sequences -- Hilbert Space -- Alphabets and Languages -- 2.5. Infinite Series and Infinite Products -- 2.6. The Limit of a Function -- Preliminary Concepts -- The Limit of a Function -- 2.7. Continuous Functions -- Types of Discontinuity -- 2.8. Complex Numbers -- 2.9. The Birth and the Development of Infinitesimal Calculus -- 2.10. Differential Calculus -- 2.10.1. Derivative -- Drawing a Tangent Line to the Graph of a Function -- The Formal Definition of the Derivative of a Function -- Higher Order Derivatives -- Table of the Derivatives of Elementary Functions -- The Differential of a Function -- A Note about Complex Derivatives -- 2.10.2. The Basic Theorems of Differential Calculus -- 2.10.3. Monotonicity, Critical Points, and Extreme Points of a Function -- 2.10.4. Concave-Up and Concave-Down Functions -- 2.10.5. Asymptotes of a Function -- 2.10.6. Steps for Function Investigation and Curve Sketching -- 2.10.7. Curvature and Radius of Curvature -- 2.10.8. Differentiation of Multivariable Functions. Differentiation of Composite Functions, Harmonic Functions, and Homogeneous Functions -- Differentiation of Implicit Functions -- Jacobian (or Functional) Determinant -- Mean Value Theorems -- 2.11. Integral Calculus -- The Definition of the Integral as the Limit of a Sum -- The Physical Significance of the Integral -- Integration of Complex Functions of One Variable -- 2.12. Standard Integration Techniques -- Integration by Substitution -- Integration by Parts -- 2.13. Reduction Formulas -- 2.14. Integration of Rational Functions -- 2.15. Integration of Irrational Functions -- 2.16. Integration of Trigonometric Functions -- 2.17. Integration of Hyperbolic Functions -- 2.18. The Theory of Riemann Integration -- The Riemann Integral -- Criteria of Integrability and Methods of Integration -- Properties of Riemann Integrable Functions -- The Equivalence of the Definitions of the Integral of a Function -- Generalized Integrals -- Riemann Integrability and Sets of Measure Zero -- The Mean Value Theorems of Integral Calculus and the Fundamental Theorem of Infinitesimal Calculus -- 2.19. Numerical Integration -- 2.20. Applications of Integration and Basic Principles of Differential Equations -- 2.20.1. The Calculation of Areas Using Integrals -- 2.20.2. The Calculation of the Area between two Arbitrary Curves -- 2.20.3. The Calculation of the Volume of a Solid of Revolution -- 2.20.4. The Arc Length of a Curve -- 2.20.5. Work -- 2.20.6. Some Basic Applications of Integral Calculus to Economics -- 2.20.7. A Social Utility Model and Optimal Control -- 2.20.8. Integration and Ordinary Differential Equations -- 2.21. Integration of Multivariable Functions -- 2.22. Vector-Valued Functions -- Chapter 3 -- Logic, Epistemology, and the Problem of Truth -- 3.1. Basic Principles of Logic -- 3.2. Predicate Calculus -- 3.3. Axiomatic Model Theory. 3.4. Common Sense, Non-Monotonic Logic, and Many-Valued Logic -- 3.5. Crises in the Foundations of Mathematics and Mathematical Philosophy -- 3.5.1. The First Crisis in the Foundations of Mathematics -- 3.5.2. The Second Crisis in the Foundations of Mathematics -- 3.5.3. Logicism -- 3.5.4. Axiomatic Set Theory and Category Theory -- 3.5.5. Intuitionism -- 3.5.6. Formalism -- 3.5.7. Conclusions -- 3.6. The Problem of Empirical Relevance in the Context of Science -- 3.7. Truth as a Discovery and Truth as an Invention -- 3.8. Degrees of Truth -- 3.9. From Logical Values to Moral Values: Ethics and Social Theory from the Perspective of Rational Dynamicity -- References -- About the Author -- Index -- Blank Page -- Blank Page. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Mathématiques Philosophie. Mathematics Philosophy fast has work: A course of philosophy and mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCGktKg9MgKV3rPCY83D76q https://id.oclc.org/worldcat/ontology/hasWork Print version: Laos, Nicolas K., 1974- Course of philosophy and mathematics New York : Nova Science Publishers, [2021] 9781536195170 (DLC) 2021018515 Mathematics research developments series. http://id.loc.gov/authorities/names/no2009139785 World philosophy series. http://id.loc.gov/authorities/names/no2012028725 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2913945 Volltext |
| spellingShingle | Laos, Nicolas K., 1974- A course of philosophy and mathematics : toward a general theory of reality / Mathematics research developments series. World philosophy series. Intro -- Contents -- Prolegomena by Giuliano di Bernardo -- Preface -- The Scope and the Structure of this Project -- Acknowledgments -- Chapter 1 -- Philosophy, Science, and The Dialectic of Rational Dynamicity -- 1.1. The Meaning of Philosophy and Preliminary Concepts -- 1.2. The Abstract Study of a Being -- 1.2.1. Epistemological Presuppositions -- 1.2.2. The Significance and the Presence of a Being -- 1.2.3. The Knowledge of a Being -- Structuralism in Physics -- Newton's Three Laws of Kinematics -- Newton's Law of Universal Gravitation -- Conservation of Mass and Energy -- Laws of Thermodynamics -- Electrostatic Laws -- Quantum Mechanics -- Structuralism in Biology -- Structuralism in Linguistics -- Philosophical Structuralism and Hermeneutics -- 1.2.4. The Modes of Being -- 1.3. The Dialectic of Rational Dynamicity -- 1.3.1. Dynamized Time -- 1.3.2. Dynamized Space and the Problem of the Extension of the Quantum Formalism -- 1.3.3. Consciousness, the World, and the Dialectic of Rational Dynamicity -- 1.3.4. Matter, Life, and Consciousness -- Chapter 2 -- Foundations of Mathematical Analysis and Analytic Geometry -- 2.1. Sets, Relations, and Groups -- 2.1.2. Basic Operations on Sets -- Applications of Set Theory to Probability Theory -- 2.1.3. Relations -- 2.1.4. Groups -- 2.2. Number Systems, Algebra, and Geometry -- 2.2.1. Axiomatic Number Theory -- The System of Natural Numbers -- Principle of Mathematical Induction -- Recursion -- Properties of the System of Natural Numbers -- Enumeration -- Order in ℕ and Ordinal Numbers -- Division -- 2.2.2. The Set of Integral Numbers -- 2.2.3. The Set of Rational Numbers -- 2.2.4. The Set of Real Numbers -- Dedekind Algebra -- ℝ as a Field -- The Absolute Value of a Real Number -- Exponentiation and Logarithm -- Properties of the System of the Real Numbers. 2.2.5. Matrices of Real Numbers and Vectors -- Vectors -- Some Applications of Matrices -- Input-Output Analysis -- Linear Programming -- Game Theory -- 2.2.6. Analytic Geometry and the Abstract Concept of a Distance -- Circle -- Trigonometric Functions -- Ellipse -- Hyperbola -- Parabola -- Analytic Geometry of Space -- The Abstract Concept of a Distance -- 2.3. Topology of Real Numbers -- 2.3.1. Neighborhoods -- 2.3.2. Open Sets -- 2.3.3. Nested Intervals and Cantor's Intersection Theorem -- 2.3.4. Closure Points and Accumulation Points -- 2.3.5. Closed Sets -- 2.3.6. Compactness -- 2.3.7. Relative Topology and Connectedness -- 2.4. Sequences of Real Numbers -- Limit and Convergence of a Sequence -- Cauchy Sequences and the Completeness of the Real Field -- Subsequences -- Monotonic Sequences -- Hilbert Space -- Alphabets and Languages -- 2.5. Infinite Series and Infinite Products -- 2.6. The Limit of a Function -- Preliminary Concepts -- The Limit of a Function -- 2.7. Continuous Functions -- Types of Discontinuity -- 2.8. Complex Numbers -- 2.9. The Birth and the Development of Infinitesimal Calculus -- 2.10. Differential Calculus -- 2.10.1. Derivative -- Drawing a Tangent Line to the Graph of a Function -- The Formal Definition of the Derivative of a Function -- Higher Order Derivatives -- Table of the Derivatives of Elementary Functions -- The Differential of a Function -- A Note about Complex Derivatives -- 2.10.2. The Basic Theorems of Differential Calculus -- 2.10.3. Monotonicity, Critical Points, and Extreme Points of a Function -- 2.10.4. Concave-Up and Concave-Down Functions -- 2.10.5. Asymptotes of a Function -- 2.10.6. Steps for Function Investigation and Curve Sketching -- 2.10.7. Curvature and Radius of Curvature -- 2.10.8. Differentiation of Multivariable Functions. Differentiation of Composite Functions, Harmonic Functions, and Homogeneous Functions -- Differentiation of Implicit Functions -- Jacobian (or Functional) Determinant -- Mean Value Theorems -- 2.11. Integral Calculus -- The Definition of the Integral as the Limit of a Sum -- The Physical Significance of the Integral -- Integration of Complex Functions of One Variable -- 2.12. Standard Integration Techniques -- Integration by Substitution -- Integration by Parts -- 2.13. Reduction Formulas -- 2.14. Integration of Rational Functions -- 2.15. Integration of Irrational Functions -- 2.16. Integration of Trigonometric Functions -- 2.17. Integration of Hyperbolic Functions -- 2.18. The Theory of Riemann Integration -- The Riemann Integral -- Criteria of Integrability and Methods of Integration -- Properties of Riemann Integrable Functions -- The Equivalence of the Definitions of the Integral of a Function -- Generalized Integrals -- Riemann Integrability and Sets of Measure Zero -- The Mean Value Theorems of Integral Calculus and the Fundamental Theorem of Infinitesimal Calculus -- 2.19. Numerical Integration -- 2.20. Applications of Integration and Basic Principles of Differential Equations -- 2.20.1. The Calculation of Areas Using Integrals -- 2.20.2. The Calculation of the Area between two Arbitrary Curves -- 2.20.3. The Calculation of the Volume of a Solid of Revolution -- 2.20.4. The Arc Length of a Curve -- 2.20.5. Work -- 2.20.6. Some Basic Applications of Integral Calculus to Economics -- 2.20.7. A Social Utility Model and Optimal Control -- 2.20.8. Integration and Ordinary Differential Equations -- 2.21. Integration of Multivariable Functions -- 2.22. Vector-Valued Functions -- Chapter 3 -- Logic, Epistemology, and the Problem of Truth -- 3.1. Basic Principles of Logic -- 3.2. Predicate Calculus -- 3.3. Axiomatic Model Theory. 3.4. Common Sense, Non-Monotonic Logic, and Many-Valued Logic -- 3.5. Crises in the Foundations of Mathematics and Mathematical Philosophy -- 3.5.1. The First Crisis in the Foundations of Mathematics -- 3.5.2. The Second Crisis in the Foundations of Mathematics -- 3.5.3. Logicism -- 3.5.4. Axiomatic Set Theory and Category Theory -- 3.5.5. Intuitionism -- 3.5.6. Formalism -- 3.5.7. Conclusions -- 3.6. The Problem of Empirical Relevance in the Context of Science -- 3.7. Truth as a Discovery and Truth as an Invention -- 3.8. Degrees of Truth -- 3.9. From Logical Values to Moral Values: Ethics and Social Theory from the Perspective of Rational Dynamicity -- References -- About the Author -- Index -- Blank Page -- Blank Page. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Mathématiques Philosophie. Mathematics Philosophy fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082153 |
| title | A course of philosophy and mathematics : toward a general theory of reality / |
| title_auth | A course of philosophy and mathematics : toward a general theory of reality / |
| title_exact_search | A course of philosophy and mathematics : toward a general theory of reality / |
| title_full | A course of philosophy and mathematics : toward a general theory of reality / Nicolas Laos. |
| title_fullStr | A course of philosophy and mathematics : toward a general theory of reality / Nicolas Laos. |
| title_full_unstemmed | A course of philosophy and mathematics : toward a general theory of reality / Nicolas Laos. |
| title_short | A course of philosophy and mathematics : |
| title_sort | course of philosophy and mathematics toward a general theory of reality |
| title_sub | toward a general theory of reality / |
| topic | Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Mathématiques Philosophie. Mathematics Philosophy fast |
| topic_facet | Mathematics Philosophy. Mathématiques Philosophie. Mathematics Philosophy |
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