The origin of the logic of symbolic mathematics :: Edmund Husserl and Jacob Klein /
Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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©2011.
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| Schriftenreihe: | Studies in Continental thought.
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| Zusammenfassung: | Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkin. |
| Beschreibung: | 1 online resource (xxx, 559 pages) |
| Bibliographie: | Includes bibliographical references (pages 545-552) and indexes. |
| ISBN: | 9780253005274 0253005272 1283235900 9781283235907 9786613235909 6613235903 |
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| 100 | 1 | |a Hopkins, Burt C., |e author. |0 http://id.loc.gov/authorities/names/n92103122 | |
| 245 | 1 | 4 | |a The origin of the logic of symbolic mathematics : |b Edmund Husserl and Jacob Klein / |c Burt C. Hopkins. |
| 260 | |a Bloomington, Ind. : |b Indiana University Press, |c ©2011. | ||
| 300 | |a 1 online resource (xxx, 559 pages) | ||
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| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Studies in continental thought | |
| 504 | |a Includes bibliographical references (pages 545-552) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |6 880-01 |a pt. 1. Klein on Husserl's phenomenology and the history of science -- pt. 2. Husserl and Klein on the method and task of desedimenting the mathematization of nature -- pt. 3. Non-symbolic and symbolic numbers in Husserl and Klein -- pt. 4. Husserl and Klein on the origination of the logic of symbolic mathematics. | |
| 520 | |a Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkin. | ||
| 546 | |a English. | ||
| 600 | 1 | 7 | |a Husserl, Edmund |d 1859-1938 |2 gnd |
| 600 | 1 | 7 | |a Husserl, Edmund. |2 idszbz |
| 600 | 1 | 7 | |a Klein, Jacob. |2 idszbz |
| 600 | 1 | 7 | |a Klein, Jacob (Philosoph) |0 (DE-604)BV0087245 |2 swd |
| 650 | 0 | |a Logic, Symbolic and mathematical. |0 http://id.loc.gov/authorities/subjects/sh85078115 | |
| 650 | 0 | |a Mathematics |x Philosophy. |0 http://id.loc.gov/authorities/subjects/sh85082153 | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 6 | |a Mathématiques |x Philosophie. | |
| 650 | 7 | |a MATHEMATICS |x Infinity. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh | |
| 650 | 7 | |a PHILOSOPHY |x Movements |x Phenomenology. |2 bisacsh | |
| 650 | 7 | |a Logic, Symbolic and mathematical |2 fast | |
| 650 | 7 | |a Mathematics |x Philosophy |2 fast | |
| 650 | 7 | |a Computeralgebra |2 gnd | |
| 650 | 7 | |a Logik |2 gnd |0 http://d-nb.info/gnd/4036202-4 | |
| 650 | 7 | |a Mathematische Logik |2 gnd |0 http://d-nb.info/gnd/4037951-6 | |
| 650 | 7 | |a Rezeption |2 gnd | |
| 650 | 7 | |a Zahlentheorie |2 gnd |0 http://d-nb.info/gnd/4067277-3 | |
| 651 | 7 | |a Griechenland |g Altertum |2 gnd | |
| 650 | 7 | |a Mathematische Logik. |2 idszbz | |
| 650 | 7 | |a Mathematik. |2 idszbz | |
| 650 | 7 | |a Philosophie. |2 idszbz | |
| 650 | 7 | |a Symbolisk logik. |2 sao | |
| 650 | 7 | |a Matematik |x teori, filosofi. |2 sao | |
| 758 | |i has work: |a The origin of the logic of symbolic mathematics (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGYm7hTY37hhJbpJbtg3gq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Hopkins, Burt C. |t Origin of the logic of symbolic mathematics. |d Bloomington, Ind. : Indiana University Press, ©2011 |z 9780253356710 |w (DLC) 2011022942 |w (OCoLC)692291398 |
| 830 | 0 | |a Studies in Continental thought. |0 http://id.loc.gov/authorities/names/n88508712 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=385454 |3 Volltext |
| 880 | 0 | 0 | |6 505-00/(S |g Machine generated contents note: |g pt. One |t Klein on Husserl's Phenomenology and the History of Science -- |g ch. One |t Klein's and Husserl's Investigations of the Origination of Mathematical Physics -- |g [ʹ] 1 |t Problem of History in Husserl's Last Writings -- |g [ʹ] 2 |t Priority of Klein's Research on the Historical Origination of the Meaning of Mathematical Physics over Husserl's -- |g [ʹ] 3 |t Importance of Husserl's Last Writings for Understanding Klein's Nontraditional Investigations of the History and Philosophy of Science -- |g [ʹ] 4 |t Klein's Commentary on Husserl's Investigation of the History of the Origin of Modern Science -- |g [ʹ] 5 |t "Curious" Relation between Klein's Historical Investigation of Greek and Modern Mathematics and Husserl's Phenomenology -- |g ch. Two |t Klein's Account of the Essential Connection between Intentional and Actual History -- |g [ʹ] 6 |t Problem of Origin and History in Husserl's Phenomenology -- |g [ʹ] 7 |t Internal Motivation for Husserl's Seemingly Late Turn to History -- |g ch. Three |t Liberation of the Problem of Origin from Its Naturalistic Distortion: The Phenomenological Problem of Constitution -- |g [ʹ] 8 |t Psychologism and the Problem of History -- |g [ʹ] 9 |t Internal Temporality and the Problem of the Sedimented History of Significance -- |g ch. Four |t Essential Connection between Intentional and Actual History -- |g [ʹ] 10 |t Two Limits of the Investigation of the Temporal Genesis Proper to the Intrinsic Possibility of the Intentional Object -- |g [ʹ] 11 |t Transcendental Constitution of an Identical Object Exceeds the Sedimented Genesis of Its Temporal Form -- |g [ʹ] 12 |t Distinction between the Sedimented History of the Immediate Presence of an Intentional Object and the Sedimented History of Its Original Presentation -- |g ch. Five |t Historicity of the Intelligibility of Ideal Significations and the Possibility of Actual History -- |g [ʹ] 13 |t Problem of Ìaτρia underlying Husserl's Concept of Intentional History -- |g [ʹ] 14 |t Two Senses of Historicity and the Meaning of the Historical Apriori -- |g [ʹ] 15 |t Historicity as Distinct from Both Historicism and the History of the Ego -- |g ch. Six |t Sedimentation and the Link between Intentional History and the Constitution of a Historical Tradition -- |g [ʹ] 16 |t Maintaining the Integrity of Knowledge Requires Inquiry into Its Original Historical Discovery -- |g [ʹ] 17 |t Two Presuppositions Are Necessary to Account for the Historicity of the Discovery of the Ideal Objects of a Science Such as Geometry -- |g [ʹ] 18 |t Sedimentation and the Constitution of a Geometrical Tradition -- |g [ʹ] 19 |t Historical Apriori of Ideal Objects and Historical Facts -- |g [ʹ] 20 |t Historical Apriori Is Not a Concession to Historicism -- |g ch. Seven |t Klein's Departure from the Content but Not the Method of Husserl's Intentional-Historical Analysis of Modern Science -- |g [ʹ] 21 |t Contrast between Klein's Account of the Actual Development of Modern Science and Husserl's Intentional Account -- |g [ʹ] 22 |t Sedimentation and the Method of Symbolic Abstraction -- |g [ʹ] 23 |t Establishment of Modern Physics on the Foundation of a Radical Reinterpretation of Ancient Mathematics -- |g [ʹ] 24 |t Vieta's and Descartes's Inauguration of the Development of the Symbolic Science of Nature: Mathematical Physics -- |g [ʹ] 25 |t Open Questions in Kleins Account of the Actual Development of Modern Science -- |g pt. Two |t Husserl and Klein on the Method and Task of Desedimenting the Mathematization of Nature -- |g ch. Eight |t Klein's Historical-Mathematical Investigations in the Context of Husserl's Phenomenology of Science -- |g [ʹ] 26 |t Summary of Part One -- |g [ʹ] 27 |t Klein's Failure to Refer to Husserl in Greek Mathematical Thought and the Origin of Algebra -- |g [ʹ] 28 |t Critical Implications of Klein's Historical Research for Husserl's Phenomenology -- |g ch. Nine |t Basic Problem and Method of Klein's Mathematical Investigations -- |g [ʹ] 29 |t Klein's Account of the Limited Task of Recovering the Hidden Sources of Modern Symbolic Mathematics -- |g [ʹ] 30 |t Klein's Motivation for the Radical Investigation of the Origins of Mathematical Physics -- |g [ʹ] 31 |t Conceptual Battleground on Which the Scholastic and the New Science Fought -- |g ch. Ten |t Husserl's Formulation of the Nature and Roots of the Crisis of European Sciences -- |g [ʹ] 32 |t Klein's Uncanny Anticipation of Husserl's Treatment of the Historical Origins of Scientific Concepts in the Crisis -- |g [ʹ] 33 |t Historical Reference Back to Origins and the Crisis of Modern Science -- |g [ʹ] 34 |t Husserl's Reactivation of the Sedimented Origins of the Modern Spirit -- |g [ʹ] 35 |t Husserl's Fragmentary Analyses of the Sedimentation Responsible for the Formalized Meaning Formations of Modern Mathematics and Klein's Inquiry into Their Origin and Conceptual Structure -- |g ch. Eleven |t "Zigzag" Movement Implicit in Klein's Mathematical Investigations -- |g [ʹ] 36 |t Structure of Klein's Method of Historical Reflection in Greek Mathematical Thought and the Origin of Algebra -- |g ch. Twelve |t Husserl and Klein on the Logic of Symbolic Mathematics -- |g [ʹ] 37 |t Husserl's Systematic Attempt to Ground the Symbolic Concept of Number in the Concept of Anzahl -- |g [ʹ] 38 |t Klein on the Transformation of the Ancient Concept of Aρiθuos (Anzahl) into the Modern Concept of Symbolic Number -- |g [ʹ] 39 |t Transition to Part Three of This Study -- |g pt. Three |t Non-symbolic and Symbolic Numbers in Husserl and Klein -- |g ch. Thirteen |t Authentic and Symbolic Numbers in Husserl's Philosophy of Arithmetic -- |g [ʹ] 40 |t Shortcomings of Philosophy of Arithmetic and Our Basic Concern -- |g [ʹ] 41 |t Husserl on the Authentic Concepts of Multiplicity and Cardinal Number Concepts, and Inauthentic (Symbolic) Number Concepts -- |g [ʹ] 42 |t Basic Logical Problem in Philosophy of Arithmetic -- |g [ʹ] 43 |t Fundamental Shift in Husserl's Account of Calculational Technique -- |g [ʹ] 44 |t Husserl's Account of the Logical Requirements behind Both Calculational Technique and Symbolic Numbers -- |g [ʹ] 45 |t Husseris Psychological Account of the Logical Whole Proper to the Concept of Multiplicity and Authentic Cardinal Number Concepts -- |g [ʹ] 46 |t Husserl on the Psychological Basis for Symbolic Numbers and Logical Technique -- |g [ʹ] 47 |t Husserl on the Symbolic Presentation of Multitudes -- |g [ʹ] 48 |t Husserl on the Psychological Presentation of Symbolic Numbers -- |g [ʹ] 49 |t Husserl on the Symbolic Presentation of the Systematic Construction of New Number Concepts and Their Designation -- |g [ʹ] 50 |t Fundamental Shift in the Logic of Symbolic Numbers Brought about by the Independence of Signitively Symbolic Numbers -- |g [ʹ] 51 |t Unresolved Question of the Logical Foundation for Signitively Symbolic Numbers -- |g [ʹ] 52 |t Summary and Conclusion -- |g ch. Fourteen |t Klein's Desedimentation of the Origin of Algebra and Husserl's Failure to Ground Symbolic Calculation in Authentic Numbers -- |g [ʹ] 53 |t Implications of Kleins Desedimentation of the Origin of Algebra for Husserl's Analyses of the Concept Proper to Number in Philosophy of Arithmetic -- |g [ʹ] 54 |t Klein's Desedimentation of the Two Salient Features of the Foundations of Greek Mathematics -- |g ch. Fifteen |t Logistic and Arithmetic in Neoplatonic Mathematics and in Plato -- |g [ʹ] 55 |t Opposition between Logistic and Arithmetic in Neoplatonic Thought -- |g [ʹ] 56 |t Logistic and Arithmetic in Plato -- |g [ʹ] 57 |t Tensions and Issues Surrounding the Role of the Theory of Proportions in Nicomachus, Theon, and Domninus -- |g ch. |
| 880 | 0 | 0 | |6 505-00/(S |t Sixteen |t Theoretical Logistic and the Problem of Fractions -- |g [ʹ] 58 |t Ambiguous Relationship between Logistic and Arithmetic in Neoplatonic Mathematics and in Plato -- |g [ʹ] 59 |t Obstacle Presented by Fractions to Plato's Demand for a Theoretical Logistic -- |g ch. Seventeen |t Concept of Aρiθuos -- |g [ʹ] 60 |t Connection between Neoplatonic Mathematics and Plato's Ontology -- |g [ʹ] 61 |t Counting as the Fundamental Phenomenon Determining the Meaning of Aρiθuos -- |g [ʹ] 62 |t "Pure" Aρiθuos -- |g [ʹ] 63 |t Why Greek Theoretical Arithmetic and Logistic Did Not Directly Study Aρiθuos -- |g ch. Eighteen |t Plato's Ontological Conception of Aρiθuos -- |g [ʹ] 64 |t Interdependence of Greek Mathematics and Greek Ontology -- |g [ʹ] 65 |t Pythagorean Context of Plato's Philosophy -- |g [ʹ] 66 |t Plato's Departure from Pythagorean Science: The Fundamental Role of Aρiθuos of Pure Monads -- |g [ʹ] 67 |t Δiavoia as the Soul's Initial Mode of Access to Noητ -- |g [ʹ] 68 |t Limits Inherent in the Dianoetic Mode of Access to Noητ -- |g ch. Nineteen |t Klein's Reactivation of Plato's Theory of Aρiθuos Eiητκo -- |g [ʹ] 69 |t Inability of Mathematical Thought to Account for the Mode of Being of Its Objects -- |g [ʹ] 70 |t Curious Kind of Koα Manifest in Aρiθuos -- |g [ʹ] 71 |t Koα Exemplified by Aρiθuos as the Key to Solving the Problem of Mθξε -- |g [ʹ] 72 |t Koα Exemplified by ̀'Aρiθuos Contains the Clue to the "Mixing" of Being and Non-being in the Image -- |g [ʹ] 73 |t Partial Clarification of the Aporia of Being and Non-being Holds the Key to the "Arithmetical" Structure of the Noητv's Mode of Being. |
| 880 | 0 | 0 | |6 505-00/(S |g Contents note continued: |g [ʹ] 74 |t Koα among "Ov, Kvητ, and Στ, Composes the Relationship of Being and Non-being -- |g [ʹ] 75 |t Contrast between Aρθm Mαθ and Aρθm E -- |g [ʹ] 76 |t Foundational Function of Aρiθuos E -- |g [ʹ] 77 |t Order of Aρiθuos' E Provides the Foundation for Both the Sequence of Mathematical À and the Relation of Family Descent between Higher and Lower -- |g [ʹ] 78 |t Inability of the A, to "Count" the M Points to Its Limits and Simultaneously Presents the First A E -- |g [ʹ] 79 |t Θατερoν as the "Twofold in General" Allows for the Articulation of Being and Non-being -- |g [ʹ] 80 |t Recognizing "the Other" as the "Indeterminate Dyad" -- |g [ʹ] 81 |t "One Itself" as the Source of the Generation of "A E -- |g [ʹ] 82 |t Γενη À E Provide the Foundation of an Eidetic Logistic -- |g [ʹ] 83 |t Plato's Postulate of the Separation of All Noetic Formations Renders Incomprehensible the Ordinary Mode of Predication -- |g ch. Twenty |t Aristotle's Critique of the Platonic Chorismos Thesis and the Possibility of a Theoretical Logistic -- |g [ʹ] 84 |t Point of Departure and Overview of Aristotle's Critique -- |g [ʹ] 85 |t Aristode's Problematic: Harmonizing the Ontological Dependence of À with Their Pure Noetic Quality -- |g [ʹ] 86 |t Aristotle on the Abstractive Mode of Being of Mathematical Objects -- |g [ʹ] 87 |t Aristotle's Ontological Determination of the Non-generic Unity of À -- |g [ʹ] 88 |t Aristotle's Ontological Determination of the Unity of À as Common Measure -- |g [ʹ] 89 |t Aristotle's Ontological Determination of the Indivisibility and Exactness of "Pure" À -- |g [ʹ] 90 |t Influence of Aristotle's View of M on Theoretical Arithmetic -- |g [ʹ] 91 |t Aristotle's Ontological Conception of À Makes Possible Theoretical Logistic -- |g ch. Twenty-one |t Klein's Interpretation of Diophantus's Arithmetic -- |g [ʹ] 92 |t Access to Diophantus's Work Requires Reinterpreting It outside the Context of Mathematics' Self-interpretation since Vieta, Stevin, and Descartes -- |g [ʹ] 93 |t Diophantus's Arithmetic as Theoretical Logistic -- |g [ʹ] 94 |t Referent and Operative Mode of Being of Diophantus's Concept of À -- |g [ʹ] 95 |t Ultimate Determinacy of Diophantus's Concept of Unknown and Indeterminate À -- |g [ʹ] 96 |t Merely Instrumental, and Therefore Non-ontological and Non-symbolic, Status of the E-Concept in Diophantus's Calculations -- |g ch. Twenty-two |t Klein's Account of Vieta's Reinterpretation of the Diophantine Procedure and the Consequent Establishment of Algebra as the General Analytical Art -- |g [ʹ] 97 |t Significance of Vieta's Generalization of the E-Concept and Its Transformation into the Symbolic Concept of Species -- |g [ʹ] 98 |t Sedimentation of the Ancient Practical Distinction between S̀aying' and ̀Thinking' in the Symbolic Notation Inseparable from Vieta's Concept of Number -- |g [ʹ] 99 |t Decisive Difference between Vieta's Conception of a "General" Mathematical Discipline and the Ancient Idea of a K I -- |g [ʹ] 100 |t Occlusion of the Ancient Connection between the Theme of General Mathematics and the Foundational Concerns of the "Supreme" Science That Results from the Modern Understanding of Vieta's "Analytical Art" as Mathesis Universalis -- |g [ʹ] 101 |t Vieta's Ambiguous Relation to Ancient Greek Mathematics -- |g [ʹ] 102 |t Vieta's Comparison of Ancient Geometrical Analysis with the Diophantine Procedure -- |g [ʹ] 103 |t Vieta's Transformation of the Diophantine Procedure -- |g [ʹ] 104 |t Auxiliary Status of Vieta's Employment of the "General Analytic" -- |g [ʹ] 105 |t Influence of the General Theory of Proportions on Vieta's "Pure," "General" Algebra -- |g [ʹ] 106 |t Klein's Desedimentation of the Conceptual Presuppositions Belonging to Vieta's Interpretation of Diophantine Logistic -- |g ch. Twenty-three |t Klein's Account of the Concept of Number and the Number Concepts in Stevin, Descartes, and Wallis -- |g [ʹ] 107 |t Stevin's Idea of a "Wise Age" and His Project for Its Renewal -- |g [ʹ] 108 |t Stevin's Critique of the Traditional À-Concept -- |g [ʹ] 109 |t Stevin's Symbolic Understanding of Numerus -- |g [ʹ] 110 |t Stevin's Assimilation of Numbers to Geometrical Formations -- |g [ʹ] 111 |t Descartes's Postulation of a New Mode of "Abstraction" and a New Possibility of "Understanding" as Underlying Symbolic Calculation -- |g [ʹ] 112 |t Fundamental Cognitive Role Attributed by Descartes to the Imaginatio -- |g [ʹ] 113 |t Descartes on the Pure Intellect's Use of the Power of the Imagination to Reconcile the Mathematical Problem of Determinacy and Indeterminacy -- |g [ʹ] 114 |t Klein's Reactivation of the "Abstraction" in Descartes as "Symbolic Abstraction" -- |g [ʹ] 115 |t Klein's Use of the Scholastic Distinction between "First and Second Intentions" to Fix Conceptually the Status of Descartes's Symbolic Concepts -- |g [ʹ] 116 |t Descartes on the Non-metaphorical Reception by the Imagination of the Extension of Bodies as Bridging the Gap between Non-determinate and Determinate Magnitudes -- |g [ʹ] 117 |t Wallis's Completion of the Introduction of the New Number Concept -- |g [ʹ] 118 |t Wallis's Initial Account of the Unit Both as the Principle of Number and as Itself a Number -- |g [ʹ] 119 |t Wallis's Account of the Nought as Also the Principle of Number -- |g [ʹ] 120 |t Wallis's Emphasis on the Arithmetical Status of the Symbol or Species of the "General Analytic" -- |g [ʹ] 121 |t Homogeneity of Algebraic Numbers as Rooted for Wallis in the Unity of the Sign Character of Their Symbols -- |g [ʹ] 122 |t Wallis's Understanding of Algebraic Numbers as Symbolically Conceived Ratios -- |g pt. Four |t Husserl and Klein on the Origination of the Logic of Symbolic Mathematics -- |g ch. Twenty-four |t Husserl and Klein on the Fundamental Difference between Symbolic and Non-symbolic Numbers -- |g [ʹ] 123 |t Klein's Critical Appropriation of Husserl's Crisis Seen within the Context of the Results of Klein's Investigation of the Origin of Algebra -- |g [ʹ] 124 |t Husserl and Klein on the Difference between Non-symbolic and symbolic Numbers -- |g [ʹ] 125 |t Husserl on the Authentic Cardinal Number Concept and Klein on the Greek À-Concept -- |g ch. |
| 880 | 0 | 0 | |6 505-01/(S |g Twenty-five |t Husserl and Klein on the Origin and Structure of Non-symbolic Numbers -- |g [ʹ] 126 |t Husserl's Appeal to Acts of Collective Combination to Account for the Unity of the Whole of Each Authentic Cardinal Number -- |g [ʹ] 127 |t Husserl's Appeal to Psychological Experience to Account for the Origin of the Categorial Unity Belonging to the Concept of Ànything' Characteristic of the Units Proper to Multiplicities and Cardinal Numbers -- |g [ʹ] 128 |t Decisive Contrast between Husserl's and Klein's Accounts of the Being of the Units in Non-symbolic Numbers -- |g [ʹ] 129 |t Klein on Plato's Account of the Purity of Mathematical À -- |g [ʹ] 130 |t Klein on Plato's Account of the "Being One" of Each Mathematical À as Different from the "Being One" of Mathematical "Monads" -- |g [ʹ] 131 |t Klein on Plato's Account of the Non-mathematical Unity Responsible for the "Being One" of the Whole Belonging to Each À -- |g [ʹ] 132 |t Klein on Plato's Account of the Solution Provided by À E to the Aporias Raised by À M -- |g [ʹ] 133 |t Klein on Aristoτle's Account of the Inseparable Mode of the Being of À from Sensible Beings -- |g [ʹ] 134 |t Klein on Aristotle's Account of the Abstracted Mode of Being of Mathematical Objects -- |g [ʹ] 135 |t Klein on Aristotle's Critique of the Platonic Solution to the Problem of the Unity of an À-Assemblage -- |g [ʹ] 136 |t Klein on Aristotle's Answer to the Question of the Unity Belonging to À -- |g [ʹ] 137 |t Klein on Aristotle's Account of the Origination of the Mov as Measure -- |g ch. Twenty-six |t Structural Differences in Husserl's and Klein's Accounts of the Mode of Being of Non-symbolic Numbers -- |g [ʹ] 138 |t Different Accounts of the Mode of Being of the "One" in Husserl, Plato, and Aristotle -- |g [ʹ] 139 |t Different Accounts of the "Being One" and Ordered Sequence Characteristic of the Wholes Composing Non-symbolic Numbers in Husserl, Plato, and Aristotle -- |g [ʹ] 140 |t Different Accounts of the Conditions Responsible for the Scope of the Intelligibility of Non-symbolic Numbers in Husserl, Plato, and Aristotle -- |g [ʹ] 141 |t Structural Differences between Husserl's and Klein's Accounts of the Mode of Being of Non-symbolic Numbers -- |g [ʹ] 142 |t Divergence in Husserl's and Klein's Accounts of Non-symbolic Numbers -- |g ch. Twenty-seven |t Digression: The Development of Husserl's Thought, after Philosophy of Arithmetic, on the "Logical" Status of the Symbolic Calculus, the Constitution of Collective Unity, and the Phenomenological Foundation of the Mathesis Universalis -- |g [ʹ] 143 |t Need to Revisit the "Standard View" of the Development of Husserl's Thought -- |g ch. Twenty-eight |t Husserl's Accounts of the Symbolic Calculus, the Critique of Psychologism, and the Phenomenological Foundation of the Mathesis Universalis after Philosophy of Arithmetic -- |g [ʹ] 144 |t Husserl's Account of the Symbolic Calculus after Philosophy of Arithmetic -- |g [ʹ] 145 |t Husserl's Critique of Philosophy of Arithmetic's Psychologism -- |g [ʹ] 146 |t Husserl's Account of the Phenomenological Foundation of the Mathesis Universalis -- |g ch. Twenty-nine |t Husserl's Critique of Symbolic Calculation in his Schroder Review. |
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Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn753552176 |
|---|---|
| _version_ | 1816881770152329216 |
| adam_text | |
| any_adam_object | |
| author | Hopkins, Burt C. |
| author_GND | http://id.loc.gov/authorities/names/n92103122 |
| author_facet | Hopkins, Burt C. |
| author_role | aut |
| author_sort | Hopkins, Burt C. |
| author_variant | b c h bc bch |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9 .H66 2011eb |
| callnumber-search | QA9 .H66 2011eb |
| callnumber-sort | QA 19 H66 42011EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | pt. 1. Klein on Husserl's phenomenology and the history of science -- pt. 2. Husserl and Klein on the method and task of desedimenting the mathematization of nature -- pt. 3. Non-symbolic and symbolic numbers in Husserl and Klein -- pt. 4. Husserl and Klein on the origination of the logic of symbolic mathematics. |
| ctrlnum | (OCoLC)753552176 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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Hopkins.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Bloomington, Ind. :</subfield><subfield code="b">Indiana University Press,</subfield><subfield code="c">©2011.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxx, 559 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Studies in continental thought</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 545-552) and indexes.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="6">880-01</subfield><subfield code="a">pt. 1. 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code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=385454</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="880" ind1="0" ind2="0"><subfield code="6">505-00/(S</subfield><subfield code="g">Machine generated contents note:</subfield><subfield code="g">pt. One</subfield><subfield code="t">Klein on Husserl's Phenomenology and the History of Science --</subfield><subfield code="g">ch. One</subfield><subfield code="t">Klein's and Husserl's Investigations of the Origination of Mathematical Physics --</subfield><subfield code="g">[ʹ] 1</subfield><subfield code="t">Problem of History in Husserl's Last Writings --</subfield><subfield code="g">[ʹ] 2</subfield><subfield code="t">Priority of Klein's Research on the Historical Origination of the Meaning of Mathematical Physics over Husserl's --</subfield><subfield code="g">[ʹ] 3</subfield><subfield code="t">Importance of Husserl's Last Writings for Understanding Klein's Nontraditional Investigations of the History and Philosophy of Science --</subfield><subfield code="g">[ʹ] 4</subfield><subfield code="t">Klein's Commentary on Husserl's Investigation of the History of the Origin of Modern Science --</subfield><subfield code="g">[ʹ] 5</subfield><subfield code="t">"Curious" Relation between Klein's Historical Investigation of Greek and Modern Mathematics and Husserl's Phenomenology --</subfield><subfield code="g">ch. Two</subfield><subfield code="t">Klein's Account of the Essential Connection between Intentional and Actual History --</subfield><subfield code="g">[ʹ] 6</subfield><subfield code="t">Problem of Origin and History in Husserl's Phenomenology --</subfield><subfield code="g">[ʹ] 7</subfield><subfield code="t">Internal Motivation for Husserl's Seemingly Late Turn to History --</subfield><subfield code="g">ch. Three</subfield><subfield code="t">Liberation of the Problem of Origin from Its Naturalistic Distortion: The Phenomenological Problem of Constitution --</subfield><subfield code="g">[ʹ] 8</subfield><subfield code="t">Psychologism and the Problem of History --</subfield><subfield code="g">[ʹ] 9</subfield><subfield code="t">Internal Temporality and the Problem of the Sedimented History of Significance --</subfield><subfield code="g">ch. Four</subfield><subfield code="t">Essential Connection between Intentional and Actual History --</subfield><subfield code="g">[ʹ] 10</subfield><subfield code="t">Two Limits of the Investigation of the Temporal Genesis Proper to the Intrinsic Possibility of the Intentional Object --</subfield><subfield code="g">[ʹ] 11</subfield><subfield code="t">Transcendental Constitution of an Identical Object Exceeds the Sedimented Genesis of Its Temporal Form --</subfield><subfield code="g">[ʹ] 12</subfield><subfield code="t">Distinction between the Sedimented History of the Immediate Presence of an Intentional Object and the Sedimented History of Its Original Presentation --</subfield><subfield code="g">ch. Five</subfield><subfield code="t">Historicity of the Intelligibility of Ideal Significations and the Possibility of Actual History --</subfield><subfield code="g">[ʹ] 13</subfield><subfield code="t">Problem of Ìaτρia underlying Husserl's Concept of Intentional History --</subfield><subfield code="g">[ʹ] 14</subfield><subfield code="t">Two Senses of Historicity and the Meaning of the Historical Apriori --</subfield><subfield code="g">[ʹ] 15</subfield><subfield code="t">Historicity as Distinct from Both Historicism and the History of the Ego --</subfield><subfield code="g">ch. Six</subfield><subfield code="t">Sedimentation and the Link between Intentional History and the Constitution of a Historical Tradition --</subfield><subfield code="g">[ʹ] 16</subfield><subfield code="t">Maintaining the Integrity of Knowledge Requires Inquiry into Its Original Historical Discovery --</subfield><subfield code="g">[ʹ] 17</subfield><subfield code="t">Two Presuppositions Are Necessary to Account for the Historicity of the Discovery of the Ideal Objects of a Science Such as Geometry --</subfield><subfield code="g">[ʹ] 18</subfield><subfield code="t">Sedimentation and the Constitution of a Geometrical Tradition --</subfield><subfield code="g">[ʹ] 19</subfield><subfield code="t">Historical Apriori of Ideal Objects and Historical Facts --</subfield><subfield code="g">[ʹ] 20</subfield><subfield code="t">Historical Apriori Is Not a Concession to Historicism --</subfield><subfield code="g">ch. Seven</subfield><subfield code="t">Klein's Departure from the Content but Not the Method of Husserl's Intentional-Historical Analysis of Modern Science --</subfield><subfield code="g">[ʹ] 21</subfield><subfield code="t">Contrast between Klein's Account of the Actual Development of Modern Science and Husserl's Intentional Account --</subfield><subfield code="g">[ʹ] 22</subfield><subfield code="t">Sedimentation and the Method of Symbolic Abstraction --</subfield><subfield code="g">[ʹ] 23</subfield><subfield code="t">Establishment of Modern Physics on the Foundation of a Radical Reinterpretation of Ancient Mathematics --</subfield><subfield code="g">[ʹ] 24</subfield><subfield code="t">Vieta's and Descartes's Inauguration of the Development of the Symbolic Science of Nature: Mathematical Physics --</subfield><subfield code="g">[ʹ] 25</subfield><subfield code="t">Open Questions in Kleins Account of the Actual Development of Modern Science --</subfield><subfield code="g">pt. Two</subfield><subfield code="t">Husserl and Klein on the Method and Task of Desedimenting the Mathematization of Nature --</subfield><subfield code="g">ch. Eight</subfield><subfield code="t">Klein's Historical-Mathematical Investigations in the Context of Husserl's Phenomenology of Science --</subfield><subfield code="g">[ʹ] 26</subfield><subfield code="t">Summary of Part One --</subfield><subfield code="g">[ʹ] 27</subfield><subfield code="t">Klein's Failure to Refer to Husserl in Greek Mathematical Thought and the Origin of Algebra --</subfield><subfield code="g">[ʹ] 28</subfield><subfield code="t">Critical Implications of Klein's Historical Research for Husserl's Phenomenology --</subfield><subfield code="g">ch. Nine</subfield><subfield code="t">Basic Problem and Method of Klein's Mathematical Investigations --</subfield><subfield code="g">[ʹ] 29</subfield><subfield code="t">Klein's Account of the Limited Task of Recovering the Hidden Sources of Modern Symbolic Mathematics --</subfield><subfield code="g">[ʹ] 30</subfield><subfield code="t">Klein's Motivation for the Radical Investigation of the Origins of Mathematical Physics --</subfield><subfield code="g">[ʹ] 31</subfield><subfield code="t">Conceptual Battleground on Which the Scholastic and the New Science Fought --</subfield><subfield code="g">ch. Ten</subfield><subfield code="t">Husserl's Formulation of the Nature and Roots of the Crisis of European Sciences --</subfield><subfield code="g">[ʹ] 32</subfield><subfield code="t">Klein's Uncanny Anticipation of Husserl's Treatment of the Historical Origins of Scientific Concepts in the Crisis --</subfield><subfield code="g">[ʹ] 33</subfield><subfield code="t">Historical Reference Back to Origins and the Crisis of Modern Science --</subfield><subfield code="g">[ʹ] 34</subfield><subfield code="t">Husserl's Reactivation of the Sedimented Origins of the Modern Spirit --</subfield><subfield code="g">[ʹ] 35</subfield><subfield code="t">Husserl's Fragmentary Analyses of the Sedimentation Responsible for the Formalized Meaning Formations of Modern Mathematics and Klein's Inquiry into Their Origin and Conceptual Structure --</subfield><subfield code="g">ch. Eleven</subfield><subfield code="t">"Zigzag" Movement Implicit in Klein's Mathematical Investigations --</subfield><subfield code="g">[ʹ] 36</subfield><subfield code="t">Structure of Klein's Method of Historical Reflection in Greek Mathematical Thought and the Origin of Algebra --</subfield><subfield code="g">ch. Twelve</subfield><subfield code="t">Husserl and Klein on the Logic of Symbolic Mathematics --</subfield><subfield code="g">[ʹ] 37</subfield><subfield code="t">Husserl's Systematic Attempt to Ground the Symbolic Concept of Number in the Concept of Anzahl --</subfield><subfield code="g">[ʹ] 38</subfield><subfield code="t">Klein on the Transformation of the Ancient Concept of Aρiθuos (Anzahl) into the Modern Concept of Symbolic Number --</subfield><subfield code="g">[ʹ] 39</subfield><subfield code="t">Transition to Part Three of This Study --</subfield><subfield code="g">pt. Three</subfield><subfield code="t">Non-symbolic and Symbolic Numbers in Husserl and Klein --</subfield><subfield code="g">ch. Thirteen</subfield><subfield code="t">Authentic and Symbolic Numbers in Husserl's Philosophy of Arithmetic --</subfield><subfield code="g">[ʹ] 40</subfield><subfield code="t">Shortcomings of Philosophy of Arithmetic and Our Basic Concern --</subfield><subfield code="g">[ʹ] 41</subfield><subfield code="t">Husserl on the Authentic Concepts of Multiplicity and Cardinal Number Concepts, and Inauthentic (Symbolic) Number Concepts --</subfield><subfield code="g">[ʹ] 42</subfield><subfield code="t">Basic Logical Problem in Philosophy of Arithmetic --</subfield><subfield code="g">[ʹ] 43</subfield><subfield code="t">Fundamental Shift in Husserl's Account of Calculational Technique --</subfield><subfield code="g">[ʹ] 44</subfield><subfield code="t">Husserl's Account of the Logical Requirements behind Both Calculational Technique and Symbolic Numbers --</subfield><subfield code="g">[ʹ] 45</subfield><subfield code="t">Husseris Psychological Account of the Logical Whole Proper to the Concept of Multiplicity and Authentic Cardinal Number Concepts --</subfield><subfield code="g">[ʹ] 46</subfield><subfield code="t">Husserl on the Psychological Basis for Symbolic Numbers and Logical Technique --</subfield><subfield code="g">[ʹ] 47</subfield><subfield code="t">Husserl on the Symbolic Presentation of Multitudes --</subfield><subfield code="g">[ʹ] 48</subfield><subfield code="t">Husserl on the Psychological Presentation of Symbolic Numbers --</subfield><subfield code="g">[ʹ] 49</subfield><subfield code="t">Husserl on the Symbolic Presentation of the Systematic Construction of New Number Concepts and Their Designation --</subfield><subfield code="g">[ʹ] 50</subfield><subfield code="t">Fundamental Shift in the Logic of Symbolic Numbers Brought about by the Independence of Signitively Symbolic Numbers --</subfield><subfield code="g">[ʹ] 51</subfield><subfield code="t">Unresolved Question of the Logical Foundation for Signitively Symbolic Numbers --</subfield><subfield code="g">[ʹ] 52</subfield><subfield code="t">Summary and Conclusion --</subfield><subfield code="g">ch. Fourteen</subfield><subfield code="t">Klein's Desedimentation of the Origin of Algebra and Husserl's Failure to Ground Symbolic Calculation in Authentic Numbers --</subfield><subfield code="g">[ʹ] 53</subfield><subfield code="t">Implications of Kleins Desedimentation of the Origin of Algebra for Husserl's Analyses of the Concept Proper to Number in Philosophy of Arithmetic --</subfield><subfield code="g">[ʹ] 54</subfield><subfield code="t">Klein's Desedimentation of the Two Salient Features of the Foundations of Greek Mathematics --</subfield><subfield code="g">ch. Fifteen</subfield><subfield code="t">Logistic and Arithmetic in Neoplatonic Mathematics and in Plato --</subfield><subfield code="g">[ʹ] 55</subfield><subfield code="t">Opposition between Logistic and Arithmetic in Neoplatonic Thought --</subfield><subfield code="g">[ʹ] 56</subfield><subfield code="t">Logistic and Arithmetic in Plato --</subfield><subfield code="g">[ʹ] 57</subfield><subfield code="t">Tensions and Issues Surrounding the Role of the Theory of Proportions in Nicomachus, Theon, and Domninus --</subfield><subfield code="g">ch.</subfield></datafield><datafield tag="880" ind1="0" ind2="0"><subfield code="6">505-00/(S</subfield><subfield code="t">Sixteen</subfield><subfield code="t">Theoretical Logistic and the Problem of Fractions --</subfield><subfield code="g">[ʹ] 58</subfield><subfield code="t">Ambiguous Relationship between Logistic and Arithmetic in Neoplatonic Mathematics and in Plato --</subfield><subfield code="g">[ʹ] 59</subfield><subfield code="t">Obstacle Presented by Fractions to Plato's Demand for a Theoretical Logistic --</subfield><subfield code="g">ch. Seventeen</subfield><subfield code="t">Concept of Aρiθuos --</subfield><subfield code="g">[ʹ] 60</subfield><subfield code="t">Connection between Neoplatonic Mathematics and Plato's Ontology --</subfield><subfield code="g">[ʹ] 61</subfield><subfield code="t">Counting as the Fundamental Phenomenon Determining the Meaning of Aρiθuos --</subfield><subfield code="g">[ʹ] 62</subfield><subfield code="t">"Pure" Aρiθuos --</subfield><subfield code="g">[ʹ] 63</subfield><subfield code="t">Why Greek Theoretical Arithmetic and Logistic Did Not Directly Study Aρiθuos --</subfield><subfield code="g">ch. Eighteen</subfield><subfield code="t">Plato's Ontological Conception of Aρiθuos --</subfield><subfield code="g">[ʹ] 64</subfield><subfield code="t">Interdependence of Greek Mathematics and Greek Ontology --</subfield><subfield code="g">[ʹ] 65</subfield><subfield code="t">Pythagorean Context of Plato's Philosophy --</subfield><subfield code="g">[ʹ] 66</subfield><subfield code="t">Plato's Departure from Pythagorean Science: The Fundamental Role of Aρiθuos of Pure Monads --</subfield><subfield code="g">[ʹ] 67</subfield><subfield code="t">Δiavoia as the Soul's Initial Mode of Access to Noητ --</subfield><subfield code="g">[ʹ] 68</subfield><subfield code="t">Limits Inherent in the Dianoetic Mode of Access to Noητ --</subfield><subfield code="g">ch. Nineteen</subfield><subfield code="t">Klein's Reactivation of Plato's Theory of Aρiθuos Eiητκo --</subfield><subfield code="g">[ʹ] 69</subfield><subfield code="t">Inability of Mathematical Thought to Account for the Mode of Being of Its Objects --</subfield><subfield code="g">[ʹ] 70</subfield><subfield code="t">Curious Kind of Koα Manifest in Aρiθuos --</subfield><subfield code="g">[ʹ] 71</subfield><subfield code="t">Koα Exemplified by Aρiθuos as the Key to Solving the Problem of Mθξε --</subfield><subfield code="g">[ʹ] 72</subfield><subfield code="t">Koα Exemplified by ̀'Aρiθuos Contains the Clue to the "Mixing" of Being and Non-being in the Image --</subfield><subfield code="g">[ʹ] 73</subfield><subfield code="t">Partial Clarification of the Aporia of Being and Non-being Holds the Key to the "Arithmetical" Structure of the Noητv's Mode of Being.</subfield></datafield><datafield tag="880" ind1="0" ind2="0"><subfield code="6">505-00/(S</subfield><subfield code="g">Contents note continued:</subfield><subfield code="g">[ʹ] 74</subfield><subfield code="t">Koα among "Ov, Kvητ, and Στ, Composes the Relationship of Being and Non-being --</subfield><subfield code="g">[ʹ] 75</subfield><subfield code="t">Contrast between Aρθm Mαθ and Aρθm E --</subfield><subfield code="g">[ʹ] 76</subfield><subfield code="t">Foundational Function of Aρiθuos E --</subfield><subfield code="g">[ʹ] 77</subfield><subfield code="t">Order of Aρiθuos' E Provides the Foundation for Both the Sequence of Mathematical À and the Relation of Family Descent between Higher and Lower --</subfield><subfield code="g">[ʹ] 78</subfield><subfield code="t">Inability of the A, to "Count" the M Points to Its Limits and Simultaneously Presents the First A E --</subfield><subfield code="g">[ʹ] 79</subfield><subfield code="t">Θατερoν as the "Twofold in General" Allows for the Articulation of Being and Non-being --</subfield><subfield code="g">[ʹ] 80</subfield><subfield code="t">Recognizing "the Other" as the "Indeterminate Dyad" --</subfield><subfield code="g">[ʹ] 81</subfield><subfield code="t">"One Itself" as the Source of the Generation of "A E --</subfield><subfield code="g">[ʹ] 82</subfield><subfield code="t">Γενη À E Provide the Foundation of an Eidetic Logistic --</subfield><subfield code="g">[ʹ] 83</subfield><subfield code="t">Plato's Postulate of the Separation of All Noetic Formations Renders Incomprehensible the Ordinary Mode of Predication --</subfield><subfield code="g">ch. Twenty</subfield><subfield code="t">Aristotle's Critique of the Platonic Chorismos Thesis and the Possibility of a Theoretical Logistic --</subfield><subfield code="g">[ʹ] 84</subfield><subfield code="t">Point of Departure and Overview of Aristotle's Critique --</subfield><subfield code="g">[ʹ] 85</subfield><subfield code="t">Aristode's Problematic: Harmonizing the Ontological Dependence of À with Their Pure Noetic Quality --</subfield><subfield code="g">[ʹ] 86</subfield><subfield code="t">Aristotle on the Abstractive Mode of Being of Mathematical Objects --</subfield><subfield code="g">[ʹ] 87</subfield><subfield code="t">Aristotle's Ontological Determination of the Non-generic Unity of À --</subfield><subfield code="g">[ʹ] 88</subfield><subfield code="t">Aristotle's Ontological Determination of the Unity of À as Common Measure --</subfield><subfield code="g">[ʹ] 89</subfield><subfield code="t">Aristotle's Ontological Determination of the Indivisibility and Exactness of "Pure" À --</subfield><subfield code="g">[ʹ] 90</subfield><subfield code="t">Influence of Aristotle's View of M on Theoretical Arithmetic --</subfield><subfield code="g">[ʹ] 91</subfield><subfield code="t">Aristotle's Ontological Conception of À Makes Possible Theoretical Logistic --</subfield><subfield code="g">ch. Twenty-one</subfield><subfield code="t">Klein's Interpretation of Diophantus's Arithmetic --</subfield><subfield code="g">[ʹ] 92</subfield><subfield code="t">Access to Diophantus's Work Requires Reinterpreting It outside the Context of Mathematics' Self-interpretation since Vieta, Stevin, and Descartes --</subfield><subfield code="g">[ʹ] 93</subfield><subfield code="t">Diophantus's Arithmetic as Theoretical Logistic --</subfield><subfield code="g">[ʹ] 94</subfield><subfield code="t">Referent and Operative Mode of Being of Diophantus's Concept of À --</subfield><subfield code="g">[ʹ] 95</subfield><subfield code="t">Ultimate Determinacy of Diophantus's Concept of Unknown and Indeterminate À --</subfield><subfield code="g">[ʹ] 96</subfield><subfield code="t">Merely Instrumental, and Therefore Non-ontological and Non-symbolic, Status of the E-Concept in Diophantus's Calculations --</subfield><subfield code="g">ch. Twenty-two</subfield><subfield code="t">Klein's Account of Vieta's Reinterpretation of the Diophantine Procedure and the Consequent Establishment of Algebra as the General Analytical Art --</subfield><subfield code="g">[ʹ] 97</subfield><subfield code="t">Significance of Vieta's Generalization of the E-Concept and Its Transformation into the Symbolic Concept of Species --</subfield><subfield code="g">[ʹ] 98</subfield><subfield code="t">Sedimentation of the Ancient Practical Distinction between S̀aying' and ̀Thinking' in the Symbolic Notation Inseparable from Vieta's Concept of Number --</subfield><subfield code="g">[ʹ] 99</subfield><subfield code="t">Decisive Difference between Vieta's Conception of a "General" Mathematical Discipline and the Ancient Idea of a K I --</subfield><subfield code="g">[ʹ] 100</subfield><subfield code="t">Occlusion of the Ancient Connection between the Theme of General Mathematics and the Foundational Concerns of the "Supreme" Science That Results from the Modern Understanding of Vieta's "Analytical Art" as Mathesis Universalis --</subfield><subfield code="g">[ʹ] 101</subfield><subfield code="t">Vieta's Ambiguous Relation to Ancient Greek Mathematics --</subfield><subfield code="g">[ʹ] 102</subfield><subfield code="t">Vieta's Comparison of Ancient Geometrical Analysis with the Diophantine Procedure --</subfield><subfield code="g">[ʹ] 103</subfield><subfield code="t">Vieta's Transformation of the Diophantine Procedure --</subfield><subfield code="g">[ʹ] 104</subfield><subfield code="t">Auxiliary Status of Vieta's Employment of the "General Analytic" --</subfield><subfield code="g">[ʹ] 105</subfield><subfield code="t">Influence of the General Theory of Proportions on Vieta's "Pure," "General" Algebra --</subfield><subfield code="g">[ʹ] 106</subfield><subfield code="t">Klein's Desedimentation of the Conceptual Presuppositions Belonging to Vieta's Interpretation of Diophantine Logistic --</subfield><subfield code="g">ch. Twenty-three</subfield><subfield code="t">Klein's Account of the Concept of Number and the Number Concepts in Stevin, Descartes, and Wallis --</subfield><subfield code="g">[ʹ] 107</subfield><subfield code="t">Stevin's Idea of a "Wise Age" and His Project for Its Renewal --</subfield><subfield code="g">[ʹ] 108</subfield><subfield code="t">Stevin's Critique of the Traditional À-Concept --</subfield><subfield code="g">[ʹ] 109</subfield><subfield code="t">Stevin's Symbolic Understanding of Numerus --</subfield><subfield code="g">[ʹ] 110</subfield><subfield code="t">Stevin's Assimilation of Numbers to Geometrical Formations --</subfield><subfield code="g">[ʹ] 111</subfield><subfield code="t">Descartes's Postulation of a New Mode of "Abstraction" and a New Possibility of "Understanding" as Underlying Symbolic Calculation --</subfield><subfield code="g">[ʹ] 112</subfield><subfield code="t">Fundamental Cognitive Role Attributed by Descartes to the Imaginatio --</subfield><subfield code="g">[ʹ] 113</subfield><subfield code="t">Descartes on the Pure Intellect's Use of the Power of the Imagination to Reconcile the Mathematical Problem of Determinacy and Indeterminacy --</subfield><subfield code="g">[ʹ] 114</subfield><subfield code="t">Klein's Reactivation of the "Abstraction" in Descartes as "Symbolic Abstraction" --</subfield><subfield code="g">[ʹ] 115</subfield><subfield code="t">Klein's Use of the Scholastic Distinction between "First and Second Intentions" to Fix Conceptually the Status of Descartes's Symbolic Concepts --</subfield><subfield code="g">[ʹ] 116</subfield><subfield code="t">Descartes on the Non-metaphorical Reception by the Imagination of the Extension of Bodies as Bridging the Gap between Non-determinate and Determinate Magnitudes --</subfield><subfield code="g">[ʹ] 117</subfield><subfield code="t">Wallis's Completion of the Introduction of the New Number Concept --</subfield><subfield code="g">[ʹ] 118</subfield><subfield code="t">Wallis's Initial Account of the Unit Both as the Principle of Number and as Itself a Number --</subfield><subfield code="g">[ʹ] 119</subfield><subfield code="t">Wallis's Account of the Nought as Also the Principle of Number --</subfield><subfield code="g">[ʹ] 120</subfield><subfield code="t">Wallis's Emphasis on the Arithmetical Status of the Symbol or Species of the "General Analytic" --</subfield><subfield code="g">[ʹ] 121</subfield><subfield code="t">Homogeneity of Algebraic Numbers as Rooted for Wallis in the Unity of the Sign Character of Their Symbols --</subfield><subfield code="g">[ʹ] 122</subfield><subfield code="t">Wallis's Understanding of Algebraic Numbers as Symbolically Conceived Ratios --</subfield><subfield code="g">pt. Four</subfield><subfield code="t">Husserl and Klein on the Origination of the Logic of Symbolic Mathematics --</subfield><subfield code="g">ch. Twenty-four</subfield><subfield code="t">Husserl and Klein on the Fundamental Difference between Symbolic and Non-symbolic Numbers --</subfield><subfield code="g">[ʹ] 123</subfield><subfield code="t">Klein's Critical Appropriation of Husserl's Crisis Seen within the Context of the Results of Klein's Investigation of the Origin of Algebra --</subfield><subfield code="g">[ʹ] 124</subfield><subfield code="t">Husserl and Klein on the Difference between Non-symbolic and symbolic Numbers --</subfield><subfield code="g">[ʹ] 125</subfield><subfield code="t">Husserl on the Authentic Cardinal Number Concept and Klein on the Greek À-Concept --</subfield><subfield code="g">ch.</subfield></datafield><datafield tag="880" ind1="0" ind2="0"><subfield code="6">505-01/(S</subfield><subfield code="g">Twenty-five</subfield><subfield code="t">Husserl and Klein on the Origin and Structure of Non-symbolic Numbers --</subfield><subfield code="g">[ʹ] 126</subfield><subfield code="t">Husserl's Appeal to Acts of Collective Combination to Account for the Unity of the Whole of Each Authentic Cardinal Number --</subfield><subfield code="g">[ʹ] 127</subfield><subfield code="t">Husserl's Appeal to Psychological Experience to Account for the Origin of the Categorial Unity Belonging to the Concept of Ànything' Characteristic of the Units Proper to Multiplicities and Cardinal Numbers --</subfield><subfield code="g">[ʹ] 128</subfield><subfield code="t">Decisive Contrast between Husserl's and Klein's Accounts of the Being of the Units in Non-symbolic Numbers --</subfield><subfield code="g">[ʹ] 129</subfield><subfield code="t">Klein on Plato's Account of the Purity of Mathematical À --</subfield><subfield code="g">[ʹ] 130</subfield><subfield code="t">Klein on Plato's Account of the "Being One" of Each Mathematical À as Different from the "Being One" of Mathematical "Monads" --</subfield><subfield code="g">[ʹ] 131</subfield><subfield code="t">Klein on Plato's Account of the Non-mathematical Unity Responsible for the "Being One" of the Whole Belonging to Each À --</subfield><subfield code="g">[ʹ] 132</subfield><subfield code="t">Klein on Plato's Account of the Solution Provided by À E to the Aporias Raised by À M --</subfield><subfield code="g">[ʹ] 133</subfield><subfield code="t">Klein on Aristoτle's Account of the Inseparable Mode of the Being of À from Sensible Beings --</subfield><subfield code="g">[ʹ] 134</subfield><subfield code="t">Klein on Aristotle's Account of the Abstracted Mode of Being of Mathematical Objects --</subfield><subfield code="g">[ʹ] 135</subfield><subfield code="t">Klein on Aristotle's Critique of the Platonic Solution to the Problem of the Unity of an À-Assemblage --</subfield><subfield code="g">[ʹ] 136</subfield><subfield code="t">Klein on Aristotle's Answer to the Question of the Unity Belonging to À --</subfield><subfield code="g">[ʹ] 137</subfield><subfield code="t">Klein on Aristotle's Account of the Origination of the Mov as Measure --</subfield><subfield code="g">ch. Twenty-six</subfield><subfield code="t">Structural Differences in Husserl's and Klein's Accounts of the Mode of Being of Non-symbolic Numbers --</subfield><subfield code="g">[ʹ] 138</subfield><subfield code="t">Different Accounts of the Mode of Being of the "One" in Husserl, Plato, and Aristotle --</subfield><subfield code="g">[ʹ] 139</subfield><subfield code="t">Different Accounts of the "Being One" and Ordered Sequence Characteristic of the Wholes Composing Non-symbolic Numbers in Husserl, Plato, and Aristotle --</subfield><subfield code="g">[ʹ] 140</subfield><subfield code="t">Different Accounts of the Conditions Responsible for the Scope of the Intelligibility of Non-symbolic Numbers in Husserl, Plato, and Aristotle --</subfield><subfield code="g">[ʹ] 141</subfield><subfield code="t">Structural Differences between Husserl's and Klein's Accounts of the Mode of Being of Non-symbolic Numbers --</subfield><subfield code="g">[ʹ] 142</subfield><subfield code="t">Divergence in Husserl's and Klein's Accounts of Non-symbolic Numbers --</subfield><subfield code="g">ch. Twenty-seven</subfield><subfield code="t">Digression: The Development of Husserl's Thought, after Philosophy of Arithmetic, on the "Logical" Status of the Symbolic Calculus, the Constitution of Collective Unity, and the Phenomenological Foundation of the Mathesis Universalis --</subfield><subfield code="g">[ʹ] 143</subfield><subfield code="t">Need to Revisit the "Standard View" of the Development of Husserl's Thought --</subfield><subfield code="g">ch. Twenty-eight</subfield><subfield code="t">Husserl's Accounts of the Symbolic Calculus, the Critique of Psychologism, and the Phenomenological Foundation of the Mathesis Universalis after Philosophy of Arithmetic --</subfield><subfield code="g">[ʹ] 144</subfield><subfield code="t">Husserl's Account of the Symbolic Calculus after Philosophy of Arithmetic --</subfield><subfield code="g">[ʹ] 145</subfield><subfield code="t">Husserl's Critique of Philosophy of Arithmetic's Psychologism --</subfield><subfield code="g">[ʹ] 146</subfield><subfield code="t">Husserl's Account of the Phenomenological Foundation of the Mathesis Universalis --</subfield><subfield code="g">ch. Twenty-nine</subfield><subfield code="t">Husserl's Critique of Symbolic Calculation in his Schroder Review.</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">6931763</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Project MUSE</subfield><subfield code="b">MUSE</subfield><subfield code="n">muse22258</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">385454</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10492910</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Coutts Information Services</subfield><subfield code="b">COUT</subfield><subfield code="n">18528488</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Recorded Books, LLC</subfield><subfield code="b">RECE</subfield><subfield code="n">rbeEB00777686</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Internet Archive</subfield><subfield code="b">INAR</subfield><subfield code="n">originoflogicofs0000hopk</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| geographic | Griechenland Altertum gnd |
| geographic_facet | Griechenland Altertum |
| id | ZDB-4-EBA-ocn753552176 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:18:00Z |
| institution | BVB |
| isbn | 9780253005274 0253005272 1283235900 9781283235907 9786613235909 6613235903 |
| language | English |
| oclc_num | 753552176 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxx, 559 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Indiana University Press, |
| record_format | marc |
| series | Studies in Continental thought. |
| series2 | Studies in continental thought |
| spelling | Hopkins, Burt C., author. http://id.loc.gov/authorities/names/n92103122 The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / Burt C. Hopkins. Bloomington, Ind. : Indiana University Press, ©2011. 1 online resource (xxx, 559 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Studies in continental thought Includes bibliographical references (pages 545-552) and indexes. Print version record. 880-01 pt. 1. Klein on Husserl's phenomenology and the history of science -- pt. 2. Husserl and Klein on the method and task of desedimenting the mathematization of nature -- pt. 3. Non-symbolic and symbolic numbers in Husserl and Klein -- pt. 4. Husserl and Klein on the origination of the logic of symbolic mathematics. Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts-especially mathematical concepts and the process of mathematical abstraction that generates them-have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkin. English. Husserl, Edmund 1859-1938 gnd Husserl, Edmund. idszbz Klein, Jacob. idszbz Klein, Jacob (Philosoph) (DE-604)BV0087245 swd Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Logique symbolique et mathématique. Mathématiques Philosophie. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh PHILOSOPHY Movements Phenomenology. bisacsh Logic, Symbolic and mathematical fast Mathematics Philosophy fast Computeralgebra gnd Logik gnd http://d-nb.info/gnd/4036202-4 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Rezeption gnd Zahlentheorie gnd http://d-nb.info/gnd/4067277-3 Griechenland Altertum gnd Mathematische Logik. idszbz Mathematik. idszbz Philosophie. idszbz Symbolisk logik. sao Matematik teori, filosofi. sao has work: The origin of the logic of symbolic mathematics (Text) https://id.oclc.org/worldcat/entity/E39PCGYm7hTY37hhJbpJbtg3gq https://id.oclc.org/worldcat/ontology/hasWork Print version: Hopkins, Burt C. Origin of the logic of symbolic mathematics. Bloomington, Ind. : Indiana University Press, ©2011 9780253356710 (DLC) 2011022942 (OCoLC)692291398 Studies in Continental thought. http://id.loc.gov/authorities/names/n88508712 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=385454 Volltext 505-00/(S Machine generated contents note: pt. One Klein on Husserl's Phenomenology and the History of Science -- ch. One Klein's and Husserl's Investigations of the Origination of Mathematical Physics -- [ʹ] 1 Problem of History in Husserl's Last Writings -- [ʹ] 2 Priority of Klein's Research on the Historical Origination of the Meaning of Mathematical Physics over Husserl's -- [ʹ] 3 Importance of Husserl's Last Writings for Understanding Klein's Nontraditional Investigations of the History and Philosophy of Science -- [ʹ] 4 Klein's Commentary on Husserl's Investigation of the History of the Origin of Modern Science -- [ʹ] 5 "Curious" Relation between Klein's Historical Investigation of Greek and Modern Mathematics and Husserl's Phenomenology -- ch. Two Klein's Account of the Essential Connection between Intentional and Actual History -- [ʹ] 6 Problem of Origin and History in Husserl's Phenomenology -- [ʹ] 7 Internal Motivation for Husserl's Seemingly Late Turn to History -- ch. Three Liberation of the Problem of Origin from Its Naturalistic Distortion: The Phenomenological Problem of Constitution -- [ʹ] 8 Psychologism and the Problem of History -- [ʹ] 9 Internal Temporality and the Problem of the Sedimented History of Significance -- ch. Four Essential Connection between Intentional and Actual History -- [ʹ] 10 Two Limits of the Investigation of the Temporal Genesis Proper to the Intrinsic Possibility of the Intentional Object -- [ʹ] 11 Transcendental Constitution of an Identical Object Exceeds the Sedimented Genesis of Its Temporal Form -- [ʹ] 12 Distinction between the Sedimented History of the Immediate Presence of an Intentional Object and the Sedimented History of Its Original Presentation -- ch. Five Historicity of the Intelligibility of Ideal Significations and the Possibility of Actual History -- [ʹ] 13 Problem of Ìaτρia underlying Husserl's Concept of Intentional History -- [ʹ] 14 Two Senses of Historicity and the Meaning of the Historical Apriori -- [ʹ] 15 Historicity as Distinct from Both Historicism and the History of the Ego -- ch. Six Sedimentation and the Link between Intentional History and the Constitution of a Historical Tradition -- [ʹ] 16 Maintaining the Integrity of Knowledge Requires Inquiry into Its Original Historical Discovery -- [ʹ] 17 Two Presuppositions Are Necessary to Account for the Historicity of the Discovery of the Ideal Objects of a Science Such as Geometry -- [ʹ] 18 Sedimentation and the Constitution of a Geometrical Tradition -- [ʹ] 19 Historical Apriori of Ideal Objects and Historical Facts -- [ʹ] 20 Historical Apriori Is Not a Concession to Historicism -- ch. Seven Klein's Departure from the Content but Not the Method of Husserl's Intentional-Historical Analysis of Modern Science -- [ʹ] 21 Contrast between Klein's Account of the Actual Development of Modern Science and Husserl's Intentional Account -- [ʹ] 22 Sedimentation and the Method of Symbolic Abstraction -- [ʹ] 23 Establishment of Modern Physics on the Foundation of a Radical Reinterpretation of Ancient Mathematics -- [ʹ] 24 Vieta's and Descartes's Inauguration of the Development of the Symbolic Science of Nature: Mathematical Physics -- [ʹ] 25 Open Questions in Kleins Account of the Actual Development of Modern Science -- pt. Two Husserl and Klein on the Method and Task of Desedimenting the Mathematization of Nature -- ch. Eight Klein's Historical-Mathematical Investigations in the Context of Husserl's Phenomenology of Science -- [ʹ] 26 Summary of Part One -- [ʹ] 27 Klein's Failure to Refer to Husserl in Greek Mathematical Thought and the Origin of Algebra -- [ʹ] 28 Critical Implications of Klein's Historical Research for Husserl's Phenomenology -- ch. Nine Basic Problem and Method of Klein's Mathematical Investigations -- [ʹ] 29 Klein's Account of the Limited Task of Recovering the Hidden Sources of Modern Symbolic Mathematics -- [ʹ] 30 Klein's Motivation for the Radical Investigation of the Origins of Mathematical Physics -- [ʹ] 31 Conceptual Battleground on Which the Scholastic and the New Science Fought -- ch. Ten Husserl's Formulation of the Nature and Roots of the Crisis of European Sciences -- [ʹ] 32 Klein's Uncanny Anticipation of Husserl's Treatment of the Historical Origins of Scientific Concepts in the Crisis -- [ʹ] 33 Historical Reference Back to Origins and the Crisis of Modern Science -- [ʹ] 34 Husserl's Reactivation of the Sedimented Origins of the Modern Spirit -- [ʹ] 35 Husserl's Fragmentary Analyses of the Sedimentation Responsible for the Formalized Meaning Formations of Modern Mathematics and Klein's Inquiry into Their Origin and Conceptual Structure -- ch. Eleven "Zigzag" Movement Implicit in Klein's Mathematical Investigations -- [ʹ] 36 Structure of Klein's Method of Historical Reflection in Greek Mathematical Thought and the Origin of Algebra -- ch. Twelve Husserl and Klein on the Logic of Symbolic Mathematics -- [ʹ] 37 Husserl's Systematic Attempt to Ground the Symbolic Concept of Number in the Concept of Anzahl -- [ʹ] 38 Klein on the Transformation of the Ancient Concept of Aρiθuos (Anzahl) into the Modern Concept of Symbolic Number -- [ʹ] 39 Transition to Part Three of This Study -- pt. Three Non-symbolic and Symbolic Numbers in Husserl and Klein -- ch. Thirteen Authentic and Symbolic Numbers in Husserl's Philosophy of Arithmetic -- [ʹ] 40 Shortcomings of Philosophy of Arithmetic and Our Basic Concern -- [ʹ] 41 Husserl on the Authentic Concepts of Multiplicity and Cardinal Number Concepts, and Inauthentic (Symbolic) Number Concepts -- [ʹ] 42 Basic Logical Problem in Philosophy of Arithmetic -- [ʹ] 43 Fundamental Shift in Husserl's Account of Calculational Technique -- [ʹ] 44 Husserl's Account of the Logical Requirements behind Both Calculational Technique and Symbolic Numbers -- [ʹ] 45 Husseris Psychological Account of the Logical Whole Proper to the Concept of Multiplicity and Authentic Cardinal Number Concepts -- [ʹ] 46 Husserl on the Psychological Basis for Symbolic Numbers and Logical Technique -- [ʹ] 47 Husserl on the Symbolic Presentation of Multitudes -- [ʹ] 48 Husserl on the Psychological Presentation of Symbolic Numbers -- [ʹ] 49 Husserl on the Symbolic Presentation of the Systematic Construction of New Number Concepts and Their Designation -- [ʹ] 50 Fundamental Shift in the Logic of Symbolic Numbers Brought about by the Independence of Signitively Symbolic Numbers -- [ʹ] 51 Unresolved Question of the Logical Foundation for Signitively Symbolic Numbers -- [ʹ] 52 Summary and Conclusion -- ch. Fourteen Klein's Desedimentation of the Origin of Algebra and Husserl's Failure to Ground Symbolic Calculation in Authentic Numbers -- [ʹ] 53 Implications of Kleins Desedimentation of the Origin of Algebra for Husserl's Analyses of the Concept Proper to Number in Philosophy of Arithmetic -- [ʹ] 54 Klein's Desedimentation of the Two Salient Features of the Foundations of Greek Mathematics -- ch. Fifteen Logistic and Arithmetic in Neoplatonic Mathematics and in Plato -- [ʹ] 55 Opposition between Logistic and Arithmetic in Neoplatonic Thought -- [ʹ] 56 Logistic and Arithmetic in Plato -- [ʹ] 57 Tensions and Issues Surrounding the Role of the Theory of Proportions in Nicomachus, Theon, and Domninus -- ch. 505-00/(S Sixteen Theoretical Logistic and the Problem of Fractions -- [ʹ] 58 Ambiguous Relationship between Logistic and Arithmetic in Neoplatonic Mathematics and in Plato -- [ʹ] 59 Obstacle Presented by Fractions to Plato's Demand for a Theoretical Logistic -- ch. Seventeen Concept of Aρiθuos -- [ʹ] 60 Connection between Neoplatonic Mathematics and Plato's Ontology -- [ʹ] 61 Counting as the Fundamental Phenomenon Determining the Meaning of Aρiθuos -- [ʹ] 62 "Pure" Aρiθuos -- [ʹ] 63 Why Greek Theoretical Arithmetic and Logistic Did Not Directly Study Aρiθuos -- ch. Eighteen Plato's Ontological Conception of Aρiθuos -- [ʹ] 64 Interdependence of Greek Mathematics and Greek Ontology -- [ʹ] 65 Pythagorean Context of Plato's Philosophy -- [ʹ] 66 Plato's Departure from Pythagorean Science: The Fundamental Role of Aρiθuos of Pure Monads -- [ʹ] 67 Δiavoia as the Soul's Initial Mode of Access to Noητ -- [ʹ] 68 Limits Inherent in the Dianoetic Mode of Access to Noητ -- ch. Nineteen Klein's Reactivation of Plato's Theory of Aρiθuos Eiητκo -- [ʹ] 69 Inability of Mathematical Thought to Account for the Mode of Being of Its Objects -- [ʹ] 70 Curious Kind of Koα Manifest in Aρiθuos -- [ʹ] 71 Koα Exemplified by Aρiθuos as the Key to Solving the Problem of Mθξε -- [ʹ] 72 Koα Exemplified by ̀'Aρiθuos Contains the Clue to the "Mixing" of Being and Non-being in the Image -- [ʹ] 73 Partial Clarification of the Aporia of Being and Non-being Holds the Key to the "Arithmetical" Structure of the Noητv's Mode of Being. 505-00/(S Contents note continued: [ʹ] 74 Koα among "Ov, Kvητ, and Στ, Composes the Relationship of Being and Non-being -- [ʹ] 75 Contrast between Aρθm Mαθ and Aρθm E -- [ʹ] 76 Foundational Function of Aρiθuos E -- [ʹ] 77 Order of Aρiθuos' E Provides the Foundation for Both the Sequence of Mathematical À and the Relation of Family Descent between Higher and Lower -- [ʹ] 78 Inability of the A, to "Count" the M Points to Its Limits and Simultaneously Presents the First A E -- [ʹ] 79 Θατερoν as the "Twofold in General" Allows for the Articulation of Being and Non-being -- [ʹ] 80 Recognizing "the Other" as the "Indeterminate Dyad" -- [ʹ] 81 "One Itself" as the Source of the Generation of "A E -- [ʹ] 82 Γενη À E Provide the Foundation of an Eidetic Logistic -- [ʹ] 83 Plato's Postulate of the Separation of All Noetic Formations Renders Incomprehensible the Ordinary Mode of Predication -- ch. Twenty Aristotle's Critique of the Platonic Chorismos Thesis and the Possibility of a Theoretical Logistic -- [ʹ] 84 Point of Departure and Overview of Aristotle's Critique -- [ʹ] 85 Aristode's Problematic: Harmonizing the Ontological Dependence of À with Their Pure Noetic Quality -- [ʹ] 86 Aristotle on the Abstractive Mode of Being of Mathematical Objects -- [ʹ] 87 Aristotle's Ontological Determination of the Non-generic Unity of À -- [ʹ] 88 Aristotle's Ontological Determination of the Unity of À as Common Measure -- [ʹ] 89 Aristotle's Ontological Determination of the Indivisibility and Exactness of "Pure" À -- [ʹ] 90 Influence of Aristotle's View of M on Theoretical Arithmetic -- [ʹ] 91 Aristotle's Ontological Conception of À Makes Possible Theoretical Logistic -- ch. Twenty-one Klein's Interpretation of Diophantus's Arithmetic -- [ʹ] 92 Access to Diophantus's Work Requires Reinterpreting It outside the Context of Mathematics' Self-interpretation since Vieta, Stevin, and Descartes -- [ʹ] 93 Diophantus's Arithmetic as Theoretical Logistic -- [ʹ] 94 Referent and Operative Mode of Being of Diophantus's Concept of À -- [ʹ] 95 Ultimate Determinacy of Diophantus's Concept of Unknown and Indeterminate À -- [ʹ] 96 Merely Instrumental, and Therefore Non-ontological and Non-symbolic, Status of the E-Concept in Diophantus's Calculations -- ch. Twenty-two Klein's Account of Vieta's Reinterpretation of the Diophantine Procedure and the Consequent Establishment of Algebra as the General Analytical Art -- [ʹ] 97 Significance of Vieta's Generalization of the E-Concept and Its Transformation into the Symbolic Concept of Species -- [ʹ] 98 Sedimentation of the Ancient Practical Distinction between S̀aying' and ̀Thinking' in the Symbolic Notation Inseparable from Vieta's Concept of Number -- [ʹ] 99 Decisive Difference between Vieta's Conception of a "General" Mathematical Discipline and the Ancient Idea of a K I -- [ʹ] 100 Occlusion of the Ancient Connection between the Theme of General Mathematics and the Foundational Concerns of the "Supreme" Science That Results from the Modern Understanding of Vieta's "Analytical Art" as Mathesis Universalis -- [ʹ] 101 Vieta's Ambiguous Relation to Ancient Greek Mathematics -- [ʹ] 102 Vieta's Comparison of Ancient Geometrical Analysis with the Diophantine Procedure -- [ʹ] 103 Vieta's Transformation of the Diophantine Procedure -- [ʹ] 104 Auxiliary Status of Vieta's Employment of the "General Analytic" -- [ʹ] 105 Influence of the General Theory of Proportions on Vieta's "Pure," "General" Algebra -- [ʹ] 106 Klein's Desedimentation of the Conceptual Presuppositions Belonging to Vieta's Interpretation of Diophantine Logistic -- ch. Twenty-three Klein's Account of the Concept of Number and the Number Concepts in Stevin, Descartes, and Wallis -- [ʹ] 107 Stevin's Idea of a "Wise Age" and His Project for Its Renewal -- [ʹ] 108 Stevin's Critique of the Traditional À-Concept -- [ʹ] 109 Stevin's Symbolic Understanding of Numerus -- [ʹ] 110 Stevin's Assimilation of Numbers to Geometrical Formations -- [ʹ] 111 Descartes's Postulation of a New Mode of "Abstraction" and a New Possibility of "Understanding" as Underlying Symbolic Calculation -- [ʹ] 112 Fundamental Cognitive Role Attributed by Descartes to the Imaginatio -- [ʹ] 113 Descartes on the Pure Intellect's Use of the Power of the Imagination to Reconcile the Mathematical Problem of Determinacy and Indeterminacy -- [ʹ] 114 Klein's Reactivation of the "Abstraction" in Descartes as "Symbolic Abstraction" -- [ʹ] 115 Klein's Use of the Scholastic Distinction between "First and Second Intentions" to Fix Conceptually the Status of Descartes's Symbolic Concepts -- [ʹ] 116 Descartes on the Non-metaphorical Reception by the Imagination of the Extension of Bodies as Bridging the Gap between Non-determinate and Determinate Magnitudes -- [ʹ] 117 Wallis's Completion of the Introduction of the New Number Concept -- [ʹ] 118 Wallis's Initial Account of the Unit Both as the Principle of Number and as Itself a Number -- [ʹ] 119 Wallis's Account of the Nought as Also the Principle of Number -- [ʹ] 120 Wallis's Emphasis on the Arithmetical Status of the Symbol or Species of the "General Analytic" -- [ʹ] 121 Homogeneity of Algebraic Numbers as Rooted for Wallis in the Unity of the Sign Character of Their Symbols -- [ʹ] 122 Wallis's Understanding of Algebraic Numbers as Symbolically Conceived Ratios -- pt. Four Husserl and Klein on the Origination of the Logic of Symbolic Mathematics -- ch. Twenty-four Husserl and Klein on the Fundamental Difference between Symbolic and Non-symbolic Numbers -- [ʹ] 123 Klein's Critical Appropriation of Husserl's Crisis Seen within the Context of the Results of Klein's Investigation of the Origin of Algebra -- [ʹ] 124 Husserl and Klein on the Difference between Non-symbolic and symbolic Numbers -- [ʹ] 125 Husserl on the Authentic Cardinal Number Concept and Klein on the Greek À-Concept -- ch. 505-01/(S Twenty-five Husserl and Klein on the Origin and Structure of Non-symbolic Numbers -- [ʹ] 126 Husserl's Appeal to Acts of Collective Combination to Account for the Unity of the Whole of Each Authentic Cardinal Number -- [ʹ] 127 Husserl's Appeal to Psychological Experience to Account for the Origin of the Categorial Unity Belonging to the Concept of Ànything' Characteristic of the Units Proper to Multiplicities and Cardinal Numbers -- [ʹ] 128 Decisive Contrast between Husserl's and Klein's Accounts of the Being of the Units in Non-symbolic Numbers -- [ʹ] 129 Klein on Plato's Account of the Purity of Mathematical À -- [ʹ] 130 Klein on Plato's Account of the "Being One" of Each Mathematical À as Different from the "Being One" of Mathematical "Monads" -- [ʹ] 131 Klein on Plato's Account of the Non-mathematical Unity Responsible for the "Being One" of the Whole Belonging to Each À -- [ʹ] 132 Klein on Plato's Account of the Solution Provided by À E to the Aporias Raised by À M -- [ʹ] 133 Klein on Aristoτle's Account of the Inseparable Mode of the Being of À from Sensible Beings -- [ʹ] 134 Klein on Aristotle's Account of the Abstracted Mode of Being of Mathematical Objects -- [ʹ] 135 Klein on Aristotle's Critique of the Platonic Solution to the Problem of the Unity of an À-Assemblage -- [ʹ] 136 Klein on Aristotle's Answer to the Question of the Unity Belonging to À -- [ʹ] 137 Klein on Aristotle's Account of the Origination of the Mov as Measure -- ch. Twenty-six Structural Differences in Husserl's and Klein's Accounts of the Mode of Being of Non-symbolic Numbers -- [ʹ] 138 Different Accounts of the Mode of Being of the "One" in Husserl, Plato, and Aristotle -- [ʹ] 139 Different Accounts of the "Being One" and Ordered Sequence Characteristic of the Wholes Composing Non-symbolic Numbers in Husserl, Plato, and Aristotle -- [ʹ] 140 Different Accounts of the Conditions Responsible for the Scope of the Intelligibility of Non-symbolic Numbers in Husserl, Plato, and Aristotle -- [ʹ] 141 Structural Differences between Husserl's and Klein's Accounts of the Mode of Being of Non-symbolic Numbers -- [ʹ] 142 Divergence in Husserl's and Klein's Accounts of Non-symbolic Numbers -- ch. Twenty-seven Digression: The Development of Husserl's Thought, after Philosophy of Arithmetic, on the "Logical" Status of the Symbolic Calculus, the Constitution of Collective Unity, and the Phenomenological Foundation of the Mathesis Universalis -- [ʹ] 143 Need to Revisit the "Standard View" of the Development of Husserl's Thought -- ch. Twenty-eight Husserl's Accounts of the Symbolic Calculus, the Critique of Psychologism, and the Phenomenological Foundation of the Mathesis Universalis after Philosophy of Arithmetic -- [ʹ] 144 Husserl's Account of the Symbolic Calculus after Philosophy of Arithmetic -- [ʹ] 145 Husserl's Critique of Philosophy of Arithmetic's Psychologism -- [ʹ] 146 Husserl's Account of the Phenomenological Foundation of the Mathesis Universalis -- ch. Twenty-nine Husserl's Critique of Symbolic Calculation in his Schroder Review. |
| spellingShingle | Hopkins, Burt C. The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / Studies in Continental thought. pt. 1. Klein on Husserl's phenomenology and the history of science -- pt. 2. Husserl and Klein on the method and task of desedimenting the mathematization of nature -- pt. 3. Non-symbolic and symbolic numbers in Husserl and Klein -- pt. 4. Husserl and Klein on the origination of the logic of symbolic mathematics. Husserl, Edmund 1859-1938 gnd Husserl, Edmund. idszbz Klein, Jacob. idszbz Klein, Jacob (Philosoph) (DE-604)BV0087245 swd Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Logique symbolique et mathématique. Mathématiques Philosophie. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh PHILOSOPHY Movements Phenomenology. bisacsh Logic, Symbolic and mathematical fast Mathematics Philosophy fast Computeralgebra gnd Logik gnd http://d-nb.info/gnd/4036202-4 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Rezeption gnd Zahlentheorie gnd http://d-nb.info/gnd/4067277-3 Mathematische Logik. idszbz Mathematik. idszbz Philosophie. idszbz Symbolisk logik. sao Matematik teori, filosofi. sao |
| subject_GND | (DE-604)BV0087245 http://id.loc.gov/authorities/subjects/sh85078115 http://id.loc.gov/authorities/subjects/sh85082153 http://d-nb.info/gnd/4036202-4 http://d-nb.info/gnd/4037951-6 http://d-nb.info/gnd/4067277-3 |
| title | The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / |
| title_auth | The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / |
| title_exact_search | The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / |
| title_full | The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / Burt C. Hopkins. |
| title_fullStr | The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / Burt C. Hopkins. |
| title_full_unstemmed | The origin of the logic of symbolic mathematics : Edmund Husserl and Jacob Klein / Burt C. Hopkins. |
| title_short | The origin of the logic of symbolic mathematics : |
| title_sort | origin of the logic of symbolic mathematics edmund husserl and jacob klein |
| title_sub | Edmund Husserl and Jacob Klein / |
| topic | Husserl, Edmund 1859-1938 gnd Husserl, Edmund. idszbz Klein, Jacob. idszbz Klein, Jacob (Philosoph) (DE-604)BV0087245 swd Logic, Symbolic and mathematical. http://id.loc.gov/authorities/subjects/sh85078115 Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Logique symbolique et mathématique. Mathématiques Philosophie. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh PHILOSOPHY Movements Phenomenology. bisacsh Logic, Symbolic and mathematical fast Mathematics Philosophy fast Computeralgebra gnd Logik gnd http://d-nb.info/gnd/4036202-4 Mathematische Logik gnd http://d-nb.info/gnd/4037951-6 Rezeption gnd Zahlentheorie gnd http://d-nb.info/gnd/4067277-3 Mathematische Logik. idszbz Mathematik. idszbz Philosophie. idszbz Symbolisk logik. sao Matematik teori, filosofi. sao |
| topic_facet | Husserl, Edmund 1859-1938 Husserl, Edmund. Klein, Jacob. Klein, Jacob (Philosoph) Logic, Symbolic and mathematical. Mathematics Philosophy. Logique symbolique et mathématique. Mathématiques Philosophie. MATHEMATICS Infinity. MATHEMATICS Logic. PHILOSOPHY Movements Phenomenology. Logic, Symbolic and mathematical Mathematics Philosophy Computeralgebra Logik Mathematische Logik Rezeption Zahlentheorie Griechenland Altertum Mathematische Logik. Mathematik. Philosophie. Symbolisk logik. Matematik teori, filosofi. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=385454 |
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