Topic
Finitism
About: Finitism is a research topic. Over the lifetime, 139 publications have been published within this topic receiving 2443 citations. The topic is also known as: Finitistic.
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Book•
27 Jan 1984
TL;DR: The Foundations of Mathematics: 1. The logicist foundations of mathematics Rudolf Carnap 2. Intuitionism and formalism L. E. J. Brouwer as discussed by the authors.
Abstract: Preface to the second edition Introduction Part I. The Foundations of Mathematics: 1. The logicist foundations of mathematics Rudolf Carnap 2. The intuitionist foundations of mathematics Arend Heyting 3. The formalist foundations of mathematics Johann von Neumann 4. Disputation Arend Heyting 5. Intuitionism and formalism L. E. J. Brouwer 6. Consciousness, philosophy, and mathematics L. E. J. Brouwer 7. The philosophical basis of intuitionistic logic Michael Dummett 8. The concept of number Gottlob Frege 9. Selections from Introduction to Mathematical Philosophy Bertrand Russell 10. On the infinite David Hilbert 11. Remarks on the definition and nature of mathematics Haskell B. Curry 12. Hilbert's programme Georg Kreisel Part II. The Existence of Mathematical Objects: 13. Empiricism, semantics, and ontology Rudolf Carnap 14. On Platonism in mathematics Paul Bernays 15. What numbers could not be Paul Benacerraf 16. Mathematics without foundations Hilary Putnam Part III. Mathematical Truth: 17. The a priori Alfred Jules Ayer 18. Truth by convention W. V. Quine 19. On the nature of mathematical truth Carl G. Hempel 20. On the nature of mathematical reasoning Henri Poincare 21. Mathematical truth Paul Benacerraf 22. Models and reality Hilary Putnam Part IV. The Concept of Set: 23. Russell's mathematical logic Kurt Goedel 24. What in Cantor's continuum problem? Kurt Goedel 25. The iterative concept of set George Boolos 26. The concept of set Hao Wang Bibliography.
382 citations
Book•
01 Jan 1997
TL;DR: In this article, the authors discuss the realism debate and argue against meaning scepticism and avoid strict finitism, and find the right logic and cognitive significance of cognitive significance regained.
Abstract: 1: Introduction 2: The Realism Debate 3: Irrealism 4: Against Meaning Skepticism 5: Avoiding Strict Finitism 6: Meaning as Graspable 7: Truth as Knowable 8: Analyticity and Syntheticity 9: Finding the Right Logic 10: Cognitive Significance Regained 11: Defeasibility and Constructive Falsifiability
230 citations
Book•
01 Jan 1994
TL;DR: In this article, the "Knowledge of Forms: Vision and Calculation" is described as a "knowledge of forms: vision and calculation" in the Tractatus of Arithmetic.
Abstract: Preface Abbreviations I. The Philosophy of Arithmetic of the Tractatus 1. Preliminaries 2. Systematic Exposition 3. The "Knowledge" of Forms: Vision and Calculation 4. Foundations of Mathematics (I) II. Verificationism and its Limits. The Intermediate Phase (1929-'33) 1. Introduction 2. Finite Cardinal Numbers: the Arithmetic of Strokes 3. Mathematical Propositions 4. The Mathematical Infinite 4.1 Quantifiers in Mathematics 4.2 Recursive Arithmetic and Algebra 4.3 Real Numbers 4.4 Set Theory 5. Foundations of Mathematics (II) III. From Facts to Concepts. The Later Writings on Mathematics (1934-'44) 1. The Crisis of Verificationism: Rule-Following 2. Mathematical Proofs as Paradigms 3. The Problem of Strict Finitism 4. Wittgenstein's Quasi-Revisionism 4.1 Cantor's Diagonal Proof and Transfinite Cardinals 4.2 The Law of Excluded Middle 4.3 Consistency References
163 citations
Book•
01 Jan 1987
TL;DR: In this paper, the authors discuss the role of criteria in anti-realist semantics and second-thoughts about criteria in Davidsonian meaning-theory in terms of assertibility.
Abstract: Part 1 The negative programme: truth-conditions and criteria Strawson on anti-realism realism, truth-value links, other minds and the past strict finitism anti-realism, timeless truth and 1984 theories of meaning and speakers' knowledge scientific realism, observation and the verification principle misunderstandings made manifest. Part 2 The positive programme: anti-realist semantics - the role of criteria second thoughts about criteria can Davidsonian meaning-theory be construed in terms of assertibility? anti-realism and revisionism realism, bivalence and classical logic.
153 citations
Book•
01 Jan 2000
TL;DR: The author revealed that within the framework of this book, three main themes - structuralism, identity, and ontological realism - had emerged: structure, identity and structure, and orientation and ontology.
Abstract: PART I. PERSPECTIVE CHAPTER 1. WHAT IS SO INTERESTING ABOUT MATHEMATICS (FOR PHILOSOPHER)? ATTRACTION - OF OPPOSITES? PHILOSOPHY AND MATHEMATICS: CHICKEN OR EGG? NATURALISM AND MATHEMATICS CHAPTER 2. A POTPOURRI OF QUESTIONS AND ATTEMPTED ANSWERS NECESSITY AND A PRIORI KNOWLEDGE GLOBAL MATTERS: OBJECTS AND OBJECTIVITY THE MATHEMATICAL AND THE PHYSICAL LOCAL MATERS: THEOREMS, THEORIES, AND CONCEPTS PART II. HISTORY CHAPTER 3. PLATO'S RATIONALISM, AND ARISTOTLE THE WORLD OF BEING PLATO ON MATHEMATICS MATHEMATICS ON PLATO ARISTOTLE, THE WORTHY OPPONENT FURTHER READING CHAPTER 4. NEAR OPPOSITES: KANT AND MILL REORIENTATION KANT MILL FURTHER READING PART III. THE BIG THREE CHAPTER 5. LOGICISM: IS MATHEMATICS (JUST) LOGIC? FREGE RUSSELL CARNAP AND LOGICAL POSITIVISM CONTEMPORARY VIEWS FURTHER READING CHAPTER 6. FORMALISM: DO MATHEMATICAL STATEMENTS MEAN ANYTHING? BASIC VIEWS: FREG'S ONSLAUGHT DEDUCTIVISM: HILBERT'S GRUNDLAGEN DER GEOMETRIE FINITISM: THE HILBERT PROGRAM INCOMPLETENESS CURRY FURTHER READING CHAPTER 7. INTUITIONISM: IS SOMETHING WRONG WITH OUR LOGIC? 1. REVISING CLASSICAL LOGIC 2. THE TEACHER, BROUWER 3. THE STUDENT, HEYTING 4. DUMMETT 5. FURTHER READING PART IV. THE CONTEMPORARY SCENE CHAPTER 8. NUMBERS EXIST GODEL THE WEB OF BELIEF SET-THEORETIC REALISM FURTHER READING CHAPTER 9. NO THEY DON'T FICTIONALISM MODAL CONSTRUCTION WHAT SHOULD WE MAKE OF ALL THIS? ADDENDUM: YOUNG TURKS FURTHER READING CHAPTER 10. STRUCTURALISM THE UNDERLYING IDEA ANTE REM STRUCTURES, AND OBJECTS STRUCTURALISM WITHOUT STRUCTURES KNOWLEDGE OF STRUCTURES FURTHER READING REFERENCES INDEX
139 citations