Wittgenstein, Finitism, and the Foundations of Mathematics (Oxford Philosophical Monographs)

This pioneering book demonstrates the crucial importance of Wittgenstein's philosophy of mathematics to his philosophy as a whole. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations . Contents List of Abbreviations 1. Introduction: Wittgenstein's Anti-Platonism 2. Logicism without Classes 2.1. Operations and Arithmetic 2.2. Truth-Functions, Generality, and Infinity 2.3. Predicativity 3. Arbitrary Functions 3.1. Identity 3.2. Ramsey's Functions in Extension and the Axiom of Infinity 3.3. The Axiom of Choice and Numerical Equivalence 4. Quantification and Finitism 4.1. Weyl, Hilbert, and Ramsey 4.2. The New Logic of 1929 5. From Truth-Functional Logic to a Logic of Equations 5.1. Logical Form and Colour Exclusion 5.2. Assertions and Hypotheses 6. Philosophy and Logical Foundations 6.1. Intuitionism, Intentionality, Rules, and Decision Procedures 6.2. Excluded Middle and Existence 6.3. Formalism, Infinity, and Epistemic Limitations 7. The Continuum 7.1. Cauchy Sequences and the Diagonal Method 7.2. Choice Sequences and Dedekind Cuts 8. Strict Finitism 8.1. Dummett's Interpretation 8.2. Complexity References Index A B C D E F G H I J K L M N O P Q R S T U V W Z

mathieu Marion Offers A Careful, Historically Informed Study Of Wittgenstein's Philosophy Of Mathematics. This Area Of His Work Has Frequently Been Undervalued By Wittgenstein Specialists And By Philosophers Of Mathematics Alike; But The Surprising Fact That He Wrote More On This Subject Than On Any Other Indicates Its Centrality In His Thought. Marion Traces The Development Of Wittgenstein's Thinking In The Context Of The Mathematical And Philosophical Work Of The Times, To Make Coherent Sense Of Ideas That Have Too Often Been Misunderstood Because They Have Been Presented In A Disjointed And Incomplete Way. In Particular, He Illuminates The Work Of The Neglected Transitional Period Between The Tractatus And The Investigations. Marion Shows That Study Of Wittgenstein's Writings On Mathematics Is Essential To A Proper Understanding Of His Philosophy; And He Also Demonstrates That It Has Much To Contribute To Current Debates About The Foundations Of Mathematics.

"Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy."--BOOK JACKET. "Mathieu Marion offers a careful, historically informed study of Wittgenstein's philosophy of mathematics. This area of his work has frequently been undervalued by Wittgenstein specialists and philosophers of mathematics alike; but the surprising fact that he wrote more on this subject than on any other indicates its centrality in his thought. Marion traces the development of Wittgenstein's thinking in the context of the mathematical and philosophical work of the times, to make coherent sense of ideas that have too often been misunderstood because they have been presented in a disjointed and incomplete way. In particular, he illuminates the work of the neglected 'transitional period' between the Tractatus and the Investigations. Marion shows that study of Wittgenstein's writings on mathematics is essential to a proper understanding of his philosophy." --Book Jacket Se demuestra la gran importancia de la filosofía de las matemáticas de Wittgenstein en su filosofía como un todo. El autor traza el desarrollo del pensamiento de Wiggenstein en el contexto de la obra matemática y filosófica, haciendo coherente el sentido de su pensamiento que a menudo ha sido malinterpretado porque ha sido presentado de forma inconexa e incompleta. En particular el autor aclara el trabajo del abandonado "periodo transicional" entre el Tractatus y el de Investigaciones Filosóficas (Philosophische Untersuchungen) This is a careful, historically informed study of Wittgenstein's philosophy of mathematics, tracing the work development of his thinking from the 1920s through to the 1950s, in the context of the mathematical and philosophical work of the times