In Wittgenstein's Philosophy of Mathematics Frascolla views the three phases of Wittgenstein's reflections on mathematics as a progressive whole, rather than as seperate entities.

Pasquale Frascolla's book is the most comprehensive presentation of Wittgenstein's views on mathematics progressively elaborated during a lifetime's reflections on the subject. The book is in three parts, corresponding to the three distinct phases in the development of Wittgenstein's philosophy of mathematics. The first part is devoted to the Tractatus and contains a systematic construction of the representation of arithmetic in logical operations. Frascolla takes this as the true objective of Wittgenstein's comments on mathematics in his first work on the subject. The second part is concerned with the so-called intermediate phase', (1929-33) which is characterised by strong verificationism and by a conception of the relation between the particular and the general in mathematics which forms the basis of Wittgenstein's later reflections on rule-following. The final section deals with the writings on mathematics in the decade 1934-44 . The main themes of the later Wittgenstein's philosophy of mathematics are understood as consequences of his considerations of rule-following.

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