Wittgenstein and the Turning Point in the Philosophy of Mathematics

In this review of Wittgenstein and the Turning Point in the Philosophy of Mathematics, the reviewer identifies who will gain most from S.G. G. Shankers study and why it matters. The book is for readers who want a focused, scholarly examination of Wittgensteins engagement with Godel and the philosophical fallout for Hilbert's Programme, and its single biggest reason to buy is the authors effort to locate the precise mistakes critics hinted at regarding Wittgensteins understanding of Godels second incompleteness theorem. The text reads like a careful historical and conceptual reconstruction rather than a survey, making it most useful for graduate students, researchers, and informed general readers interested in the intersection of logic and philosophy.

Key Features

• Focused historical analysis: The author reconstructs the debate around Wittgenstein and Godel to clarify what critics meant by claims of misunderstanding, which helps readers assess competing interpretations.
• Detailed discussion of meta-mathematics: The book examines Wittgensteins critique of meta-mathematics and explains how that critique relates to the aims of formal systems.
• Contextualization of Hilbert's Programme: Shanker situates Wittgensteins attack within the broader historical project of Hilbert, illuminating philosophical stakes for foundations of mathematics.
• Concise scholarly presentation: First published in 2005, the study keeps a tight focus on specific philosophical claims rather than sprawling into unrelated topics, which benefits readers seeking depth.
• Suitable for advanced readers: The treatment assumes familiarity with basic logical concepts, making it efficient for readers already versed in Godel and Wittgenstein to deepen their understanding.

Who It's For

Graduate students, researchers, and informed general readers who want a concentrated study of Wittgensteins relation to Godel and the philosophical implications for Hilbert's Programme will find this work rewarding. The book is particularly well suited to those with prior exposure to the second incompleteness theorem and an interest in analytic philosophy of mathematics.

Not for absolute beginners or casual readers: Those without foundational knowledge of formal logic or the history of 20th century analytic philosophy may struggle with the subject matter; a more general introduction to Wittgenstein or Godel would be a better starting point.

Pros & Cons

Pros

• Clear focus on the specific alleged mistakes critics referenced, which sharpens philosophical debate.
• Illuminates Wittgensteins attack on meta-mathematics in relation to Hilberts Programme, aiding historical understanding.
• Concise, scholarly style that makes dense material manageable for informed readers.

Cons

• Not aimed at novices; the discussion assumes familiarity with technical concepts and offers limited introductory material.

Specifications

Title	Wittgenstein and the Turning Point in the Philosophy of Mathematics
Author	S.G. G. Shanker
First published	2005
Primary focus	Wittgenstein, Godel's second incompleteness theorem, meta-mathematics
Historical context	Hilbert's Programme and modern analytic philosophy
Intended readership	Graduate students, researchers, informed general readers

Our Verdict

The verdict: This is a valuable, tightly argued study for readers who already understand basic logical results and want a clearer picture of the contested claims about Wittgenstein and Godel. Its focused analysis of meta-mathematics and Hilberts Programme makes it good value for scholars and advanced students seeking to resolve ambiguities in prior criticism.

Frequently Asked Questions

Does this book explain Godels second incompleteness theorem?
The book discusses the theorem in the context of critiques of Wittgenstein rather than providing a full textbook treatment, so it assumes some prior knowledge.

Is the book suitable for undergraduate reading?
Undergraduates with a strong background in logic may benefit, but most readers at that level will find it challenging without supplemental introductions.

Does the study cover Hilberts Programme?
Yes, the book situates Wittgensteins attack within the aims and history of Hilberts Programme to clarify philosophical stakes.