Wittgenstein's Philosophy of Mathematics

Mathematics is a human activity that characterizes ways of seeing conceptual possibilities and empirical situations, with proof and logical methods central to its progress. It is an activity of constructing standpoints on equalities and differences of these, and Wittgenstein's Later Philosophy of Mathematics (1934–1951) grew from his Early and Middle philosophies.

\n Format: Paperback / softback
\n Length: 75 pages
\n Publication date: 12 August 2021
\n Publisher: Cambridge University Press
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Mathematics, as envisioned by Wittgenstein, encompasses a profound human endeavor that revolves around the exploration and interpretation of conceptual possibilities and empirical realities. It is characterized by the use of rigorous proof and logical methods, which serve as the driving forces behind its progress. Within the realm of mathematics, sentences manifest a rich tapestry of diverse aspects or dimensions of meaning, each projecting a distinct mathematical reality. These sentences serve as the building blocks of mathematical thought, enabling us to construct perspectives on the equalities and differences that underpin these realities.

Wittgenstein's Later Philosophy of Mathematics, which emerged between 1934 and 1951, evolved from his earlier philosophies of the Early (1912–1921) and Middle (1929–1933) periods. This philosophical journey is reconstructed herein, partly as a response to the limitations imposed by the works of Gödel and Turing. It represents a dialectical path that delves into the intricacies of mathematics, seeking to unravel its mysteries and uncover new insights.

Through his philosophical lens, Wittgenstein emphasizes the importance of understanding mathematics as a language-like activity. He posits that mathematical concepts and propositions are not abstract entities existing independently of human perception and interpretation. Instead, they are deeply intertwined with the ways in which we perceive and understand the world around us. Wittgenstein's approach to mathematics is characterized by a focus on the linguistic and cultural aspects of mathematical practice. He argues that the meanings of mathematical expressions and concepts are not fixed and universal, but rather are shaped by the historical, social, and linguistic contexts in which they are used.

One of the central themes of Wittgenstein's Later Philosophy of Mathematics is the notion of "games." According to Wittgenstein, mathematics is a kind of game that involves the construction of frameworks and rules for interpreting and evaluating mathematical statements. These games are not abstract or purely logical exercises, but rather are grounded in the practical and empirical aspects of mathematical inquiry. By engaging in these games, mathematicians can develop new insights and understandings of mathematical phenomena.

Wittgenstein also emphasizes the importance of intuition in mathematics. He argues that intuition plays a crucial role in the construction of mathematical proofs and in the development of mathematical understanding. Intuition, according to Wittgenstein, is not a direct perception of mathematical truths, but rather a way of organizing and interpreting mathematical ideas. It is through the interplay between intuition and logical reasoning that mathematicians can arrive at new mathematical discoveries and develop deeper insights into the nature of mathematics.

In conclusion, Wittgenstein's philosophy of mathematics is a rich and complex exploration of the human activity of constructing standpoints on equalities and differences of mathematical realities. Through his emphasis on the linguistic and cultural aspects of mathematical practice, the notion of "games," and the role of intuition, Wittgenstein offers a unique perspective on the nature and significance of mathematics. His philosophy continues to inspire and influence mathematicians and philosophers alike, as they seek to understand the deeper truths and implications of mathematical inquiry.

\n Weight: 152g\n
Dimension: 151 x 228 x 11 (mm)\n
ISBN-13: 9781108456302\n \n