Abstract
AbstractThis work explores the later Wittgenstein’s philosophy of mathematics in relation to Lakatos’ philosophy of mathematics and the philosophy of mathematical practice. I argue that, while the philosophy of mathematical practice typically identifies Lakatos as its earliest of predecessors, the later Wittgenstein already developed key ideas for this community a few decades before. However, for a variety of reasons, most of this work on philosophy of mathematics has gone relatively unnoticed. Some of these ideas and their significance as precursors for the philosophy of mathematical practice will be presented here, including a brief reconstruction of Lakatos’ considerations on Euler’s conjecture for polyhedra from the lens of late Wittgensteinian philosophy. Overall, this article aims to challenge the received view of the history of the philosophy of mathematical practice and inspire further work in this community drawing from Wittgenstein’s late philosophy.
Highlights
It is worth noting that Lakatos dealt with, and underscored the importance of, aspects of the mathematical practice that would later be studied in more detail, such as proving and explaining, visualization, the interrelations between informal and formal mathematics, and how mathematics “grows”
This work has been concerned with two main objectives: (1) to justify a place for the later Wittgenstein as a hitherto unrecognized “maverick” in the context of the philosophy of mathematical practice, and (2) to show how the philosophy of mathematical practice may benefit from the framework that the later Wittgenstein’s philosophy of mathematics provides
Mathematics has been considered a source of immaculate knowledge, more resilient to “contaminating” factors that can be found in the sciences from time to time
Summary
It argues that the later Wittgenstein is a forerunner of the philosophy of mathematical practice, thereby challenging the received view that Lakatos’s work is the first in this direction. It highlights features of the later Wittgenstein’s philosophy of mathematics which are relevant to the philosophy of mathematical practice, in order to draw the attention of this community. This section intends to stimulate further work inspired by late Wittgensteinian philosophy in the context of the philosophy of mathematical practice
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