On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought

Authors

  • Sören Stenlund Department of Philosophy Uppsala University

DOI:

https://doi.org/10.15845/nwr.v4i1.3302

Keywords:

calculation, symbolism, formalism, blind thought, infinity, symbolic mathematics, Wittgenstein Ludwig, Hertz Heinrich, Weyl Hermann

Abstract

The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolism and started to use the word ‘symbolic’ in the relevant, non-ontological sense. This approach has played an important role for many of the great inventions in modern mathematics such as the introduction of the decimal place-value system of numeration, Descartes’ analytic geometry, and Leibniz’s infinitesimal calculus. It was also central for the rigorization movement in mathematics in the late nineteenth century, as well as for the mathematics of modern physics in the 20th century.

However, the nature of symbolic mathematics has been concealed and confused due to the strong influence of the heritage from the Euclidean and Aristotelian traditions. This essay sheds some light on what has been concealed by approaching some of the crucial issues from a historical perspective. Furthermore, I argue that the conception of modern mathematics as symbolic mathematics was essential to Wittgenstein’s approach to the foundations and nature of mathematics. This connection between Wittgenstein’s thought and symbolic mathematics provides the resources for countering the still prevalent view that he defended an uttrely idiosyncratic conception, disconnected from the progress of serious science. Instead, his project can be seen as clarifying ideas that have been crucial to the development of mathematics since early modernity.

Author Biography

Sören Stenlund, Department of Philosophy Uppsala University

Sören Stenlund was appointed professor of theoretical philosophy at Uppsala University (Sweden) in 2000. He has acted as head of the Philosophy Department in Uppsala and was the Director of Graduate Studies in the Department of Philosophy and the coordinator of the seminar for theoretical philosophy until his retirement in 2008. Since his dissertation in 1972, Stenlund has published books and articles on various themes in the philosophies of language, logic and mathematics, such as Language and Philosophical Problems (Routledge 1991). Apart from these themes, Stenlund has discussed a vast array of other philosophical issues concerning the nature and history of philosophy and the philosophy of culture.

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Published

2015-07-24