Department
Natural Sciences and Mathematics
Document Type
Article
Source
Le present est plein de l’avenir, et chargé du passé: Vorträge des XI. Internationalen Leibniz-Kongresses
Publication Date
2023
First Page
326
Last Page
339
Abstract
Since the 1980s, wicked problems have represented a category of challenges that defy clear description, cannot be addressed with existing models or theories, and resist experimentation in trying to solve them. This class of problems existed before they were identified and have been unsuccessfully addressed with Thomas Kuhn’s model of scientific discovery, an expectation that requires the identification of a new object and the development of its correct interpretation. This paper proposes an alternative view of scientific discovery using the invention of Calculus as a case study that describes a successful process addressing wicked-like problems from a philosophical perspective, develops ideas that have an epistemological objective and are multidisciplinary in their applications, and results in additions to the Body of Knowledge that permeate human language and understanding. Leibniz’s wicked problem was to produce a universal method of discovery at the centre of his idea of a ‘General Science’ and the compilation of an encyclopaedia of all knowledge available at the time. From the existing paradigm of geometrical arguments and deductive processes, there is a gestalt shift in Leibniz’s leap in understanding mathematical methods and the language used in describing and solving problems that was rooted in the idea of infinitesimals and in a more general method of analysis. In doing so, the transition that began with his methods and notation became the first stage in a Kuhnian paradigm shift and the incorporation of Calculus and its applications into the mainstream of science. I will start by giving some background on wicked problems and describing the concept of discovery associated with Kuhn’s ideas, and I will then introduce the process of additions to knowledge advocated in this essay. These ideas will form the antecedent to summarise the paradigm in 17th century mathematics and from there I will proceed to describe Leibniz’s leap and the inherent gestalt shift that occurred in the mathematics of the 18th century. That gestalt shift was not exempt from acrimonious discussions over alternate formulations and I will present some differences between the views of Newton and Leibniz and of two of their supporters; Maclaurin and l’Hôpital. I will then describe some of the efforts that helped to expand the acceptance of Calculus and to embed it in the mainstream of science. I will conclude by proposing that there are other examples from the History and Philosophy of Science that follow a similar process of additions to the Body of Knowledge.
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