On the applicability of mathematics in physics : a critical review of Wigner's puzzle
- This dissertation takes up on the question of why mathematics is effective in the natural sciences, especially in physics. The answer proposed is that modern physics is the result of a historical idealization, began by Galilee and developed fully by Newton, which makes its mathematization possible. Physicists of the modern era came up with a set of idealized assumptions, invariance principles in our jargon, that allowed them to abstract from many conditions that could in principle effect the result of an experiment, and if so would make the formulation of the laws of nature impossible (or far too complicated to be of any use). Among these invariance principles, there is the assumption that time is uniform and space homogenous. Thus the regularity that the experimenter detects among events at the time t and location x of the experiment holds elsewhere, in fact universally, under the same initial conditions. Such idealizations make for the mathematical and precise formulation of laws of physics. This precision has proved to be extremely useful in the study of nature, which itself is a very complicated and at times unpredictable totality. Chapter 2 (first main chapter) examines the physicist Eugene Wigner's remarkable paper on "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", offers an original and contextual reading of the paper, and explains the role of invariance principles in modern physics. Chapter 3 examines two common readings of the "Unreasonable Effectiveness", by the philosopher Mark Steiner and the mathematician Richard Hamming, and responds to their criticisms based on the reading proposed in chapter 2. Chapter 4 examines the case of quantization as one of the most difficult cases of the "Unreasonable Effectiveness", and proposes a solution on the basis of the early developments of quantum mechanics and the route to the canonical commutation relations. Chapter 5 examines the development of complex numbers from their first appearance in the 16th century to their use in the fundamental equations of quantum mechanics, and explains their effectiveness based on their calculational power demonstrated in a series of mathematical theorems. It is my hope that this dissertation sheds light on the much debated question of the applicability of mathematics through a historical understanding of the relationship between mathematics and physics. The uncriticized philosophical idealization surrounded the applicability problem so far, I hope, finds a historical grounding through the study of the kind conducted in this dissertation.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Philosophy.
|Donaldson, Tom, (Philosopher)
|Donaldson, Tom, (Philosopher)
|Statement of responsibility
|Submitted to the Department of Philosophy.
|Thesis (Ph.D.)--Stanford University, 2016.
- © 2016 by Arezoo Islami
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