Related papers: Reductionism and the Universal Calculus
The importance of language in physics has gained emphasis in recent times, on the one hand through Hilbert's views that concern formalism and intuition applied for outer inquiry, and on the other hand through Brouwer's point of view that…
As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently…
The Wigner's friend thought experiment was intended to illustrate the difficulty one has in describing an agent as a quantum system when that agent performs a measurement. While it does pose a challenge to the orthodox interpretation of…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of…
It is shown that for a wide class of analytic Lagrangians which depend only on the scalar curvature of a metric and a connection, the application of the so--called ``Palatini formalism'', i.e., treating the metric and the connection as…
This paper examines various methods and ideas for humanizing mathematics. The term 'humanizing mathematics' which includes elements of 'aesthetic mathematics' refers to approaches that emphasize the aesthetic, philosophical, and subjective…
Mathematics is the language of science. Fluent and productive use of mathematics requires one to understand the meaning embodied in mathematical symbols, operators, syntax, etc., which can be a difficult task. For instance, in algebraic…
This is the first of four papers prompted by a recent literature about a doctrine dubbed spacetime functionalism. This paper gives our general framework for discussing functionalism. Following Lewis, we take it as a species of reduction. We…
Complex numbers are basic. An inconsistency would question Wigner's unreasonable effectiveness of mathematics. A vehicle to study this question is Kirchoff's scalar diffraction theory. In the paper, an inconsistency in complex phase angle…
Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an…
Wigner found unreasonable the "effectiveness of mathematics in the natural sciences". But if the mathematics we use to describe nature is simply a coded expression of our experience then its effectiveness is quite reasonable. Its…
According to QBism, quantum states, unitary evolutions, and measurement operators are all understood as personal judgments of the agent using the formalism. Meanwhile, quantum measurement outcomes are understood as the personal experiences…
We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…
Deutsch, Feynman, and Manin viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a…
In this paper we offer a reconstruction of the evolution of Leibniz's thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability and syncategorematicity, and the closely related…
In glaring contrast to its indisputable century-old experimental success, the ultimate objects and meaning of quantum physics remain a matter of vigorous debate among physicists and philosophers of science. This article attempts to shed new…
In the Philosophical Investigations, Ludwig Wittgenstein wrote, " 'I' is not the name of a person, nor 'here' of a place, .... But they are connected with names. ... [And] it is characteristic of physics not to use these words." This…