Related papers: Why Mathematics Works So Well
It is argued that quantum mechanics follows naturally from the assumptions that there are no fundamental causal laws but only probabilities for physical processes that are constrained by symmetries, and reality is relational in the sense…
Despite its apparent complexity, our world seems to be governed by simple laws of physics. This volume provides a philosophical introduction to such laws. I explain how they are connected to some of the central issues in philosophy, such as…
What science does, what science could do, and how to make science work? If we want to know the answers to these questions, we need to be able to uncover the mechanisms of science, going beyond metrics that are easily collectible and…
As David Berlinski writes (1997), the existence and nature of mathematics is a more compelling and far deeper problem than any of the problems raised by mathematics itself. Here we analyze the essence of mathematics making the main emphasis…
A perplexing problem in understanding physical reality is why the universe seems comprehensible, and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather…
The stipulation that no measurable quantity could have an infinite value is indispensable in physics. At the same time, in mathematics, the possibility of considering an infinite procedure as a whole is usually taken for granted. However,…
In this paper I propose a new principle in physics: the principle of "finiteness". It stems from the definition of physics as a science that deals (among other things) with measurable dimensional physical quantities. Since measurement…
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to…
Ever since its foundations were laid nearly a century ago, quantum theory has provoked questions about the very nature of reality. We address these questions by considering the universe, and the multiverse, fundamentally as complex…
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
The view of nature we adopt in the natural attitude is determined by common sense, without which we could not survive. Classical physics is modelled on this common-sense view of nature, and uses mathematics to formalise our natural…
Mathematics is usually regarded as a kind of language. The essential behavior of physical phenomena can be expressed by mathematical laws, providing descriptions and predictions. In the present essay I argue that, although mathematics can…
Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…
In the past century many fundamental results on unpredictability, undecidability and uncertainty have compelled scientists to grapple with the idea that some questions may never be resolved within our current theories. While this…
Modern mathematics is known for its rigorous proofs and tight analysis. Math is the paradigm of objectivity for most. We identify the source of that objectivity as our knowledge of the physical world given through our senses. We show in…
This paper establishes grounds for deeper exploration into the question of dual nature of mathematics as an abstract discipline and as a concrete science. It is argued, as one of the consequences of the discussion, that the division into…
Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
Measurement outcomes provide data for a physical theory. Unless they are objective they support no objective scientific knowledge. So the outcome of a quantum measurement must be an objective physical fact. But recent arguments purport to…
The key difference between math as math and math in science is that in science we blend our physical knowledge with our knowledge of math. This blending changes the way we put meaning to math and even to the way we interpret mathematical…