相关论文: Galileo, Ignoramus: Mathematics versus Philosophy …

This article is the first part of a study of the so-called 'mathematical part' of Plato's Theaetetus (147d-148b). The subject of this 'mathematical part' is the irrationality, one of the most important topics in early Greek mathematics. As…

We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are…

In different passages of his dialogues, Plato showed deep mathematically-based physical insights. Regrettably most readers overlooked the respective statements, or they utterly did not understand those hints since they were full of…

In the seminal essay, "On the unreasonable effectiveness of mathematics in the physical sciences," physicist Eugene Wigner poses a fundamental philosophical question concerning the relationship between a physical system and our capacity to…

There are growing uncertainties surrounding the classical model of computation established by G\"odel, Church, Kleene, Turing and others in the 1930s onwards. The mismatch between the Turing machine conception, and the experiences of those…

The classical platonist/formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: is new mathematics discovered or invented? Using an example from my own mathematical life, I argue that…

Causality is one of the most fundamental -- and yet elusive -- concepts in physics. From its intuitive role in everyday experience to its formal and often implicit role in scientific theories, causality has challenged philosophers and…

Galileon gravity is a robust theoretical alternative to general relativity with a cosmological constant for explaining cosmic acceleration, with interesting properties such as having second order field equations and a shift symmetry. While…

Some attack scientific rationality, others defend it, but both miss the point. What both parties take to be scientific rationality is actually a species of irrationality masquerading as scientific rationality. The current orthodox…

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

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…

This paper frames calculus as a global, centuries-long development rather than a subject that began only with Newton and Leibniz. Drawing on ideas from Greek, Indian, Islamic, and later European mathematics, it highlights how concepts like…

In the context of physics didactics, alternative instructional approaches have often been employed to facilitate conceptual understanding of various topics. In this article, an alternative formulation for analyzing the motion of bodies on…

This paper wants to show how practical geometry, created to give a concrete help to people involved in trade, in land-surveying and even in astronomy, underwent a transformation that underlined its didactical value and turned it first into…

We study how the paradigm of Newton's science, based on the organization of scientific knowledge as a series of mathematical laws, was definitively accepted in science courses - in the last decades of the XVIII century, in England as well…

I provide a critical commentary regarding the attitude of the logician and the philosopher towards the physicist and physics. The commentary is intended to showcase how a general change in attitude towards making scientific inquiries can be…

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…

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…

An alternative for the construction of fundamental theories is the introduction of Galileons. These are fields whose action leads to non higher than second-order equations of motion. As this is a necessary but not sufficient condition to…

In January of 1616, the month before before the Roman Inquisition would infamously condemn the Copernican theory as being "foolish and absurd in philosophy", Monsignor Francesco Ingoli addressed Galileo Galilei with an essay entitled…