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

Feyerabend frequently discussed physics. He also referred to the history of the subject when motivating his philosophy of science. Alas, as some examples show, his understanding of physics remained superficial. In this respect, Feyerabend…

Engineering needs mathematics, but the converse is also increasingly evident. Indeed, mathematics is still recovering from the drawbacks of several "reforms". Encouraging is the revived interest in proofs indicated by various recent…

In 1492, for the first time, an unknown ocean opened up before sailors: weeks of navigation and no idea how to pinpoint their location. Since ancient times, navigators had known how to determine latitude by using the North Star, but the…

In the middle of the seventeenth century, Andr\'e Tacquet, S.J. briefly discussed a scientific argument regarding the structure of a Copernican universe, and commented on Galileo Galilei's discussion of that same argument -- Galileo's…

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…

Experiments may not reveal their full import at the time that they are performed. The scientists who perform them usually are testing a specific hypothesis and quite often have specific expectations limiting the possible inferences that can…

The classical platonist / formalist dilemma in philosophy of mathematics can be expressed in lay terms as a deceptively naive question: \emph{Is new mathematics discovered or invented? Using examples from my own mathematical work during the…

I discuss Ren{\'e} Thom's approach to philosophy based on his mathematical background. At the same time, I will highlight his connection with Aristotle, his criticism of the modern view of science as a predictive process, his ideas on…

Data scientists are not mathematicians, but they make heavy use of mathematics in their daily work. While mathematicians can study a mathematical object which is inaccessible to our five senses, data scientists must deal with real-world…

This paper argues that philosophers of science have before them an important new task that they urgently need to take up. It is to convince the scientific community to adopt and implement a new philosophy of science that does better justice…

Most discussions of G\"odel's theorems fall into one of two types: either they emphasize perceived philosophical, cultural "meanings" of the theorems, and perhaps sketch some of the ideas of the proofs, usually relating G\"odel's proofs to…

Einstein initially objected to the probabilistic aspect of quantum mechanics - the idea that God is playing at dice. Later he changed his ground, and focussed instead on the point that the Copenhagen Interpretation leads to what Einstein…

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…

In a previous article we gave the general foundations of the theory of movement considered from a philosophical and mathematical point of view. Philosophical it meant to understand the opposition of the one and the multiple, mathematically…

This paper revisits the foundations of mathematical proof through the lens of Aristotle's threefold conception of truth: sensory evidence, axiomatic definition, and syllogistic deduction. I argue that modern mathematics has too often…

The cultural infrastructure that let Galileo invent the modern physics is discussed. The key new element of modern physics was firm belief in its fundamental structure, which could be expressed in the double postulate: 1) There are…

An intriguing reference to the existence of a self-portrait by Galileo Galilei is contained in the biography of the scientist by Thomas Salusbury dated ca. 1665, of which only one incomplete and inaccessible copy exists. Galileo grew up in…

The Italian astronomer Giovanni Battista Riccioli is commonly credited with performing the first precise experiments to determine the acceleration of a freely falling body. Riccioli has been discussed by historians of science, sometimes…

I reflect on some of the basic aspects of present day Beyond the Standard Model particle physics, focusing mostly on the issues of naturalness, in particular on the so-called hierarchy problem. To all of us, physics as natural science…

We state the defining characteristic of mathematics as a type of symmetry where one can change the connotation of a mathematical statement in a certain way when the statement's truth value remains the same. This view of mathematics as…