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

Great opportunities arise for teaching physics, astronomy, and their histories when new discoveries are made that involve concepts accessible to students at every level. Such an opportunity currently exists thanks to the fact that notes…

We report on a pedagogical experiment to make mathematics easy by changing its philosophy. The Western philosophy of math originated in religious beliefs about mathesis, cursed by the church. Later, mathematics was "reinterpreted", in a…

Mathematics is an essential element of physics problem solving, but experts often fail to appreciate exactly how they use it. Math may be the language of science, but math-in-physics is a distinct dialect of that language. Physicists tend…

We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…

While philosophy of science is the study of problems of knowledge concerning science in general, there also exists - or should exist - a '' philosophy in science'' directed at finding out in what ways our actual scientific knowledge may…

Galileo's realization that nature is not scale invariant, motivating his subsequent discovery of scaling laws, is traced to two lectures he gave on the geography of Dante's Inferno.

Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism - mathematics exists and is…

My purpose is to examine some concepts of mathematical logic, which have been studied by Carlo Cellucci. Today the aim of classical mathematical logic is not to guarantee the certainty of mathematics, but I will argue that logic can help us…

Astronomers in the early 17th century misunderstood the images of stars that they saw in their telescopes. For this reason, the data a skilled observer of that time acquired via telescopic observation of the heavens appeared to support a…

A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…

This paper attributes the sudden emergence of mathematical probability and statistics in the second half of the seventeenth century to Calvin's Reformed theology. Calvin accommodated Epicurean chance with Stoic determinism and synthesised…

Philosophy of science attempts to describe all parts of the scientific process in a general way in order to facilitate the description, execution and improvements of this process. So far, all proposed philosophies have only covered existing…

The situation surrounding the Olympiads is paradoxical. On the one hand, considerable resources are spent on the Olympiads. On the other hand, there are widespread arguments about the harm of the Olympiads, often very strange ones. For…

In Plato's dialogues Republic and Laws, the most important disciplines for the best education of the rulers of the city are identified with arithmetic, geometry and astronomy. Those disciplines, however, are not intended for practical…

Work published in Sky and Telescope in 2004 discusses Galileo's observations of the star Mizar. These observations raise questions regarding Galileo's assumptions about the universe and the conclusions he drew from his observations. Galileo…

In their account of theory change in logic, Aberdein and Read distinguish 'glorious' from 'inglorious' revolutions--only the former preserves all 'the key components of a theory' [1]. A widespread view, expressed in these terms, is that…

It is difficult for the common sense to admit that an object dropped from the top of the mast of a ship moving at a constant velocity falls down at the bottom of the mast because it keeps inside the horizontal movement of the ship. This…

We argue that the boldest claims of Big Data are in need of revision and toning-down, in view of a few basic lessons learned from the science of complex systems. We point out that, once the most extravagant claims of Big Data are properly…

Contrary to claims about the irrelevance of philosophy for science, I argue that philosophy has had, and still has, far more influence on physics than is commonly assumed. I maintain that the current anti-philosophical ideology has had…

Galileo's support to the Copernican theory was decisive for the revolutionary astronomical discoveries he achieved in 1610. We trace the origins of Galileo's conversion to the Copernican theory, discussing in particular the "Dialogo de…