Inertia as a theorem in Galileo's Discorsi

Perspectivas

The clearly recognized innovation in Galileo’s work on free fall has been a stimulus and a challenge for the history and philosophy of science. This article will analyze the experimental and theoretical aspects of Galileo’s work on free fall. It draws on several authors’ results to justify the claim that the research model established by Galileo remains valid today (Sections 2 and 3). The article draws this parallel with current science by focusing on Galileo’s method, way of considering scientific instruments, and practice of confrontation between theory and experiments. The Galilean mode of investigation can be interpreted from a variety of possible philosophical perspectives: Section 3 examines how relevant the so-called constructivist and conventionalist perspectives are to analysis of Galileo’s innovations. Section 4 discusses Galileo’s contribution to the mathematization of science and the Platonic character of his thought. Finally, the article attempts to show that Galileo’s ...

Galileo's refutation of the speed-distance law of fall in his Two New Sciences is routinely dismissed as a moment of confused argumentation. We urge that Galileo's argument correctly identified why the speed-distance law is untenable, failing only in its very last step. Using an ingenious combination of scaling and self-similarity arguments, Galileo found correctly that bodies, falling from rest according to this law, fall all distances in equal times. What he failed to recognize in the last step is that this time is infinite, the result of an exponential dependence of distance on time. Instead, Galileo conflated it with the other motion that satisfies this ‘equal time’ property, instantaneous motion.

Doing Philosophy via Thought Experiments, 2022

This chapter focuses on Galileo's famous thought experiment concerning the nature of falling bodies and how it successfully overturned Aristotle's theory of proportionality, which stated that the speed of falling bodies is weight-dependent--heavier objects fall faster than lighter objects. Galileo's thought experiment is described in some detail, explaining precisely how it exposed a serious contradiction in Aristotle's theory and resulted in the discovery of a scientific law, which demonstrated that all falling bodies are governed by 'universal acceleration'' and travel at the same speed irrespective of size, shape or weight. There is a brief discussion of 'a priori' and 'a posteriori' knowledge and the remarkable fact that Galileo discovered an important feature of the natural world by 'a priori' (non-empirical) means.

The approximative only nature of Galileo's "law" has already been evidenced sporadically in the past but its status of "universal law" continues unchallenged in scientific text books. The traded misinterpretation of Galileo's "law" of Free Fall is based on the overseeing that the translational acceleration measured in the Galilean setup (referred to the earth centre) is in fact the vector sum of two Newtonian accelerations, namely that of the falling test body mass m and that of the earth mass M towards the common centre of the participating masses. It can be shown that it is a composite acceleration incremented with respect to the Newtonian acceleration by the factor (M + m)/M correcting the distortion from the "simplest form" caused by the offset of the reference frame. Galileo's law is therefore only approximately true for terrestrial fall situations with m/M typically in the order of 10 −24. Several causes are discussed in the current paper, which have contributed to the missed review of Galileo's "law", persisting up today.

is article analyzes Galileo's mathematization of motion, focusing in particular on his use of geometrical diagrams. It argues that Galileo regarded his diagrams of acceleration not just as a complement to his mathematical demonstrations, but as a powerful heuristic tool. Galileo probably abandoned the wrong assumption of the proportionality between the degree of velocity and the space traversed in accelerated motion when he realized that it was impossible, on the basis of that hypothesis, to build a diagram of the law of fall. e article also shows how Galileo's discussion of the paradoxes of infinity in the First Day of the Two New Sciences is meant to provide a visual solution to problems linked to the theory of acceleration presented in Day ree of the work. Finally, it explores the reasons why Cavalieri and Gassendi, although endorsing Galileo's law of free fall, replaced Galileo's diagrams of acceleration with alternative ones.

In this reply, we respond to the comments of Palmerino and Laird on our article, "Galileo's Refutation of the Speed Distance Law of Fall Rehabilitated," published in the same issue of Centaurus.

Physics in Perspective, 2019

Recent historiographic results in Galilean studies disclose the use of proportions, graphical representation of the kinematic variables (distance, time, speed), and the medieval double distance rule in Galileo's reasoning; these have been characterized as Galileo's ''tools for thinking.'' We assess the import of these ''tools'' in Galileo's reasoning leading to the laws of fall (v 2 / D and v / t). To this effect, a reconstruction of folio 152r shows that Galileo built proportions involving distance, time, and speed in uniform motions, and applied to them the double distance rule to obtain uniformly accelerated motions; the folio indicates that he tried to fit proportions in a graph. Analogously, an argument in Two New Sciences to the effect that an earlier proof of the law of fall started from an incorrect hypothesis (v µ D) can be recast in the language of proportions, using only the proof that v µ t and the hypothesis.

Society and Politics (SAGE Publishing), 2017

This article surveys Galileo's contribution to the conceptualisation of the problem of isochronism, as his most important input in the study of the oscillation of heavy bodies. We will deal essentially with the mathematical aspects of his various attempts to discover mathematical proofs for his theorems of isochronism, in his early manuscripts (1600-1609), bound in Volume 72 of the Galilean Manuscripts, and in his later two major publications, the Dialogo and the Discorsi. The experimental procedures he implemented in his research will be dealt with as far as they shed light on different aspects of properly mathematical issues of the Galilean analysis of iscohronism. Alternating between the analysis of Galileo's private manuscripts and the relevant passages in his mature works, we follow the emergence and evolution of Galileo's theory of the pendulum within his physics of motion, and we witness how his investigation was faced with serious challenges, mathematical and experimental, that he could never overcome completely. Keywords: Isochronism, Galileo Galilei, theory of the pendulum, law of isochronism, law of length, experiments with pendulum, modern physics, chronometry.

Hobbes tried to develop a strict version of the mechanical philosophy, in which all physical phenomena were explained only in terms of bodies in motion, and the only forces allowed were forces of collision or impact. This ambition puts Hobbes into a select group of original thinkers, alongside Galileo, Isaac Beeckman, and Des-cartes. No other early modern thinkers developed a strict version of the mechanical philosophy (not even Newton who allowed forces of attraction and repulsion operating at a distance). Natural philosophies relying solely on bodies in motion require a concept of inertial motion. Beeckman and Descartes assumed rectilinear motions were rectilinear, but Galileo adopted a theory which has been referred to as circular inertia. Hobbes's natural philosophy depended to a large extent on what he called " simple circular motions. " In this paper, I argue that Hobbes's simple circular motions derived from Galileo's belief in circular inertia. The paper opens with a section outlining Galileo's concept, the following section shows how Hobbes's physics depended upon circular motions, which are held to continue indefinitely. A third section shows the difficulty Hobbes had in maintaining a strictly mecha-nistic philosophy, and the conclusion offers some speculations as to why Galileo's circular inertia was never entertained as a serious rival to rectilinear inertia, except by Hobbes. Keywords Thomas Hobbes – Galileo Galilei – inertia – kinematics – mechanical philosophy

Studies in History and Philosophy of Science Part A, 2004

Galileo claimed inconsistency in the Aristotelian dogma concerning falling bodies and stated that all bodies must fall at the same rate. However, there is an empirical situation where the speeds of falling bodies are proportional to their weights; and even in vacuo all bodies do not fall at the same rate under terrestrial conditions. The reason for the deficiency of Galileo's reasoning is analyzed, and various physical scenarios are described in which Aristotle's claim is closer to the truth than is Galileo's. The purpose is not to reinstate Aristotelian physics at the expense of Galileo and Newton, but rather to provide evidence in support of the verdict that empirical knowledge does not come from prior philosophy.