Online research in philosophy

: Although Galileo's struggle to mathematize the study of nature is well known and oft discussed, less discussed is the form this struggle takes in relation to Galileo's first new science, the science of the second day of the Discorsi. This essay argues that Galileo's first science ought to be understood as the science of matter—not, as it is usually understood, the science of the strength of materials. This understanding sheds light on the convoluted structure of the Discorsi's first day. It suggests that the day's meandering discussions of the continuum, infinity, the vacuum, and condensation and rarefaction establish that a formal treatment of the "eternal and necessary" properties of matter is possible; i.e., that matter as such can be considered mathematically. This would have been a necessary, and indeed revolutionary, preliminary to the mathematical science of the second day because matter itself was thought in the Aristotelian tradition to be responsible for the departure of natural bodies from the unchanging and thus mathematizable character of abstract objects. In addition, the first day establishes that when considered physically, these properties account for matter's force of cohesion and resistance to fracture. This essay closes by showing that this dual style of reasoning accords with the conceptual structure of mixed mathematics.

In this contribution I intend to reconstruct and evaluate one of Galileo's famous arguments given in the Discorsi against a well-entrenched thesis of Aristotelian physics. It will be shown that Galileo's reduction-to-the-absurd type of counterargument is, although seemingly cogent, after all fallacious. I ascribe Galileo's committing of this fallacy to his looking at the Aristotelian physics through the (Kuhnian type) paradigmatic “spectacles” of his own new physics.

Abstract In this contribution I intend to reconstruct and evaluate one of Galileo's famous arguments given in the Discorsi against a well?entrenched thesis of Aristotelian physics. It will be shown that Galileo's reduction?to?the?absurd type of counterargument is, although seemingly cogent, after all fallacious. I ascribe Galileo's committing of this fallacy to his looking at the Aristotelian physics through the (Kuhnian type) paradigmatic ?spectacles? of his own new physics.

This paper examines geometrical arguments from Galileo's Mechanics and Two New Sciences to discern the influence of the Aristotelian Mechanical Problems on Galileo's dynamics. A common scientific procedure is found in the Aristotelian author's treatment of the balance and lever and in Galileo's rules concerning motion along inclined planes. This scientific procedure is understood as a development of Eudoxan proportional reasoning, as it was used in Eudoxan astronomy rather than simply as it appears in Euclid's Elements. Topics treated include the significance of the circle in Galileo's demonstrations, the substitution of rectilinear elements for heterogeneous factors like weight and curvilinear distance, and the way in which elements of a motion are used to measure other elements of the same motion. The indirectness of Galileo's proofs, his conception of speed as relative and comparative, and the meaning of his concept of moment all come into clearer focus. Conclusions are drawn about Galilean idealization, and also about the contrast of literal versus figural modes of explanation in Galileo's science.

In this essay, I shall take up the theme of Galileo’s notion of cause, which has already received considerable attention. I shall argue that the participants in the debate as it stands have overlooked a striking and essential feature of Galileo’s notion of cause. Galileo not only reformed natural philosophy, he also – as I shall defend – introduced a new notion of causality and integrated it in his scientific practice (hence, this new notion also has its methodological repercussions). Galileo’s conception of causality went hand in hand with his methodology. It is my claim that Galileo was trying to construct a new scientifically useful notion of causality. This new notion of causality is an interventionist notion.

Starting with a discussion of what I call Koyré’s paradox of conceptual novelty, I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo’s work. I then argue that although the view of Damerow et al. on the nature of Galileo’s conceptual innovation is convincing, it misses an essential element: Galileo’s use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. Central to my analysis is the idea that Galileo’s pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way Galileo’s experiments constitute an essential part of the meaning of the new concepts of classical mechanics.

Starting with a discussion of what I call `Koyré's paradox of conceptual novelty', I introduce the ideas of Damerow et al. on the establishment of classical mechanics in Galileo's work. I then argue that although their view on the nature of Galileo's conceptual innovation is convincing, it misses an essential element: Galileo's use of the experiments described in the first day of the Two New Sciences. I describe these experiments and analyze their function. Central to my analysis is the idea that Galileo's pendulum experiments serve to secure the reference of his theoretical models in actually occurring cases of free fall. In this way, Galileo's experiments constitute an essential part of the meaning of the new concepts of classical mechanics.

By carefully examining one of the most famous thought experiments in the history of science—that by which Galileo is said to have refuted the Aristotelian theory that heavier bodies fall faster than lighter ones—I attempt to show that thought experiments play a distinctive role in scientific inquiry. Reasoning about particular entities within the context of an imaginary scenario can lead to rationally justified concluusions that—given the same initial information—would not be rationally justifiable on the basis of a straightforward argument.

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.

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.