: 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. (shrink)
Machine generated contents note: Introduction Andrew Janiak and Eric Schliesser; Part I. Newton and his Contemporaries: 1. Newton's law-constitutive approach to bodies: a response to Descartes Katherine Brading; 2. Leibniz, Newton and force Daniel Garber; 3. Locke's qualified embrace of Newton's Principia Mary Domski; 4. What geometry postulates: Newton and Barrow on the relationship of mathematics to nature Katherine Dunlop; Part II. Philosophical Themes in Newton: 5. Cotes' queries: Newton's Empiricism and Conceptions of Matter Zvi Biener and Chris Smeenk; (...) 6. Newton's Scientific Method and the Universal Law of Gravitation Ori Belkind; 7. Measurement and method: some remarks on Newton, Huygens and Euler on natural philosophy William Harper; 8. What did Newton mean by 'Absolute Motion'? Nick Huggett; 9. From velocities to fluxions Marco Panza; Part III. The Reception of Newton: 10. Newton, Locke, and Hume Graciela de Pierris; 11. Maupertuis on attraction as an inherent property of matter Lisa Downing; 12. The Newtonian refutation of Spinoza: Newton's Challenge and the Socratic Problem Eric Schliesser; 13. Dispositional explanations: Boyle's problem, Newton's solution, Hume's response Lynn Joy; 14. Newton and Kant on Absolute Space: from theology to transcendental philosophy Michael Friedman; 15. How Newton's Principia changed physics George Smith; Bibliography. (shrink)
Footnote: My thanks to Zvi Biener and Balazs Gyenis for comments. 1. What is the relationship between philosophy and physics? What should the relationship be? To someone who does not work in philosophy of physics, it can be hard to distinguish what a theoretical physicist does from what a philosopher of physics does. The differences lie in two areas: their goals and their methods. The highest goal of theoretical physicists is to find the next theory. That profoundly colors the (...) way they approach foundational ideas. Any idea that aids in finding the next theory is deemed useful. Sometimes the most suggestive ideas are so because they are on the edge of plausibility. However if they show promise of opening new pathways, physicists are quite willing to suspend critical scrutiny. There is no point abandoning a goose about to lay a golden egg because you suspect it may be a turkey! Gold is gold. As a result they may put up with what seems like patent nonsense to a philosopher. For philosophers of physics, the goal is different. The basic questions remain those asked by philosophers for milennia: What is the nature of space? What is the nature of time? What is the nature of matter? How are things in the world connected? And so on. They seek answers from our best understanding of space, time and matter -modern physics. There is no room for tolerance of fringe thinking for that would compromise the project. They ask: What is our understanding now on the basis of our best science? Philosophy of physics also differs from physics in its method. Philosopher of physics bring the sensibilities of philosophy to physics. To those outside physics, philosophy is synonymous with gazing in wonder at intractable mysteries. To the professional philosopher, the project is just the reverse. It is to take things that are conceptually puzzling and, through rigorous analysis, render them simple and transparent so that the original sense of mystery evaporates. Their method looks to the traditional demands of philosophy that theses must be clearly enunciated and defended by clear and cogent argumentation; and that these demands cannot be compromised.. (shrink)
The article aims at (1) organizing the theoretical ideas of critical thinking on the basis of an overall and systematic conception of education, (2) exposing tensions and contradictions in the various conceptions of critical thinking and (3) suggesting a directing principle for the teaching of critical thinking. In order to achieve these far-reaching aims, the author projects “The Cognitive Map of Instruction” developed by Zvi Lamm on the discourse of critical thinking. Through this “map” it seems that all sub-trends of (...) teaching critical thinking may be divided into three defined “logics,” and that these sub-trends harbor two kinds of internal contradictions: between the different “logics” of teaching, and between their pattern of teaching and the idea of critical thinking. Since none of the three “logics” suggested by Lamm (1976) in “The Cognitive Map of Instruction” suits the purpose of teaching critical thinking, the article turns away from this “map,” that served it so well to locate and expose the various trends of critical thinking. This turn is made on behalf of another idea of Lamm—that of undermining pedagogy. This well-rooted idea may direct the pedagogy of critical thinking toward a coherent and effective instruction. (shrink)
Confessions both hold a great promise and pose a grave danger. When the accused speaks against his interest and assumes responsibility for criminal actions this is viewed as a compelling sign of guilt. It is not, therefore, for naught that the confession has been crowned the "queen of evidence." Yet research conducted in the last few decades has shown that a substantial number of confessions are false, ranking the out of court confession high among the factors leading to the conviction (...) of innocent people. The acceptance of DNA testing, has further substantiated this finding, igniting a renewed interest in out-of-court confessions. It is hard to assess the magnitude of social harm caused by the widespread and persistent resort to obtaining confessions, but one thing is evident from the vast literature on the matter: this evidentiary mechanism is currently overused, much beyond the optimal level. The reasons for this over-use are varied, among them the fact that confessions are readily available for law enforcement officers, and that those in charge of trying the facts tend to overwhelmingly convict based on out-of-court confessions, while underestimating the associated dangers. As a result, confessions have come to play a paramount role in the criminal justice system. Many attempts have been made to deal with confession-based wrongful convictions. Examples include the Miranda rules or the requirements for varying degrees and types of corroborating evidence. To date, all the rules and proposals share a common characteristic: They all attempt to correct the evidentiary fallacies associated with out-of-court confessions by evidentiary means, whether admissibility oriented or weight oriented. In the article we argue that none of the proposed mechanisms is likely to solve the problem. The root of the problem lies in the fact that the entire criminal justice system is currently organized around confessions. Law enforcement officers focus on obtaining confessions and the prosecution uses it as its evidentiary centerpiece. Further restricting admissibility or requiring a higher degree of corroboration will not change this trend. Moreover, the confessional lure is too strong to resist. Like the Sirens' Song, the confession casts a spell on all those subjected to it and, no matter how strong a corroboration we require, we will eventually fall back on the confession. We propose an entirely different solution to the tendency to over-use confessions, one that utilizes penal means to change the incentive structure within the criminal justice system. We propose to incorporate into the sentencing guidelines a mandatory reduction of the criminal sanction whenever an out-of-court confession is introduced into evidence by the prosecution. In other words, our proposal is to elevate the cost of using out-of court confessions, as compared to other types of evidence. The article will demonstrate how placing such a "sentencing price tag" on the use of out-of-court confessions will correct the current bias in favor of using this evidence and induce law enforcement officials to seek extrinsic evidence, thus turning confessions into a residual evidentiary devise. The article will also show that the proposed regime will improve the court's ability to distinguish between true and false confessions. After discussing the proposed model's normative appeal, the article will proceed to deal with possible criticisms which can be leveled against it, whether retributive, utilitarian or expressive. (shrink)
