The problem of Galileo's logical methodology has long interested scholars. In this volume William A. Wallace offers a solution that is completely unexpected, yet backed by convincing documentary evidence. His analysis starts with an early notebook Galileo wrote at Pisa, appropriating a Jesuit professor's exposition of the Posterior Analystics of Aristotle, and ends with one of the last letters Galileo wrote, stating that in logic he has been a Peripatetic all his life. Wallace's detective work unearths the complete logic course (...) from which the notebook was excerpted, then proceeds to show how its terminology and methodology continue to surface in Galileo's later writings in which he founds his new sciences of the heavens and of local motion. The result is a tour de force that commends itself not only to Galileo's scholars and to logicians, philosophers, and historians, but to anyone interested in the epistemic roots of modern science. (shrink)

This paper is about the use of analogical reasoning, models and metaphors in Galileo's discovery of the mountains of the moon, which he describes in the Starry Messenger, a short but groundbreaking treatise published in 1610. On the basis of the observations of the Moon he has made with the newly invented telescope, Galileo shows that the Moon has mountains and that therefore it shares the same solid, opaque and rugged nature of the Earth. I will first reconstruct Galileo's reasoning, (...) and illustrate the counterintuitive and quasi-circular way in which discovery depends on analogy: in order for analogical reasoning to succeed in bridging ontological gaps and thus serve as a discovery tool, a certain similarity between what are considered as radically different domains has to be presupposed. More particularly, in order for analogical reasoning to lead to genuine discoveries, salient features have to be selected in the source domain that will be mapped onto the target domain. There is disagreement as to how this mapping is successfully carried out: the syntactical, pragmatic and ontological-categorical approaches, all illuminate some features of this selection in the mapping process. On the basis of an analysis of Galileo's discovery, I will argue that we need a different "bootstrapping" approach which involves the construction of an imaginary temporary model encompassing both the source and the target domains, and which is occasionally strengthened by metaphors which serve as incomplete transitional models. (shrink)

The sixteenth-century philosopher Jacopo Zabarella stands near the end of the long Aristotelian dominance of western academic philosophy. Yet, despite the fact that Aristotelianism was soon to be overwhelmed by other currents of thought, Zabarella’s influence on western thought would continue into at least the nineteenth century, and he still provides useful discussions relevant to today’s Aristotle scholars. In what follows, I discuss the existence and essence of matter, and show how Zabarella argues for his claims. What is especially notable (...) about the existence and essence of matter as a topic is that matter is clearly at the center of his well-known interest concerning the nature of scientific methodology. (shrink)

Francis Bacon’s method of induction is often understood as a form of eliminative induction. The idea, on this interpretation, is to list the possible formal causes of a phenomenon and, by reference to a copious and reliable natural history, to falsify all of them but one. Whatever remains must be the formal cause. Bacon’s crucial instances are often seen as the crowning example of this method. In this article, I argue that this interpretation of crucial instances is mistaken, and it (...) has caused us to lose sight of why Bacon assigns crucial instances a special role in his quest for epistemic certainty about formal causes. If crucial instances are interpreted eliminatively, then they are subject to the two problems related to underdetermination raised by Duhem: (1) that it is impossible to be certain one has specified all of the possible alternatives and (2) that an experiment falsifies a whole theory, not just a single hypothesis in isolation. I show that Bacon anticipates and aims to dodge both of these problems by conceiving of crucial instances as working, in the ideal case, through direct affirmations that are supported by links to more foundational knowledge. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

early modern philosophers commonly appeal to a mathematical method to demonstrate their philosophical claims. Since such claims are not always followed by what we would recognize as mathematical proofs, they are often dismissed as mere rhetoric. René Descartes, Thomas Hobbes, and Benedict de Spinoza are perhaps the most well-known early modern philosophers who fall into this category. It is a matter of dispute whether the ordo geometricus amounts to more than a method of presentation in Spinoza’s philosophy. Descartes and Hobbes (...) clearly appeal to a method of discovery modeled after geometry, but neither employs it to develop a heavily quantitative physics. Whereas Descartes’s version of the geometrical method .. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Notes and Discussions GALILEO AND THE SCHOOL OF PADUA The first issue of the Journal of the History of Ideas, appearing in 1940, contained an article on the development of scientific method in northern Italy during the Renaissance and its significance for the growth of modern science. It is no exaggeration to say that this article, by John H. Randall, Jr., has been one of the most important and (...) influential contributions to the history of ideas in recent years, casting new light on a much-neglected tradition (Italian Aristotelianism) and suggesting an entirely different picture of Galileo's relations to the school philosophy of his day. Randall's thesis has won wide acceptance, by such competent and careful scholars as Crombie, Dijksterhuis, Butterfield, and the Kneales. Giacomo Zabarella (1532-1589) has been restored to the high esteem in which he was held in the Renaissance, and has been hailed as the thinker who "summed up the collective wisdom of the Padua school" and "formulated the classic version of their teaching method, in the terms and with the distinctions so fruitfully employed and consciously expressed by Galileo." Now the article has been reprinted (John H. Randall, Jr., The School of Padua and the Emergence of Modern Science [Padua, 1961], 141 pp.) with several other provocative articles reassessing the thought of Pomponazzi and Leonardo Da Vinci, as the first in a series of monographs sponsored jointly by the universities of Padua and Columbia. It has also been incorporated in a chapter of Randall's admirable Career of Philosophy, but without the Latin texts that make the present edition definitive. In the face of the almost universal acceptance of Randall's thesis, I find it an uncongenial task to express a dissenting opinion with regard to its crucial point, namely, the presumed debt of Galileo to Zabarella. Uncongenial, because much of what Randall has urged seems well taken, and because there is an initial attractiveness about the view that philosophical discussions at Padua could have contributed to the birth of the new science. Historians of science are usually so unfair to philosophy that it is refreshing to be able to entertain the view that scientific research may even have received some encouragement from philosophers. And it is prima facie plausible that this encouragement should have come to a focus at Padua in the sixteenth century, for here if anywhere the new science was born. Unfortunately, the resulting picture of Galileo leaves us with some puz- [zz3] 224 HISTORY OF PHILOSOPHY zling facts, or more precisely, non-facts: if we accept it, we are left wondering why there is so little tangible evidence of Zabarella's influence on Galileo. It may well be that there is evidence that I have missed, and for the sake of the reputation and prestige of Italian Aristotelianism, I hope there is. But I should like to present some of the difficulties I have with Professor Randall's thesis, in the hopes that some defender of his view will be inspired to allay my misgivings. Anyone who has ever read a page of Galileo's writings knows how often and violently he expressed his opposition to "the Aristotelians" and with what withering scorn he treated the contemporary representatives of the Peripatetic tradition. He often concedes that Aristotle would have been more flexible than his so-called followers, and would have yielded to new evidence in natural philosophy. But Galileo never admits that Aristotle's followers have developed anything of scientific value in the way of methodology. The methodology of the Aristotelians relied exclusively on the syllogism ; but Galileo specifically insists that the syllogism has no value in scientific discovery, whatever its other uses may be. In the face of these stronglyexpressed and consistently-held attitudes, it is hard to see how Zabarella, a loyal Aristotelian who relied exclusively on the syllogism as the "instrument of science," could have escaped Galileo's general condemnation. This point would lose its force if Galileo had ever expressly singled Zabarella out as a shining exception among the run-of-the-mill Aristotelians. Unfortunately, there is no mention of Zabarella in the whole mass of Galileo 's writings, and there is no evidence that... (shrink)

Un essai sur la portée épistémologique des instruments d'optique au XVIIe siècle, axé sur les travaux des Anglais, et notamment l'oeuvre de Robert Hooke, qui entre tous a su donner une consistance philosophique au modèle instrumental.

Galileo’s telescopic lunar observations, announced in Siderius Nuncius (1610), were a triumph of observational skill and ingenuity. Yet, unlike the Medicean stars, Galileo’s lunar “discoveries” were not especially novel. Indeed, Plutarch had noted the moon’s uneven surface in classical times, and many other renaissance observers had also turned their gaze moonward, even (in Harriot’s case) aided by telescopes of their own. Moreover, what Galileo and his contemporaries saw was colored by the assumptions they already had. Copernicans assumed the moon was (...) a terrestrial satellite, thus Galileo saw its mountains and Kepler “saw” the dwellings of its inhabitants. Aristotelians assumed the moon was a perfect sphere, so they saw differences in density and rarity in the lunar body. Theory corrected the results of observation, so Galileo’s lunar observations, like those that had come before, proved nothing. Yet this failure contained the germ of Galileo’s success, since the Siderius Nuncius gave observation a rhetorical force it did not have before. Observers on all sides set out to see for themselves what Galileo reported. Hence, all parties now had to answer to what they saw, whatever they believed. Thus, the Siderius Nuncius ultimately changed the grounds upon which natural philosophical argument and debate was carried out. In this new empirical arena, the Galilean science would eventually prevail. (shrink)

Scholars often saw 'Sidereus nuncius' as inaugurating a novel genre of scientific writing; one that mixes elements of astronomy and natural philosophy, mixed-mathematics and travel reports, cosmography and the conventions of baroque drawing, elements of humanist pedagogy and elements of natural history. Although some of these influences were subject of extensive treatment, the natural historical elements of 'Sidereus nuncius' were, comparatively, less carefully investigated. And yet, as I will show in this paper, the natural historical outlook of 'Sidereus nuncius' played (...) a significant role in its reception. My purpose in this paper is to investigate some of the elements of natural history present in 'Sidereus nuncius'. Firstly, I show that in writing Sidereus nuncius, Galileo often made appeal to the “specialized observations” and “expert reports” of natural historians. Secondly, I show that some of the early readers of Sidereus nuncius, such as Johannes Kepler and Francis Bacon, read Galileo’s book as a natural history. I also discuss the ways in which some of them were read and interpreted in the same vein by some of Galileo’s early readers, such as Johannes Kepler and Francis Bacon. (shrink)