The pendulum clock was one of the most important metaphors for early modern philosophers. Christiaan Huygens (1629-1695) discovered his pendulum clock in 1656 based on the principle of isochronism discovered by Galileo (1564-1642). This paper aims at exploring the broad historical context of this invention, showing the role of some key figures such as Andreas Colvius (1594-1671), Elia Diodati (1576-1661), Hugo Grotius (1583-1645) and Constantijn Huygens, the father of Christiaan Huygens. Secondly, it suggests - based on this context (...) - that it is hard to believe that Huygens did not know about Galileo’s idea to construct a pendulum regulated clock. Finally, this article illustrates how the Dutch philosopher Spinoza (1632-1677) might have been inspired by Huygens’ discovery of the synchronization of the pendulum clocks in his views on the agreement between bodies in the universe. -/- Resumo: O relógio de pêndulo foi uma das metáforas mais importantes para os filósofos modernos. Christiaan Huygens (1629-1695) inventou o relógio de pêndulo em 1656 baseado no princípio do isocronismo descoberto por Galileo (1564-1642). Este artigo busca explorar o amplo contexto histórico dessa invenção, demonstrando o papel de algumas figuras-chave como Andreas Colvius (1594-1671), Elia Diodati (1576-1661), Hugo Grotius (1583-1645) e Constantijn Huygens, o pai de Christiaan Huygens. Em segundo lugar, sugere-se - baseado nesse contexto - que é difícil acreditar que Huygens não sabia da ideia de Galileo de construir um relógio regulado por um pêndulo. Por fim, este artigo ilustra como o filósofo holandês Espinosa (1632-1677) pode ter se inspirado nessa invenção de Huygens da sincronização do relógio de pêndulo em suas visões sobre o acordo entre os corpos no universo. -/- Palavras-chave: Galileo; Relógio de pêndulo; Huygens; República holandesa; Espinosa. -/- . (shrink)

This essay proposes that the only publication of the Accademia del Cimento, referred to as Saggi,Footnote11 Accademia del Cimento, Saggi di naturali esperienze fatte nell’ Accademia del Cimento sotto la protezione del serenissimo principe Leopoldo di Toscana e descritte dal segretario di essa Accademia (Firenze: Per Giuseppe Cocchini, 1667). had as one of its main goals the celebration of the House of Medici’s paternity of cutting-edge experiments and instruments during the reign of Grand Duke Ferdinando II. These included Ferdinando II’s (...) thermometers and hygrometers, Torricelli’s experiment and barometer, and Galileo’s pendulum as a clock-regulator. It seems that this agenda went unnoticed, not at the time of its initial circulation, but rather in modern historiography. Christiaan Huygens’s challenged invention of the pendulum clock provides a case study to explore the agenda of this publication and the problem of defining an invention in seventeenth-century Europe. This paper presents for the first time the document that attests to when the first specimen of Huygens’s clock arrived in Florence, disproving the previously believed date of September 1657. The paper argues that over the last two centuries, this error has made the Medici narratives of this dispute appear inconsistent and marginalized them. In light of this new find, they must be reconsidered. (shrink)

The recent debate about whether gauge symmetries can be empirically significant has focused on the possibility of 'Galileo's ship' types of scenarios, where the symmetries effect relational differences between a subsystem and the environment. However, it has gone largely unremarked that apart from such Galileo's ship scenarios, Greaves and Wallace (2014) proposed that gauge transformations can also be empirically significant in a 'non-relational' manner that is analogous to a Faraday-cage scenario, where the subsystem symmetry is related to a change in (...) a charged boundary state. In this paper, we investigate the question of whether such non-relational scenarios are possible for gauge theories. Remarkably, the answer to this question turns out to be closely related to a foundational puzzle that has driven a host of recent developments at the frontiers of theoretical physics. By drawing on these recent developments, we show that a very natural way of elaborating on Greaves and Wallace's claim of non-relational empirical significance for gauge symmetry is incoherent. However, we also argue that much of what they suggest is correct in spirit: one can indeed construct non-relational models of the kind they sketch, albeit ones where the empirical significance is not witnessed by a gauge symmetry but instead by a superficially similar boundary symmetry. Furthermore, the latter casts doubt on whether one really abandons Galileo's ship in such scenarios. (shrink)

"This is a very creative piece of work which merits the highest praise. It should be of great value for students and for the general reader."—I. Bernard Cohen, author of Guide to Newton's "Principia" "Finocchiaro has done a superb job of presenting Galileo to the modern reader. The Dialogue is a work of extreme difficulty, requiring a compendious introduction, careful selection, translation and analysis of texts, and thoughtful evaluation of its impact on Western culture. With his well-known logical ability and (...) a feel for pedagogy rare among scholars, Finocchiaro meets these demands in an exceptional way. His is a classic introduction to Galileo's masterpiece."—William A. Wallace, author of Galileo's Logic of Discovery and Proof "I recommend Galileo on the World Systems for any course on Galileo. The introduction does a fine job of situating the book in the intellectual climate of the time, and the notes make Galileo's prose and arguments thoroughly accessible."—Albert Van Helden, translator of Galileo's Sidereus Nuncius. (shrink)

Galileo's paradox of infinity involves comparing the set of natural numbers, N, and the set of squares, {n2 : n ∈ N}. Galileo sets up a one-to-one correspondence between these sets; on this basis, the number of the elements of N is considered to be equal to the number of the elements of {n2 : n ∈ N}. It also characterizes the set of squares as smaller than the set of natural numbers, since ``there are many more numbers than squares". (...) As a result, it concludes that infinities cannot be compared in terms of greater--lesser and the law of trichotomy does not apply to them. Cantor's cardinal numbers provide a measure for sets. Cantor gives a definition of the relation greater–lesser between cardinal numbers and establishes the law of trichotomy for these numbers. Yet, when Cantor's theory is applied to subsets of N, it gives that any set can be either finite or of the power ℵ0. Thus, although the set of squares is the subset of N, they are of the same cardinality. Benci, Di Nasso introduces specific numbers to measure sets called numerosities. With numerosities, the following claim is true: numerosity of A < numerosity of B, whenever A ⊈ B. In this paper, we present a simplified version of the theory of numerosities that applies to subsets of N. This theory complies with Galileo's presupposition that when A ⊈ B, then the number of elements in A is smaller than the number of elements in B. Specifically, we show that as the numerosity of N is the number α, the numerosity of the set of squares is the integer part of the number √α, that is ⌊√α⌋, and the inequality ⌊√α⌋ < α holds. (shrink)

V pričujočem sklopu so prevedena izbrana pisma Galilea Galileija ter njegovih korespondentov o problematiki razmerja med naravoslovnim oz. filozofskim raziskovanjem in Svetim pismom in s to problematiko povezani dokumenti iz Vatikanskega tajnega arhiva iz obdobja t. i. Galileijevega prvega procesa. Sklop zaključuje Galileijeva Razprava o morskem plimovanju, ki vsebinsko sicer ne zadeva omenjene problematike, je pa nastala kot posledica takratnega dogajanja. Vsa pisma so prevedena po kritični izdaji Galileijevih del, Le Opere di Galileo Galilei, ur. Antonio Favaro, Barbèra, Firence 1890–1909. (...) Dokumenti iz Vatikanskega tajnega arhiva so prevedeni po kritični izdaji I documenti vaticani del processo di Galileo Galilei. Nuova edizione accresciuta, rivista e annotata da Sergio Pagano, Archivio segreto vaticano, Mesto Vatikan 2009. Prevod Mojca Mihelič. Besedili Galileo Galilei poklican h kardinalu Bellarminu in Ukor kardinala Roberta Bellarmina Galileu Galileiju je prevedel Gašper Kvartič. Opombe in komentarji Matjaž Vesel in Mojca Mihelič. (shrink)

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)

In this essay, I will lay out first in some detail the exegetical principles implicit in Augustine's treatment of an early apparent conflict between Scripture and the findings of “sense or reason.” Then I will analyze Galileo's two major discussions of the issue, first in his Letter to Castelli, and then in his Letter to the Grand Duchess, touching on Foscarini's ill-fated Letter in between. I will turn then to an internal tension that many commentators have perceived within the exegetic (...) principles that Galileo deploys in meeting the theological challenge to Copernicanism. The tension was, broadly speaking, between two rather different strategies for dealing with that challenge. According to the more radical choice, the strategy would be to deny the relevance of Scripture to our knowledge of the natural world. The more conservative strategy would be to allow that the authority of divine revelation extended to passages in Scripture describing features of the natural world but also to admit that where this description clashed with something that could be demonstrated through “sense or reason,” an alternative to the literal, everyday, meaning of the Scripture passage should be sought. This latter proviso would imply that even in this, the most conservative, approach, theology is not being given absolute priority over natural philosophy. (shrink)

This article investigates and resolves the question whether gauge symmetry can display analogs of the famous Galileo’s ship scenario. In doing so, it builds on and clarifies the work of Greaves and Wallace on this subject.

It is widely acknowledged that the Galilean Relativity Principle, according to which the laws of classical systems are the same in all inertial frames in relative motion, has played an important role in the development of modern physics. It is also commonly believed that this principle holds the key to answering why, for example, we do not notice the orbital velocity of the Earth as we go about our day. And yet, I argue in this paper that the precise content (...) of this principle is ambiguous: standard presentations, in both physics and philosophy, fail to distinguish between two principles that are ultimately inequivalent, the “External Galilean Relativity Principle” (EGRP) and the “Internal Galilean Relativity Principle” (IGRP). I demonstrate that EGRP and IGRP play distinct roles in physics practice (e.g., EGRP is connected to the concept of Galilean invariance, but IGRP is not) and that many classical systems that satisfy IGRP fail to satisfy EGRP. I further show that the Relativity Principle introduced by Einstein in 1905—which is not restricted to classical systems—also leads to two inequivalent principles, an external one analogous to EGRP, and an internal one analogous to IGRP. I conclude by noting that the phenomenon originally captured by Galileo’s famous ship passage is much more general than contemporary discussions in the philosophy of symmetries suggest. (shrink)

Galileo’s impractical science Content Type Journal Article Pages 1-3 DOI 10.1007/s11016-011-9534-4 Authors David Marshall Miller, Department of Philosophy, Duke University, 201 West Duke, Durham, NC 27708, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

The aim of Galileo’s tidal theory was to show that the tides were produced entirely by the earth’s motion and thereby to demonstrate the physical truth of Copernicanism. However, in the Dialogue Concerning the Two Chief World Systems Galileo did not explain some of the most significant aspects of the theory completely. As a consequence, the way the theory works has long been disputed. Though there exist a number of interpretations in the literature, the most widely accepted are based (...) on ideas that are not explicitly articulated by Galileo in the Dialogue. This essay attempts to understand the way the theory functions in terms of Galilean physics. It is an interpretation of the theory based solely on Galileo’s arguments—and one that reveals it to have had some unrecognized consequences. This interpretation indicates that Galileo’s theory would not have worked in the manner he described in the Dialogue. (shrink)

Summary One aim of this paper is to provide an assessment of the recent attempts to interpret the development of Galileo's theory of motion in the late Paduan period 1604?1610. In addition to this a new interpretation of this process of development is advanced. This interpretation is the first that proves able to provide a full account of all the features on folio 152r of volume 72 of the Galilean manuscripts which has been claimed to be of crucial significance. The (...) major feature of the interpretation is that it is the first to account for the relationship between Galileo's theoretical and experimental work in the period 1604?1610. (shrink)

: 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)

This paper proposes a reading of Galileo’s Letter to the Grand Duchess Christina as analogous to a legal brief submitted to a court en banc. The Letter develops a theory of the general issues underlying the case at hand, but it is organized around advocacy for a particular judgment. I have drawn two architectonic implications from this framework, each of which helps to resolve an issue still standing in the literature. First, the Letter anticipates varying degrees of acquiescence to (...) its general account, and provides ‘hooks’ for different readers to interpret variously while still converging on the particular judgment. This reading allows for a coherent Galilean interpretation of passages that notoriously concede priority to Scripture, while also explaining their dialectical function. Galileo is neither self-contradictory nor dissimulating here, but strategically leaves the specification of key distinctions for the reader. Second, the Letter, and particularly its apparent shifting of the burden of proof, must be understood in light of the tripartite ‘adversarial-judicial’ framework that Galileo sets up. The burden of proof is shifted to anti-Copernicans within the Church, not as a rhetorical trick, but because of the benefits of adversarial procedure that will accrue to the Church as the responsible judge. (shrink)

Galileo’s 1638 Two New Sciences, a canonical text of early modern science, is analyzed as a window into period practices of mixed-mathematical reading. Galileo’s depiction of reading reflects common scholarly practices, including those of summarizing, commenting, repeated study, and an interest in mathematical diagrams. With this text, Galileo also attempted to shape his readers’ practices, inciting them to approach topical-based reading strategies with care and to use experiment and experience to validate the written word. It is suggested that (...) the concern with reading practices exhibited in the text derived from circumstances surrounding Galileo’s 1633 condemnation. (shrink)

Using Galileo Galilei's Saggiatore and Ludovico Ariosto's Orlando furioso as a focal point, this article evaluates a mixed methods approach for identifying matches of words and phrases that are rich material for close reading and contextualization. The method focuses on ngram matches and networks of phrases that are used together. The similarity of Galileo's treatise to Ariosto's poem is compared to 45 other early modern Italian texts to evaluate the relative exceptionalism or normality of the findings. Ngram matches reveal a (...) series of previously unknown connections between the Saggiatore and Furioso, which indicate an analytical understanding of the poem, rather than borrowing of narrative or figurative expression. Network analysis offers a preliminary outline for two communities of texts that frequently use the same ngrams found in the Furioso. (shrink)

The aim of this paper is to take Galileo's mathematization of nature as a springboard for contrasting the time-honoured empiricist conception of phenomena, exemplified by Pierre Duhem's analysis in To Save the Phenomena , with Immanuel Kant's. Hence the purpose of this paper is twofold. I) On the philosophical side, I want to draw attention to Kant's more robust conception of phenomena compared to the one we have inherited from Duhem and contemporary empiricism. II) On the historical side, I want (...) to show what particular aspects of Galileo's mathematization of nature find a counterpart in Kant's conception of phenomena.------------------------------------------------------------------------------------------ ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------- --------------------------------------------------. (shrink)

Galileo’s last publication, his Discorsi e dimostrazioni matematiche intorno a due nuove scienze attenenti alla mecanica & i movimenti locali (1638), is widely considered to be one of the most influential contributions of early modern science to the emergence of classical physics. As the title of Galileo’s book indicates, he himself claimed to have established “two new sciences,” including a new science of motion which, from the perspective of classical physics, indeed turned the Aristotelean theory of motion, which (...) had prevailed for hundreds of years, into an obscure medieval relic. (shrink)

Until fairly recently a common way of doing history of science was to pick up an important strand of contemporary scientific thought and to trace its origin back to the philosophical tangle of the scientific revolution. This approach conveniently by-passed the breakdowns of once useful and pervasive theories, and neglected the long intellectual journeys along devious routes. History of science read like a success story; the pioneers who failed were neither dismissed nor excused; they were simply ignored. The historian knew (...) what he was hunting for and he was careful to limit his search to areas where his quarry was sure to be found. This method, which has been dubbed the precursor-view, stands in contrast—albeit, not in opposition—to the contextual method, which aims at a better understanding of the actual thought-processes of the early scientists. On this second view, history of science must not only account for present theories in the light of past developments, it must also assess old theories in terms of the scientist's conceptual framework, and judge them against the background of the world picture of his age. This may lead the historian down the blind alleys of the past, chasing spurious attempts at explaining the nature of physical reality, but it can clear the ground for a less anachronistic interpretation of the emergence of modern science and the actual process of discovery. History of science acts as a winnowing fork, but we cannot suppose that the discoverer himself always separated the wheat from the chaff, and we must be ever wary of equating the dream with the task. (shrink)

The empirical content of the modern definition of relativity given in the Andersonian approach to spacetime theory has been overestimated. It does not imply the empirical relativity Galileo illustrated in his famous ship thought experiment. I offer a number of arguments—some of which are in essential agreement with a recent analysis of Brown and Sypel [1995]—which make this plausible. Then I go on to present example spacetime theories which are modern relativistic but violate Galileo's relativity. I end by briefly discussing (...) the prospects for improving on modern relativity. (shrink)

The paper explores the question of the relationship between science and religion today in light of its modern origin in the Galileo affair. After first presenting Ian Barbour’s four standard models for the possible relationships between science and religion, it then draws on the work of Richard Blackwell and Ernan McMullin to consider the Augustinian principles at work in Galileo’s understanding of science and religion. In light of this the paper proposes a fifth, hybrid model, “dialogical convergence,” as a (...) more adequate model of the relationship in-between science and religion because it is epistemically just in its coherence with the last fifty years of philosophy of science by which it affords more than the mere tolerance of an independence view which leaves no space for the possibility of a theological understanding of nature. (shrink)

The first attempted derivation by Galileo of the law relating space and time in free fall that has survived is preserved on an otherwise unidentified sheet bound among his manuscripts preserved at Florence. It is undoubtedly closely associated with a letter from Galileo to Paolo Sarpi, dated 16 October 1604, which somehow found its way into the Seminary of Pisa, where it is still preserved. Those two documents, together with the letter from Sarpi to Galileo which seems to have inspired (...) them, are translated in full below. Sarpi's letter, dated 9 October 1604, suggests that recent oral discussions of problems of motion had recently taken place between the two men. It reads as follows:“In sending you the enclosure, it occurs to me to propose to you a problem to resolve, and another that seems to me paradoxical. (shrink)

SummaryA heretofore overlooked response to Galileo's 1638 Discorsi is described by examining two extant copies of the text which are heavily annotated. It is first demonstrated that these copies contain annotations made by Seth Ward and Sir Christopher Wren. This article then examines one feature of Ward's and Wren's responses to the Discorsi, namely their decision to re-write several of Galileo's geometrical demonstrations into the language of symbolic algebra. It is argued that this type of active reading of period mathematical (...) texts may have been part of the regular scholarly and pedagogical practices of early modern British mathematicians like Ward and Wren. A set of Appendices contains a transcription and translation of the analytical solutions found in these annotated copies. (shrink)

Summary This contribution examines the history of the production of Galileo's 1638 Discorsi. It provides a detailed narrative of Galileo's and his collaborators' attempts to secure a printer for the work. Through analysis of surviving correspondence, manuscripts, and proof copies, I examine in greater detail the working methods of Galileo and his correspondents, particularly in regards to the text's images. This examination serves as a boon to historians of the early modern book, as Galileo's surviving correspondence provides an unusually rich (...) record of his and his collaborators' activities. I show that the volume was produced through a collaborative process in which Galileo's correspondents played a significant role in determining the work's layout, images, and content. The study thus complements the claims of previous scholars, who have argued for the collaborative nature of much of Galileo's intellectual work. It also offers a new perspective on the Discorsi, a text which is often studied for insight into Galileo's process of discovery. (shrink)

This article considers the research ethics appropriate to Paul Feyerabend’s notorious ‘methodological anarchist’ approach to the history and philosophy of science, concluding that it might be especially appropriate for our ‘post-truth’ times. The article begins by noting that Feyerabend favorite historical figure, Galileo, appears Janus-faced in his corpus. The article focuses on the positive image of someone who broke institutionalized rules of inquiry in pursuit of a ‘higher truth’ that was fully realized by Newton and his successors. The logic of (...) Galileo’s early seventeenth century situation was that decisions about permissible forms of inquiry and inference were based on mixed political and epistemic criteria – and that this was known, and sometimes admitted, by all parties. Galileo played with this ambiguity to some but by no means complete success, largely because he could not properly ground his ‘higher truth’. The article proceeds to show that Galileo’s situation was not unique but commonplace in the history of science, a point that has become clearer since the rise of archival historical research in the nineteenth century. Moreover, the institutional incentives to commit, cover up and detect what we now call ‘research fraud’ have been very uneven. Most such fraud has probably passed undetected sufficiently long to be incorporated in the body of accepted scientific knowledge. In recent years, however, increased attention has been given to research fraud due to the increased existential and financial stakes involved, which in turn have contributed to science’s larger legitimacy crisis in the post-truth era. The article ends on a Feyerabendian note, suggesting that research findings should include sunset clauses and statues of limitations. (shrink)

Galileo’s lessons on critical reasoning Content Type Journal Article Pages 1-3 DOI 10.1007/s11016-011-9541-5 Authors Luciano Boschiero, Campion College, PO Box 3052, Toongabbie East, NSW 2146, Australia Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

How Galileo created the problem of consciousness -- Is there a ghost in the machine? -- Can physical science explain consciousness? -- How to solve the problem of consciousness -- Consciousness and the meaning of life.

Based on an examination of Galileo’s mechanics, Peter Machamer and Andrea Woody proposed the scientific use of what they call models of intelligibility. As they define it, a model of intelligibility is a concrete phenomenon that guides scientific understanding of problematic cases. This paper extends Machamer and Woody’s analysis by elaborating the semantic function of MOIs. MOIs are physical embodiments of theoretical representations. Therefore, they eliminate the interpretive distance between theory and phenomena, creating classes of concrete referents for theoretical (...) concepts. Meanwhile, MOIs also provide evidence for historical analyses of concepts, like ‘body’ or ‘motion’, that are otherwise thought to be too basic for explicit explication. These points are illustrated by two examples also drawn from Galileo. First, I show how the introduction of the balance as an MOI leads Galileo to reject the Aristotelian conception of elemental natures. Second, Galileo’s rejection of medieval MOIs of circular motion constrains the reference of ‘conserved motion’ to curvilinear translations, thereby excluding the rotations that had been included in its scope. Both uses of MOIs marked important steps toward modern classical mechanics. (shrink)

ABSTRACT: In Die Frage nach dem Ding, Martin Heidegger characterizes Galileo as an important transitional figure in the struggle to replace the Aristotelian conception of nature with that of Newton. However, Heidegger only attends to Galileo’s modernity and not to those Aristotelian elements still discernible in Galileo’s work. This article fleshes out both aspects in Galileo in light of Heidegger’s discussion. It concludes by arguing that the lacuna in Heidegger’s account of Galileo is the consequence of Heidegger’s own (...) self-conscious modernity − a modernity that he slyly hints at in a remark he makes in FD concerning Galileo and Democritus.RÉSUMÉ : Dans Die Frage nach dem Ding, Martin Heidegger qualifie Galilée de figure importante dans la lutte pour remplacer la conception aristotélicienne de la nature par celle de Newton. Toutefois, Heidegger examine seulement les traits modernes de Galilée et non ceux qui ressemblent à Aristote. Cet article précise ces deux aspects à partir de la discussion dans Die Frage nach dem Ding. Il conclut par l’affirmation que la lacune dans le portrait de Galilée est la conséquence de la modernité consciente de Heidegger lui-même — une modernité à laquelle il fait allusion dans une remarque concernant Galilée et Démocrite. (shrink)

Having been found ‘vehemently suspected of heresy’ by the Holy Office in 1633, at the time of his death Galileo's remains were laid to rest in the tiny vestry of a lateral chapel of the Santa Croce Basilica, Florence. Throughout his life, Vincenzo Viviani, Galileo's last disciple, struggled to have his master's name rehabilitated and his banned works reprinted, as well as a proper funeral monument erected. He did not live to see all this come true, but his efforts triggered (...) a mechanism that eventually led to the fulfilment of his wishes. A key element of his project was the transformation of the facade of his palace into a private tribute to Galileo, with two long inscriptions celebrating Galileo's achievements and calling Florence's attention to the need to pay a proper tribute to him. Shortly afterwards, he revised the text and circulated it in print. This article presents the first critical edition and annotated translation of Viviani's original manuscript, long thought to be lost, and describes its role in Viviani's lifelong struggle for Galileo's intellectual legacy, as well as its impact on future historiography. (shrink)

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 Platonism also involves experiments, as he conceives them. Keywords: Inclined Plane. Mathematics. Platonism. (shrink)

A recent English translation (Discoveries and opinions of Galileo, transl. by Stillman Drake. New York: Doubleday, 1957) of selections from the writings of Galileo will doubtless bring to the attention of many readers the statements about Copernicus in the great Italian scientist’s "Letter to the Grand Duchess Christina". These statements by Galileo contain five serious errors. To impede their further spread is the aim of the present article.

Thought experiments provide a conspicuous case study for epistemologists of the imagination. Galileo’s famous thought experiment about falling stones is a central example in the debate about how thought experiments in science work. According to a standard interpretation, the thought experiment poses a challenge to an Aristotelian principle about falling bodies that conceives of bodies in an extremely liberal way. This chapter argues that this interpretation is implausible and then shows how the thought experiment might present a challenge to (...) a principle that conceives of bodies in a less permissive, more plausible way. The new interpretation of the thought experiment relies on a distinction between two ways of imagining Galileo’s experiment, one of which requires Aristotelians to temporarily ignore their belief in the principle under challenge. It is suggested that the distinction tracks an increasingly familiar distinction among dual-process theories in psychology: ‘intuitive’ and ‘reflective’ imagination. In order for Aristotelians to appreciate the thought experiment’s challenge to their theory, they are expected to use their intuitive imagination and not just their reflective imagination. (shrink)

V. 1 is a detailed analysis of a previously unknown proof copy of the first edition of Galileo's Sidereus nuncius, in which watercolor drawings appear in place of the etchings of the published edition, consigned in 2005 to the antiquarian bookselling firm of Martayan Lan. V. 2 is an account of the composition and production of the edition, based on analysis of extant copies as well as the New York proof copy. V. 3 was written in response to the discovery, (...) soon after the publication of v. 2, that the proof copy was in fact an elaborate forgery produced between 2003 and 2005 under the direction of Marino Massimo de Caro, as first reported in the article "A very rare book," by Nicholas Schmidle, in The New Yorker issue of 16 December 2013. V. 4, in German, is a heavily revised edition of Horst Bredekamp's Galilei der Künstler, which had included a chapter on the then unrecognized forgery. (shrink)

This 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. The 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 Three 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. (shrink)

In On Local Motion in the Two New Sciences, Galileo distinguishes between ‘time’ and ‘quanto time’ to justify why a variation in speed has the same properties as an interval of time. In this essay, I trace the occurrences of the word quanto to define its role and specific meaning. The analysis shows that quanto is essential to Galileo’s mathematical study of infinitesimal quantities and that it is technically defined. In the light of this interpretation of the word quanto, (...) Evangelista Torricelli’s theory of indivisibles can be regarded as a natural development of Galileo’s insights about infinitesimal magnitudes, transformed into a geometrical method for calculating the area of unlimited plane figures. (shrink)