: We question the claim, common since Duhem, that sixteenth century astronomy, and especially the Wittenberg interpretation of Copernicus, was instrumentalistic rather than realistic. We identify a previously unrecognized Wittenberg astronomer, Edo Hildericus (Hilderich von Varel), who presents a detailed exposition of Copernicus's cosmology that is incompatible with instrumentalism. Quotations from other sixteenth century astronomers show that knowledge of the real configuration of the heavens was unattainable practically, rather than in principle. Astronomy was limited to quia demonstrations, although demonstration propter (...) quid remained the ideal. We suggest that Osiander's notorious preface to Copernicus expresses these sixteenth century commonplaces rather than twentieth century instrumentalism, and that neither `realism', nor `instrumentalism', in their modern meanings, apply to sixteenth century astronomy. (shrink)

First Published in 2008. Routledge is an imprint of Taylor & Francis, an informa company.

At the turn of the seventeenth century, Bruno and Cavalieri independently developed two theories, central to which was the concept of the geometrical indivisible. The introduction of indivisibles had significant implications for geometry – especially in the case of Cavalieri, for whom indivisibles provided a forerunner of the calculus. But how did this event occur? What can we learn from the fact that two theories of indivisibles arose at about the same time? These are the questions addressed in this paper. (...) Relying on the methodology of “historical epistemology”, this paper asserts that the similarities and differences between the theories of Bruno and Cavalieri can be explained in terms of “shared knowledge”. The paper shows that the idea – on which both Bruno and Cavalieri build – that geometrical objects are generated by motion was part of the mathematical culture of the time. Tracing this idea back to its Pythagorean origins thus sheds light on the relationship between motion and continuum in mathematics. (shrink)

Generally speaking, virtual displacement or work concerns to a timely idea according to which a motion of a certain body is not the unique possible motion. The process of reducing this motion to a particular magnitude and concept, eventually minimizing as a hypothesis, can be traced back to the Aristotelian school. In the history and philosophy of science one finds various enunciations of the Principle of Virtual Laws and its virtual displacement or work applications, i.e., from Aristotle to Leibniz’s vis (...) viva, from Maupertuis’ least action to Euler and Lagrange with calculus of variations to Lazare Carnot’s mechanics. In this case study, I will demonstrate that a particular approach used by Lazare Carnot is original by explaining within the historical context of rival approaches such as the development of the Principle of virtual Laws. I will also discuss Carnot’s geometric motion as one of the possible but invertible movements applied to virtual displacement as employed in his theories of machines and collisions. I will then go on to explore how the originality of an invertible motion within his mechanical and, in general, mathematical research program permitted Carnot to introduce a new way of structuring a scientific theory and making mechanics, with respect to the Newtonian paradigm, to scholars and his students of the École polytechnique de Paris. (shrink)

In his first work, the Dialecticae Institutiones of 1543, Peter Ramus urged those who wanted to learn the truth about the world not to approach scholars, but vineyard workers. “From their minds, as...

One of the distinctive features of modern science is a commitment to empiricism—a fundamental expectation that theoretical hypotheses will survive encounters with observations. Those that comport with the theory's explanations and predictions confirm the theory. Anomalous observations that do not fit theoretical expectations disconfirm it. Moreover, experiments can be contrived to generate observations that might serve to confirm or disconfirm a theory. Philosophers of science may disagree as to how exactly all of this is supposed to work, but the basic (...) empiricist expectation almost goes without saying. To deny it is to rule one's self out of the bounds of the scientificenterprise.Strange as it might seem to modern... (shrink)

In this paper I show that proofs by contradiction were a serious problem in seventeenth century mathematics and philosophy. Their status was put into question and positive mathematical developments emerged from such reflections. I analyse how mathematics, logic, and epistemology are intertwined in the issue at hand. The mathematical part describes Cavalieri's and Guldin's mathematical programmes of providing a development of parts of geometry free of proofs by contradiction. The logical part shows how the traditional Aristotelean doctrine that perfect demonstrations (...) are causal demonstrations influenced the reflection on proofs by contradiction. The main protagonist of this part is Wallis. Finally, I analyse some epistemological developments arising from the Cartesian tradition. In particular, I look at Arnauld's programme of providing an epistemologically motivated reformulation of Geometry free of proofs by contradiction. The conclusion explains in which sense these epistemological reflections can be compared with those informing contemporary intuitionism. (shrink)

This article sets out to investigate aspects of the uptake of Renaissance law and medicine from some of the logical and natural-philosophical components of the university arts course. Medicine is shown to have a much laxer operative logic than law, reflecting its commitment to the theory of idiosyncrasy as opposed to the demands made upon the law by the need for a uniform application of justice. Symptomatic of the different uptake arc the contrasting meanings of "regulariter" and "generaliter" in the (...) two disciplines. Whereas the law treats the rule as inviolable and the exception as only valid if made explicit in due legal form, medicine is able to conceive of a nature as a field of knowledge broader than that encompassed by its rules of art. Both law and medicine approach evidence. (shrink)

How does Newton approach the challenge of mechanizing gravity and, more broadly, natural philosophy? By adopting the simple machine tradition’s mathematical approach to a system’s co-varying parameters of change, he retains natural philosophy’s traditional goal while specifying it in a novel way as the search for impressed forces. He accordingly understands the physical world as a divinely created machine possessing intrinsically mathematical features, and mathematical methods as capable of identifying its real features. The gravitational force’s physical cause remains an outstanding (...) problem, however, as evidenced by Newton’s onetime reference to active principles as the “genuine principles of the mechanical philosophy”. (shrink)

Seth Pringle-Pattison (233n1) observed that Locke “teaches a twofold mystery—in the first place, of the essence (‘for the powers or qualities that are observable by us are not the real essence of that substance, but depend upon it or flow from it’), and in the second place, of the substance itself (‘Besides, a man has no idea of substance in general, nor knows what substance is in itself.’ Bk. II.31.13).” In this paper, I’ll explain the relation between the two mysteries. (...) Our Rosetta Stone is Locke’s argument that we understand body and spirit equally well since we are ignorant of their underlying substances but we “have distinct clear Ideas of two primary Qualities, or Properties” (2.23.30) of each. I’ll show that he is working with a restricted notion of primary quality in this passage, but one that demonstrably falls under the kind defined in his chapter on primary and secondary qualities. According to Locke, the fundamental primary qualities of bodies flow from corporeal substances and the determinations of these fundamental qualities constitute real essences. Locke’s discussion can’t be understood without understanding the relevant scholastic background. In the first half of my paper, I’ll explain his argument as an idiosyncratic application of doctrines he learned and taught at Oxford. In the second half, I’ll use lessons from my interpretation of the argument to explain the relation that Locke believes obtains between a substance and its fundamental primary qualities, and then I’ll build upon that explanation to elucidate his general account (insofar as he has a general account) of the inherence of qualities in corporeal substances. (shrink)

This paper offers a caution that emphasis upon the importance of mathematics in recent historiography is in danger of obscuring the historical fact that, for the most part, mathematics was not seen as important in the pre-modern period. The paper proceeds by following a single case study, and in so doing offers the first account of the mathematical writings of Jean Fernel (1497–1558), better known as a leading medical innovator of the 16th century. After establishing Fernel's early commitment to mathematics, (...) and attempt to forge a career as a cosmographer, it goes on to explain his abandonment of mathematics for a career in medicine. The ‘mathematization of the world picture’ is usually explained in terms of the perceived usefulness of mathematics, but Fernel's case shows that for many pre-modern thinkers mathematics was not regarded as a useful pursuit. The paper should serve as a reminder, therefore, that the take-up of mathematics by natural philosophers was by no means inevitable, but had to be carefully managed by early modern mathematical practitioners. The case of Fernel indicates that perhaps he was not the only would-be mathematical practitioner to abandon mathematics in favour of a calling that was more appreciated by contemporaries. (shrink)

This paper draws attention to the crucial importance of a new kind of precisely defined law of nature in the Scientific Revolution. All explanations in the mechanical philosophy depend upon the interactions of moving material particles; the laws of nature stipulate precisely how these interact; therefore, such explanations rely on the laws of nature. While this is obvious, the radically innovatory nature of these laws is not fully acknowledged in the historical literature. Indeed, a number of scholars have tried to (...) locate the origins of such laws in the medieval period. In the first part of this paper these claims are critically examined, and found at best to reveal important aspects of the background to the later idea, which could be drawn upon for legitimating purposes by the mechanical philosophers. The second part of the paper argues that the modern concept of laws of nature originates in René Descartes's work. It is shown that Descartes took his concept of laws of nature from the mathematical tradition, but recognized that he could not export it to the domain of physico-mathematics, to play a causal role, unless he could show that these laws were underwritten by God. It is argued that this is why, at an early stage of his philosophical development, Descartes had to turn to metaphysics. (shrink)

In the Renaissance, educating for philosophy was integrated with educating for an active role in society, and both were conditioned by the prevailing educational theories based on humanist revisions of the trivium. I argue that women's education in the Renaissance remained tied to grammar while the education of men was directed toward action through eloquence. This is both a result of and a condition for the greater restriction on the social opportunities for women.

Giacomo Zabarella es considerado uno de los aristotélicos más prestigiosos y más influyentes del siglo XVI. Su obra lógica, sus escritos sobre física y sus comentarios, publicados póstumamente, tuvieron un enorme impacto especialmente en las primeras décadas del siglo XVII, y sirvieron como verdaderos manuales con los que se formaron muchos universitarios europeos. Este artículo analiza la figura de Zabarella centrándose en su obra sobre física, el De rebus naturalibus libri XXX, editado en 1590, apenas unos días antes de su (...) muerte. (shrink)

Although one would not wish to classify Copernicus’ own intentions as belonging to the late-medieval and Renaissance tradition of nominalist philosophy, if we are to turn our consideration to what was responsible for the eventual success of the Copernican Revolution, we must also attend to other features of the dialectical context in relation to which the views of Copernicus and his followers were articulated, interpreted, and evaluated. Accordingly, this paper discusses the significance of the erosion of the Aristotelian prohibition against (...) metabasis to the eventual success of the Copernican Revolution. (shrink)

This dissertation examines the way Philip Melanchthon, author of the Augsburg Confession and Martin Luther's closest co-worker, sought to establish the relationship between faith and reason in the cradle of the Lutheran tradition, Wittenberg University. While Melanchthon is widely recognized to have played a crucial role in the Reformation of the Church in the sixteenth century as well as in the Renaissance in Northern Europe, he has in general received relatively little scholarly attention, few have attempted to explore his philosophy (...) in depth, and those who have examined his philosophical work have come to contradictory or less than helpful conclusions about it. He has been regarded as an Aristotelian, a Platonist, a philosophical eclectic, and as having been torn between Renaissance humanism and Evangelical theology. An understanding of the way Melanchthon related faith and reason awaits a well-founded and accurate account of his philosophy. Having stated the problem and finding it inadequately treated in the secondary literature, this dissertation presents an account of Melanchthon's philosophical development. Finding that his philosophy was ultimately founded upon his understanding of and method in rhetoric and dialectics, this dissertation explicates his mature accounts of these arts. It then presents an account of Melanchthon's philosophy as both humanistic (i.e., rhetorically based and practically rather than speculatively oriented) and fideistic (i.e, skeptical about the product of human reason alone, but finding certainty in philosophy founded upon, and somewhat limited by, Christian faith). After a final assessment of claims about Melanchthon's philosophy from the secondary literature, this dissertation considers how such a humanistic, fideistic philosophy might be helpful for Christians in a philosophically post-modern situation. (shrink)

A revisionist account of how philosophical induction was conceived in the ancient world and how that conception was transmitted, altered, and then rediscovered. I show how philosophers of late antiquity and then the medieval period came step-by-step to seriously misunderstand Aristotle’s view of induction and how that mistake was reversed by humanists in the Renaissance and then especially by Francis Bacon. I show, naturally enough then, that in early modern science, Baconians were Aristotelians and Aristotelians were Baconians.

Este artículo analiza las condiciones a través de las cuales las matemáticas pasan de un estado de subordinación a desempeñar un papel rector frente a la filosofía natural. Esta transformación se manifestó esencialmente en un cambio de actitud frente al pensamiento tradicional, mediante la sustitución de la explicación cualitativa de los fenómenos naturales por una explicación cuantitativa. En el texto se abordarán los aspectos epistemológicos e institucionales que están implicados en el debate sobre la cientificidad de las matemáticas. A su (...) vez, se hará un recorrido historiográfico señalando las diferentes posturas que tuvieron lugar en la polémica, para ofrecer elementos históricos y conceptuales de análisis respecto de las matemáticas como herramienta de la ciencia moderna. (shrink)