Stephen Gaukroger (Sydney) Stephen.gaukroger@arts.usyd.edu.au

“The problem of calculus: Leibniz and Newton on blind reasoning”.

Newton developed a version of infinitesimal calculus in the early 1670s but abandoned it one the grounds that it used procedures that could not be justified. They were black boxes: one put in the premisses and generated the right results, but had no grasp on what was going on in the middle. In fact, both Newton and Leibniz agreed that infinitesimal calculus required justification in terms of limit procedures, which were geometrical and open to inspection at every stage. The difference was that Newton believed that this meant that any procedure using infinitesimal calculus had to be translated into geometrical limit procedures, whereas Leibniz believed that it was only the general technique that had to be justified in terms of limit procedures, and that once this was done, it was not required that one justify each and every operation employing infinitesimals in this way. Leibniz's approach is not driven by pragmatic concerns, however, but rather by a view that the calculus extends human capacities in new ways into new areas: it goes beyond our natural faculties and hence we cannot expect our natural faculties to be able to legitimate it.

Commentary: Mark Colyvan (Sydney)

 

John Schuster (New South Wales) j.a.schuster@unsw.edu.au

“What Was the Relation of Baroque Culture to the Trajectory of Early Modern Natural Philosophy? An Historiographical Reflection, Inspired by Maravall’s Culture of the Baroque–Analysis of a Historical Structure”

Was there Baroque Science? Well, actually, there wasn’t:  Because at the time there was no ‘science’ in the senses in which we are interested, and by the time there was, the Baroque was well over.  However, what there may well have been; that is, what may be worth our time as historians to model and empirically explore is this: a particular Baroque phase in that longer process of change in the field of natural philosophical contestation which we term ‘the scientific revolution’. 

This paper explores a possible conception of a Baroque stage in the Scientific Revolution, whose genealogy reaches back into traditional historiography about the Baroque, in political and cultural history, with Carl Friedrich, as well as into the older historiography about a ‘crisis of the early 17th century’, particularly in T.K.Rabb’s acceptation of it, which spans political, religious and economic history, yet reaches down, or up, to intellectual history and in particular to history of science, or more properly the history of natural philosophising and its subordinate fields or sciences. There it meets a theme of historiography of science per se, which identifies a critical or crisis moment in the process of the Scientific Revolution within and as part of that larger crisis.  The idea becomes one of a period in the early to mid 17th century of turmoil and crisis within and about the cultural and institutional field of natural philosophy, including turbulence and debate about the nature and role of those subordinate ‘sciences’, such as the mixed mathematical sciences’, in relation to variously types of natural philosophy competing for systematic coherence and cultural hegemony. 

The key spaces to watch in all this are the ‘hot spots’ in the field of natural philosophising, where various radical, mathematically literate, natural philosophical players sought new articulations the amongst three domains: practical mathematical tools, techniques and values/aims; mixed mathematical fields now increasingly pushed by them as ‘physico-mathematical’ [that is as relevant to issues of matter and cause], and, finally, their own natural philosophical agendas, whether explicitly systematising or not.  The players and plays in these natural philosophical hot spots not only inflected the process we term the scientific revolution in important ways, but also set down the first models for the highly competitive, discovery-driven character of the soon to emerge modern sciences.

Commentary: John Sutton (Macquarie University)

 

Alan Salter (Sydney) asal9472@mail.usyd.edu.au

 “The midwife, the shepherd, the keeper and the butcher: knowledge and practice in Harvey’s system of inquiry”

In his two major published works on circulation and embryology Harvey defers to the knowledge of tradesmen. In De Motu Cordis he relies on the testimony of butchers as to the volume of blood flowing from a slaughtered ox; and in De Generatione Animalium he praises ‘experienced midwives’ for their judgment that the watery humours in the secundines were of little use in facilitating the delivery of the foetus.

It is not because of their civil status that Harvey acknowledges the superior claims of tradesmen. There is no Shapin-like trust here of one gentleman accepting the word of another for midwives and butchers are of low rank. Nor is it because their knowledge can be objectively validated by employers, customers or peers.

Harvey trusts tradesmen, I contend, because his own way of inquiry is grounded in craftsmanship. There is the same refinement of skills learnt in apprenticeship through diligent practice, doing rather than contemplating, absorption in the world of the craft and not just in its technical skills, a preoccupation with the particular thing and a conviction that time is necessary and active in the production of knowledge. The craftsman has experience which is personal, locally defined and superior to the knowledge of philosophers. It is this emphasis on personal experience properly acquired that we see in Harvey. ‘Per me,’ by me, he announces on the title page of his Lumleian lectures presented to the London College of Physicians: this is my knowledge and it is grounded in my experience.

Commentary:  Antonio Clericuzio

 

John Gascoigne (New South Wales) j.gasgoigne@unsw.edu.au

“Crossing the Pillars of Hercules": the expansion of Europe and the beginnings of the scientific movement”

The object of this paper is to explore the view that the expansion of Europe from the time of Columbus and the beginnings of the scientific movement were connected. Such a view was widespread among contemporaries notably Bacon and has been the subject of some recent secondary works. This paper will analyse the basis of such claims and examine the extent to which it is possible to document them.

Commentary: Dror Wahrman

 

Victor Boantza (Toronto) Boantza@rogers.com

“Chemical Philosophy and Boyle’s Incongruous Philosophical Chemistry”

 
The seventeenth-century rise of mechanical philosophy had profound metaphysical and religious implications.  In contemporary chemical philosophy, these are most evidently seen in debates over the nature and origin of matter.  Boyle, the most prominent advocate of the mechanization of chemistry, held that the function of mechanism demonstrated the wisdom and providence of God as well as the rationality and orderly nature of His Creation.  Samuel Cottereau Duclos (1598-1685), establisher of the chemical laboratory and research program at the newly inaugurated Parisian Académie Royale des Sciences presented a rigorous defense of chemical philosophy against what he considered as the dangerous mechanistic reductionism of Cartesian and Boylean thought.  Illustrating the uselessness of hypotheses about primary qualities to laboratory practice, Duclos explained chemical phenomena operationally, by recourse to substances and elements as part of a self-styled corpuscular-vitalist cosmology.  Examining Duclos’s critique of Boyle (1668/9) demonstrates how in attempting to reconcile the chemical with the mechanical Boyle not only failed to rehabilitate chymistry, but severely compromised its exclusive status as the ultimate science of matter.  To read Duclos is to see Boyle as creating difficulties and mysteries where there are none, as using qualitative language, as reducing the multitude of chemical phenomena to the unverifiable imagined shapes, sizes, and motions of invisible particles, as mistaking chemical reactions for physical reactions.  Depicted as impossibly reaching beyond his practice of explanation, of refashioning secondary qualities (e.g. airiness, fieriness) as the attributes of atoms, Boyle’s radical rhetoric against chemical philosophy is exposed and disarmed, his metaphysics rendered circular and discordant.

Commentary: Peter Anstey

 

Dror Wahrman (Indiana University) dwahrman@indiana.edu

“The eighteenth-century end-run around providence and chance: complexity,
causality, and the roots of modern order”

Where does order come from? And how are seemingly random moments of disorder accounted for? The late seventeenth and eighteenth centuries mark a new and important departure in Western responses to these questions, one that can be seen in domains as far apart as religion and philosophy, science and economy, law and politics: a family of new ideas
about the origins of order and harmony, about causality and chance. My paper, drawing on a book-in-progress co-authored with Jonathan Sheehan, will take as its point of departure a key early moment in the story: the unprecedented and dramatically experienced financial crises of 1720 (Law's System, the South Sea Bubble). These events brought into relief
key questions of randomness and chance, order and disorder, human agency versus divine providence, and the limitations of linear causality. The paper will then look back at the preceding half-century, in order to identify earlier developments (social, theological, scientific) that made it possible for some Europeans to think about these questions in new ways; and forward to the following half-century and beyond, in order to show how these novel ways of thinking of the 1720s were to become an important component in European understandings of order and disorder across a wide array of disciplines and bodies of knowledge, central (inter alia) to Adam Smith, Marx and Darwin.

Commentary: Koen Vermeir

 

Raz Chen (Bar Ilan) chenraz@mail.biu.ac.il

“The Formation of Nothing, or Kepler's Visual Economy of Science”

In his early treatise of the Mysteries of Cosmography Kepler contended that the planets are embedded in an invisible geometrical structure composed of the five platonic solid bodies.  This geometrical structure was not a mere heuristic device to save the phenomena of apparent planetary motions.  However, Kepler expected these invisible, incorporeal platonic solids to physically account for the planets' real motions and speeds. In the years to come Kepler investigated how invisible mathematical entities that are almost nothing (nihil), can be used to explore the nature of corporeal visible things.  His conception of the formation of anima motrix (interchangeable with vigor, or with vis); the central place shadows occupy in his astronomical observations; his definition of the ray of light; and especially his speculations on the formations of the snowflake present a methodological investigation of no-thing.  In effect, this was an economic exchange of sensory experience for artificially constructed, yet epistemologically valid, abstract configurations of natural phenomena. Following Kepler's initial fascination with nothing, other early modern scientists pierced through corporeal reality to grasp the incorporeal and invisible structure that lay beneath its surface to gave nothing an observable form.

Commentary: Paula Findlen

 

Ofer Gal (Sydney) o.gal.usyd.edu.au

“From divine archetypes to independent constants: the changing import of baroque mathematics."

In chapter 2 of his Astronomia Nova Kepler invites his readers to consider a diagram of the orbit of a planet moving according to either Ptolemy or Tycho.  The very complexity of this orbit is an argument against its feasibility.  70 years later Newton will use another diagram to make an analogous argument to Hooke.  But following their communication Newton forsakes the assumption about the origins of the power of mathematics to capture nature that underlies his and Kepler's arguments for a new one. In place of a mathematical order embedded in nature, Newton posits a constant of no mathematical significance of its own, which allows controlling the complex orbits in an approximate way.  The paper will follow some stages in the development of this new understanding of the import of mathematics and its relation to nature.

Commentary: Rivka Feldhay