Ofer Gal

Seventeenth-century optics naturalizes the eye while estranging the mind from objects. A mere screen, on which rests a blurry array of light stains, the eye no longer furnishes the observer with genuine re-presentations of visible objects. The intellect is thus compelled to decipher flat images of no inherent epistemic value, accidental effects of a purely causal process, as vague, reversed reflections of wholly independent objects. Reflecting on and trespassing the boundaries between natural and artificial, orderly and disorderly, this optical paradox is a Baroque phenomenon; and it is the origin of Descartes’ celebrated doubt---whether we know anything at all.

The following is the second part of our Archaeology of the Inverse Square Law. Together these papers examine the transformation of the inverse square ratio from its origins in a metaphysical image of medieval thought in Grosseteste and the perspectivist tradition, through a playful magical practice in the Renaissance with Cusanus and Dee, and into a mathematical tool, applicable to the physical world. This last transformation allowed Newton to condense the geometrical image into a celebrated algebraic equation for universal gravity, but it proved particularly confusing for the people who wrought it, Kepler and Hooke.

The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. ‘The mathematization of nature’ (Koyré 1957 , From the closed world to the infinite universe , 5) is commonly hailed as the great achievement of the ‘scientific revolution’, but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters, physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied on. Newton finally erased the distinction between nature’s and artificial mathematics altogether, equating all of geometry with mechanical practice.

Robert Hooke’s development of the theory of matter-as-vibration provides coherence to a career in natural philosophy which is commonly perceived as scattered and haphazard. It also highlights aspects of his work for which he is rarely credited: besides the creative speculative imagination and practical-instrumental ingenuity for which he is known, it displays lucid and consistent theoretical thought and mathematical skills. Most generally and importantly, however, Hooke’s ‘Principles … of Congruity and Incongruity of bodies’ represent a uniquely powerful approach to the most pressing challenge of the New Science: legitimizing the application of mathematics to the study of nature. This challenge required reshaping the mathematical practices and procedures; an epistemological framework supporting these practices; and a metaphysics which could make sense of this epistemology. Hooke’s ‘Uniform Geometrical or Mechanical Method’ was a bold attempt to answer the three challenges together, by interweaving mathematics through physics into metaphysics and epistemology. Mathematics, in his rendition, was neither an abstract and ideal structure (as it was for Kepler), nor a wholly-flexible, artificial human tool (as it was for Newton). It drew its power from being contingent on the particularities of the material world.

Long after its alleged demise, phlogiston was still presented, discussed and defended by leading chemists. Even some of the leading proponents of the new chemistry admitted its ‘absolute existence’. We demonstrate that what was defended under the title ‘phlogiston’ was no longer a particular hypothesis about combustion and respiration. Rather, it was a set of ontological and epistemological assumptions and the empirical practices associated with them. Lavoisier's gravimetric reduction, in the eyes of the phlogistians, annihilated the autonomy of chemistry together with its peculiar concepts of chemical substance and quality, chemical process and chemical affinity. The defence of phlogiston was the defence of a distinctly chemical conception of matter and its appearances, a conception which reflected the chemist's acquaintance with details and particularities of substances, properties and processes and his skills of adducing causal relations from the interplay between their complexity and uniformity

“The present book,” acknowledges Wilson in her Preface, “owes its origins to a study of the preface to Robert Hooke‘s Micrographia undertaken in a seminar on reappraisals of the scientific revolution under the direction of Robert S. Westman.” It is in that very preface that Hooke proclaims: “my ambition is, that I may serve to the great Philosophers of this Age, as the makers and grinders of my Glasses did to me”, and it seems that for Wilson, the reappraisal of paragraphs like this have served to erode Westman’s conception of the scientific revolution as a “long-term event–some one hundred fifty years in the making”. From Wilson’s perspective, this time frame does not appear as an ‘event’ at all.

The ArgumentThis paper contains two main sections. In the first I suggest a mechanism of interpretation, based on a distinction between two aspects of meaning, analyzed using two kinds of rhetorical-poetical constructions:tropesto explore the linguistic relations—metaphors, metonyms, synecdoches, etc.—that endow terms with content, andtopicsto account for the structuring function of key expressions, which enables the recognition and adjudication of phrases, arguments, texts, genres, etc. In the second section I substantiate my claims by demonstrating how new light is shed on Galileo Galilei's neglected and obscureDe Motuif these two aspects of the meaning of its central theoretical terms are taken into consideration; interpreted through this approach it is revealed as a text revolutionary in its ideas, while the communicative efficacy of its continuous use of the traditional terminology is unveiled.

: Bereft of the illusion of an epistemic vantage point external to science, what should be our commitment towards the categories, concepts and terms of that very science? Should we, despaired of the possibility to found these concepts on rock bottom, adopt empiricist skepticism? Or perhaps the inexistence of external foundations implies, rather, immunity for scientific ontology from epistemological criticism? Philosophy's "realism debate" died out without providing a satisfactory answer to the dilemma, which was taken over by the neighboring disciplines. The "symmetry principle" of the "StrongProgramme" for the sociology of science-the requirement that truth and error receive the same kind of causal explanations-offered one bold metaphysical answer, under the guise of a methodological decree. Recently, however, it has been argued that this solution is not bold enough, that the social constructivists replaced the naïve presumption of an independent nature which adjudicates our beliefs with a mirror-image presumption of a sui generis society which furnishes these beliefs autonomously. The proper metaphysics for a foundationless epistemology, argues Bruno Latour, is one which grants nature and society, object and subject, equal roles in the success and failure of science and technology; one in which history of society merges with a history of things-in-themselves. The paper analyzes the philosophical and methodological motivations and ramifications of this extraordinary suggestion

This work is an argument for the notion of knowledge production. It is an attempt at an epistemological and historiographic position which treats all facets and modes of knowledge as products of human practices, a position developed and demonstrated through a reconstruction of two defining episodes in the scientific career of Robert Hooke : the composition of his Programme for explaining planetary orbits as inertial motion bent by centripetal force, and his development of the spring law in relation to his invention of the spring watch. ;The revival of interest in the history of experimental and technological knowledge has accorded Hooke much more attention than before. However, dependent on the conception of knowledge as a representation of reality, this scholarship is bound to the categories of influence and competition, and concentrates mainly on Hooke's numerous passionate exchanges with Isaac Newton and Christiaan Huygens. I favourably explore the neo-pragmatist criticism of representation epistemology in the writing of Richard Rorty and Ian Hacking. This criticism exposes the conventional portrayal of Hooke as "a mechanic of genius, rather than a scientist" as a reification of the social hierarchy between Hooke's Royal Society employers and his artisan-experimenters employees. ;However, Rorty and Hacking's efforts to do away with the image of the human knower as an enclosed realm of 'ideas' have not been completed. Undertaking this unfinished philosophical task, my main strategy is to erase the false gap between knowledge which is clearly produced--practical, technological and experimental, 'know how', and knowledge which we still think of as representation--theoretical 'knowing that'. I present Hooke, Newton and Huygens as craftsmen, who, employing various resources, labor to manufacture material and theoretical artifacts. Eschewing the category of independent facts awaiting discovery, I attempt to compare practices and techniques rather than to adjudicate priority claims, replacing ideas which 'develop', 'inspire', and 'influence', with tools and skills which are borrowed, appropriated and modified for new uses. ;This approach enables tracing Hooke's creation of his Programme from his microscopy, and reconstructing his use of springs to structure a theory of matter. With his unique combination of technical and speculative talents Hooke comes to personify the relations between the theoretical-linguistic and the experimental-technological in their full complexity