Hermann von Helmholtz’s geometrical papers have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception (...) from those describable in terms of axiomatic geometry. This paper offers a partial defense of the group-theoretical reading of Helmholtz along the lines of Ernst Cassirer in the fourth volume of The Problem of Knowledge of 1940. In order to avoid the problem raised by Schlick, Cassirer relied on a Kantian view of space not so much as an object of geometry, but as a precondition for the possibility of measurement. Although the concept of group does not provide a description of space, the modern way to articulate the concept of space in terms of transformation groups reveals something about the structure and the transformation of spatial concepts in mathematical and natural sciences. (shrink)

Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. The book provides a bracing and painstakingly researched re-appreciation of the work of Hermann von Helmholtz and Ernst Cassirer, and of their place in the tradition, and is worth study for that alone. The contributions of the book go far beyond that, (...) however. It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory. (shrink)

Recenze: Biagioli, Mario - Riskin, Jessica. Nature Engaged: Science in Practice from the Renaissance to the Present. New York: Palgrave Macmillan 2012, 301 s.

Well prior to the invention of the term ‘biology’ in the early 1800s by Lamarck and Treviranus, and also prior to the appearance of terms such as ‘organism’ under the pen of Leibniz in the early 1700s, the question of ‘Life’, that is, the status of living organisms within the broader physico-mechanical universe, agitated different corners of the European intellectual scene. From modern Epicureanism to medical Newtonianism, from Stahlian animism to the discourse on the ‘animal economy’ in vitalist medicine, models (...) of living being were constructed in opposition to ‘merely anatomical’, structural, mechanical models. It is therefore curious to turn to the ‘passion play’ of the Scientific Revolution – whether in its early, canonical definitions or its more recent, hybridized, reconstructed and expanded versions: from Koyré to Biagioli, from Merton to Shapin – and find there a conspicuous absence of worry over what status to grant living beings in a newly physicalized universe. Neither Harvey, nor Boyle, nor Locke (to name some likely candidates, the latter having studied with Willis and collaborated with Sydenham) ever ask what makes organisms unique, or conversely, what does not. In this paper I seek to establish how ‘Life’ became a source of contention in early modern thought, and how the Scientific Revolution missed the controversy. (shrink)