Hermann Grassmann's ideas on the nature and foundations of mathematics were published as an integral part of his mathematical treatise, the Ausdehnungslehre, in 1844. In spite of its notoriously obscure style we can better understand the work if we view it as an expression of the dialectical philosophy of his mentor, the theologian F. Schleiermacher. The relation to Schleiermacher is presented here through an analysis of the principal ideas of the Ausdehnungslehre.

In 1826 André-Marie Ampère published the ‘Mathematical theory of electrodynamic phenomena, uniquely derived from experiment’, in which he showed how the mathematical law for the force between current elements could be derived from four ingenious equilibrium experiments. He made a great show of following a Newtonian inductivist methodology, and his law, like Newton's for gravitation, was presented as a purely descriptive mathematical expression for a certain class of phenomena, one for which its author did not provide any causal or ontological (...) justification. Ampère's electrodynamics would accordingly seem to have been a solid contribution to the Laplacian-Newtonian approach to physics so actively pursued in France during the first quarter of the nineteenth century. It does not surprise us to read that his electrodynamic force law and his molecular-currents theory of magnetism were immediately and widely accepted by his French contemporaries. Ampère was, in this view, just another of the many great French mathematical physicists of the period. (shrink)

A self-conscious antagonism to Newtonian science is widely seen as characteristic of the Romantic movement, and Coleridge is routinely portrayed as one of the major representatives of this anti-Newtonian sentiment. Although such a view of Coleridge is correct, his hostility to Newton is puzzling. The attitudes that Coleridge objected to are often expressly denied in Newton's published writings, and Coleridge's own ‘dynamic’ philosophy was, in fact, remarkably like the conception of nature personally favoured by Newton. Coleridge, then, must have been (...) objecting to something other than Newton's beliefs—to beliefs not in fact held by Newton, but by others. Commentators have noted Coleridge's distortion of Newton's philosophies, but have not explored this matter in any detail. The present paper attempts to redress this situation. As much of the historiography of Western philosophy presumes an unequivocal opposition between Romanticism and the Enlightenment, it is of importance to find that Coleridge and Newton held strikingly similar views about the nature of the universe. (shrink)

Summary Kant's critique of corpuscular theory created a tabula rasa situation in natural philosophy and opened up a vast new field of research, particularly related to the study of heat, light, electricity and magnetism. ?rsted introduced Kantian epistemology in Scandinavia and made friends with J. W. Ritter, an outstanding experimenter who was the first to make dynamical philosophy productive. The ?rsted?Ritter partnership aimed at the construction of a cosmology based on dynamical philosophy as well as galvanic interpretations of the Lichtenberg (...) and Chladni patterns. It is suggested that Kantian critique and dynamical cosmology provided the framework within which ?rsted and Ritter made their epochal discoveries as well as their bold speculations. Finally, it is argued that the Romantics widened the scope of natural philosophy itself. (shrink)

The publication of L. Pearce Williams's definitive biography of Faraday has led to lively discussion of the influence of Naturphilosophie on Davy and Faraday, and of the role played by Bosco vichean atomism in their scientific development. In a recent article J. Brookes Spencer argued that Boscovich's force law, involving interaction between point atoms independent of surrounding particles, was only compatible with Faraday's view of gravity and not with his views on other forces. This would of course contradict the notion (...) of unity which is absolutely fundamental to Boscovich's Theoria. (shrink)

A rather cheeky philosopher, I think it was Hamlet, Prince of Denmark, said that there were a lot of things in heaven and on earth that were not in our textbooks. If this simpleminded man, who as known was out of his mind, so sneered at our textbooks, then one might answer him, consoled: Good, but there are also a lot of things in our textbooks that are neither in heaven nor on earth.