In this paper I present an interpretation of du Bois-Reymond’s thesis on the impossibility of a scientific explanation of consciousness and of its present importance. I reconsider du Bois-Reymond’s speech “On the limits of natural science” (1872) in the context of nineteenth-century German philosophy and neurophysiology, pointing out connections and analogies with contemporary arguments on the “hard problem of consciousness.” Du Bois-Reymond’s position turns out to be grounded on an epistemological argument and characterized by a metaphysical skepticism, motivated by the unfruitful speculative tendency of contemporary German philosophy and natural science. In the final sections, I show how contemporary research can benefit from a reconsideration of this position and its context of emergence, which is a good vantage point to trace open problems in consciousness studies back to their historical development.

Nineteenth-century Prussia was deeply entrenched in philhellenism, which affected the ideological framework of its public institutions. At Berlin’s Friedrich Wilhelm University, philhellenism provided the rationale for a persistent elevation of the humanities over the burgeoning experimental life sciences. Despite this outspoken hierarchy, professor of physiology Emil du Bois-Reymond eventually managed to increase the prestige of his discipline considerably. We argue that du Bois-Reymond’s use of philhellenic repertoires in his expositions on physiology for the educated German public contributed to the rise of physiology as a renowned scientific discipline. Du Bois-Reymond’s rhetorical strategies helped to disassociate experimental physiology from clinical medicine, legitimize experimental practices, and associate the emerging discipline with the more esteemed humanities and theoretical sciences. His appropriation of philhellenic rhetoric thus spurred the late nineteenth-century change in disciplinary hierarchies and helped to pave the way for the current hegemonic position of the life sciences.

The study of algebra in China has often focused on the algebraic “procedure of the Celestial Source.” Its geometrical ancestors are less known. The Yigu yanduan, authored by Li Ye (1192-1279), presents the procedure alongside its two geometrical counterparts, the “Section of Pieces [of Areas]” and the “Old Procedure.” The three procedures are known to represent three generations of algorithms used to set up quadratic equations. A similar geometrical procedure appears in a treatise written by Yang Hui (second half of thirteenth century). Although the procedures look alike at first glance, the two treatises reveal different moments in their work on the relation between counting materials and geometrical representation. This study challenges their chronology trying to identify the meander of the geometrical roots of the Celestial Source. The construction of negative coefficients plays a pivotal role in this mutation and shows several layers of composition.

This article documents the reasoning in a mathematical work by Mei Wending, one of the most prolific mathematicians in seventeenth-century China. Based on an analysis of the mathematical content, we present Mei’s systematic treatment of this particular genre of problems, fangcheng, and his efforts to refute the traditional practices in works that appeared earlier. His arguments were supported by the epistemological values he utilized to establish his system and refute the flaws in the traditional approaches. Moreover, in the context of the competition between the Chinese and Western approaches to mathematics, Mei was motivated to demonstrate that the genre of fangcheng problems was purely a “Chinese” achievement, not discussed by the Jesuits. Mei’s motivations were mostly expressed primarily in the prefaces to his works, in his correspondence with other scholars, in synopses of his poems, and in biographical records of some of his contemporaries.