Benjamin Wilck

In this article, I tackle a heretofore unnoticed difficulty with the application of Pyrrhonian scepticism to science. Sceptics can suspend belief regarding a dogmatic proposition only by setting up opposing arguments for and against that proposition. Since Sextus provides arguments exclusively against particular geometrical definitions in Adversus Mathematicos III, commentators have argued that Sextus’ method is not scepticism, but negative dogmatism. However, commentators have overlooked the fact that arguments in favour of particular geometrical definitions were absent in ancient geometry, and hence unavailable to Sextus. While this might explain why they are also absent from Sextus’ text, I survey and evaluate various strategies to supply arguments in support of particular geometrical definitions.

Relying upon a very close reading of all of the definitions given in Euclid’s Elements, I argue that this mathematical treatise contains a philosophical treatment of mathematical objects. Specifically, I show that Euclid draws elaborate metaphysical distinctions between substances and non-substantial attributes of substances, different kinds of substance, and different kinds of non-substance. While the general metaphysical theory adopted in the Elements resembles that of Aristotle in many respects, Euclid does not employ Aristotle’s terminology, or indeed, any philosophical terminology at all. Instead, Euclid systematically uses different types of definition to distinguish between metaphysically different kinds of mathematical object.

We present a study of the linguistic output of the German-speaking writer Robert Walser using Natural Language Processing (NLP). We curated a corpus comprising texts written by Walser during periods of sound health, and writings from the year before his hospitalization, and writings from the first year of his stay in a psychiatric clinic, all likely attributed to schizophrenia. Within this corpus, we identified and analyzed a total of 20 linguistic markers encompassing established metrics for lexical diversity, semantic similarity, and syntactic complexity. Additionally, we explored lesser-known markers such as lexical innovation, concreteness, and imageability. Notably, we introduced two additional markers for phonological similarity for the first time within this context. Our findings reveal significant temporal dynamics in these markers closely associated with Walser’s contemporaneous diagnosis of schizophrenia. Furthermore, we investigated the relationship between these markers, leveraging them for classification of the schizophrenic episode.