Aristotle‘s categories are presented as a system relying on logic and syntax instead of on meanings. His square of oppositions is found to be of crucial importance.

Heidegger's comments about a pair of shoes painted by van Gogh are read with attention to their historical context.

The Five Greatest Kinds discussed in Plato‘s Sophist are taken to be just one instance of a fivefold structure found in various related texts. Contemporary linguistic theories are a source for ideas about its functioning.

Plato's Timaeus is taken as a background for certain views presented by Aristotle in his On the Heavens. The author discusses possible arguments for introducing a new (“fifth”) element.

Reading the Timaeus as an early attempt at mathematizing natural science runs into serious difficulties. The so-called Platonic Solids are five in number, more by one than the traditional 'elements'. Plato provides a proportional ratio for these elements but this ratio fails to tie in with their geometrical features. Appealing to the authority of mathematics appears to be a rhetorical move with no further consequences.