Here is some interesting and perhaps timely news, from a scientific angle:Sixth Sense: Numerosity - Science
The paper in Science is entitled: "Topographic Representation of Numerosity in the Human Parietal Cortex".
Numerosity, the set size of a group of items, is processed by the association cortex, but certain aspects mirror the properties of primary senses. Sensory cortices contain topographic maps reflecting the structure of sensory organs.
Are the cortical representation and processing of numerosity organized topographically, even though no sensory organ has a numerical structure?
Using high-field functional magnetic resonance imaging (at a field strength of 7 teslas), we described neural populations tuned to small numerosities in the human parietal cortex.
They are organized topographically, forming a numerosity map that is robust to changes in low-level stimulus features. The cortical surface area devoted to specific numerosities decreases with increasing numerosity, and the tuning width increases with preferred numerosity.
These organizational properties extend topographic principles to the representation of higher-order abstract features in the association cortex.
This perspective on numerosity as an actual sense, along the lines of sight, sound, smell, taste, and touch should be of substantial interest to neuroscientists, philosophers, mathematicians, and philosophers of mathematics alike.