Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

There is no satisfactory theory of three-dimensional non-Euclidean geometry, from an intuitional point of view, unless it gives us a clear three-dimensional image in our ordinary space, assuming, of ...

Mathematical knowledge has puzzled philosophers for millennia. The LSE’s own Imre Lakatos coined the term “Euclidean Programme” for the historically dominant way of thinking about this phenomenon. In ...

THIS is a philosophical thesis by a writer who is really familiar with the subject of non-Euclidean geometry, and as such it is well worth reading. The first three chapters are historical; the ...