Carving Content at the Joints

Abstract

Here is Frege in Foundations of Arithmetic, §64:The judgment ‘Line a is parallel to line b', in symbols: a | | b, can be taken as an identity. If we do this, we obtain the concept of direction, and say: ‘The direction of line a is equal to the direction of line b.’ Thus we replace the symbol | | by the more generic symbol =, through removing what is specific in the content of the former and dividing it between a and b. We carve up the content in a way different from the original way, and this yields us a new concept. (Frege 1997, 110-11)