chapter  10
20 Pages

Prototopology

Togetherness is a key notion in philosophy generally as well as in mathematics. The Great Chain of Being binds the disparate levels of Reality into One Coherent Whole, and togetherness is a mark of being integrated into a single unity. The part of relation is a simple mereological one, as sketched in Chapter Nine, §9.12, but the concept of being a whole is stronger than a simple correlative of being a part. The theory of measurement depends on there being some extensive magnitudes for which the measure of the whole is the sum of the measures of the parts. In the next chapter (§11.4), we shall need the thesis that two regions are parts of one connected, or unseparated, whole, if they share a common boundary; but though we can often recognise their doing this in practice, we have also to give a theoretical account. Togetherness is the chief concern of topology, and is taken for granted in geometry.