Page:An Enquiry Concerning the Principles of Natural Knowledge.djvu/115



27. The Relation of Extension, Fundamental Properties. 27.1 The fact that event a extends over event b will be expressed by the abbreviation aKb. Thus ‘K’ is to be read ‘extends over’ and is the symbol for the fundamental relation of extension.

27.2 Some properties of K essential for the method of extensive abstraction are,

(i) aKb implies that a is distinct from b, namely, ‘part’ here means ‘proper part’:

(ii) Every event extends over other events and is itself part of other events: the set of events which an event e extends over is called the set of parts of e:

(iii) If the parts of b are also parts of a and a and b are distinct, then aKb:

(iv) The relation K is transitive, i.e. if aKb and bKc, then aKc:

(v) If aKc, there are events such as b where aKb and bKc:

(vi) If a and b are any two events, there are events such as e where eKa and eKb.

It follows from (i) and (iv) that aKb and bKa are inconsistent. Properties (ii) and (v) and (vi) together