You will remember that in my last lecture I defined the concept of an abstractive set of durations. This definition can be extended so as to apply to any events, limited events as well as durations. The only change that is required is the substitution of the word 'event' for the word 'duration.' Accordingly an abstractive set of events is any set of events which possesses the two properties, (i) of any two members of the set one contains the other as a part, and (ii) there is no event which is a common part of every member of the set. Such a set, as you will remember, has the properties of the Chinese toy which is a nest of boxes, one within the other, with the difference that the toy has a smallest box, while the abstractive class has neither a smallest event nor does it converge to a limiting event which is not a member of the set. Thus, so far as the abstractive sets of events are concerned, an abstractive set converges to nothing. There is the set with its members growing indefinitely smaller and smaller as we proceed in thought towards the smaller end of the series; but there is no absolute minimum of any sort which is finally reached. In fact the set is just itself and indicates nothing else in the way of events, except itself. But each event has an intrinsic character in the way of being a situation of objects and of having parts which are situations of objects and--to state the matter more generally--in the way of being a field of the life of nature. This character can be defined by quantitative expressions expressing relations between various quantities intrinsic to the event or between such quantities and other quantities intrinsic to other events. In the case of events of considerable spatio-temporal extension this set of quantitative expressions is of bewildering complexity. If e be an event, let us denote by q(e) the set of quantitative expressions defining its character including its connexions with the rest of nature. Let e₁, e₂, e₃, etc. be an abstractive set, the members being so arranged that each member such as e_{n} extends over all the succeeding members such as e_{n+1}, e_{n+2} and so on. Then corresponding to the series e₁, e₂, e₃, ..., e_{n}, e_{n+1}, ..., there is the series q(e₁), q(e₂), q(e₃), ..., q(e_{n}), q(e_{n+1}), .... Call the series of events s and the series of quantitative expressions q(s). The series s has no last term and no events which are contained in every member of the series. Accordingly the series of events converges to nothing. It is just itself. Also the series q(s) has no last term. But the sets of homologous quantities running through the various terms of the series do converge to definite limits. For example if Q₁ be a quantitative measurement found in q(e₁), and Q₂ the homologue to Q₁ to be found in q(e₂), and Q₃ the homologue to Q₁ and Q₂ to be found in q(e₃), and so on, then the series Q₁, Q₂, Q₃, ..., Q_{n}, Q_{n+1}, ...,