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Throughout Concept of Nature Whitehead adds different types of characteristics to his most basic concept - events.

For example, he talks of objects, the situation of the event in space and time, its relation to other events et cetra.

I kind of expected, from a mathematician that uses a systematic/formulaic kind of philosophical explanation of his system of nature, to have a very definitive set of characteristics for his concepts - especially events. Instead I see that in every chapter he adds more characteristics and always keeps it vague as saying "there are more but I won't explore it now". I'm reaching the end of the book and it still seems that he hasn't explored them all.

So, my question would be, did Whitehead actually defined a set of characteristics to the concept of an event - and if so what are they?

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Maybe it is useful to refer to Whitehead's scientific background.

See Alfred North Whitehead The Principle of Relativity with Applications to Physical Science (1922), page 21:

"Nature usually presents itself to our imagination as being composed of all those entities which are to be found somewhere at some time. [...] Thus an essential significance of a factor of nature is its reference to something that happened in time and space. I give the name "event" to a spatio-temporal happening. An event does not in any way imply rapid change; the endurance of a block of marble is an event. Nature presents itself to us as essentially a becoming, and any limited portion of nature which preserves most completely such concreteness as attaches to nature itself is also a becoming and is what I call an event. By this I do not mean a bare portion of space-time. Such a concept is a further abstraction. I mean a part of the becomingness of nature, coloured with all the hues of its content.

Compare with Process and Reality. An Essay in Cosmology (1929), page 73:

The philosophy of organism starts by agreeing with ‘the vulgar’ except that the term ‘sensible object’ is replaced by ‘actual entity’; so as to free our notions from participation in an epistemological theory as to sense-perception. [...] I will also use the term ‘actual occasion’ in the place of the term ‘actual entity’. Thus the actual world is built up of actual occasions; and by the ontological principle whatever things there are in any sense of ‘existence’, are derived by abstraction from actual occasions. I shall use the term ‘event’ in the more general sense of a nexus of actual occasions, interrelated in some determinate fashion in one extensive quantum. An actual occasion is the limiting type of an event with only one member.

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    I think that this is more than a mere long comment: It defines events as spatiotemporal happenings. That he "adds" more (possible) characteristics when discussing particular types of events is not surprising if one considers the vast set this definition of event comprises.
    – Philip Klöcking ♦
    Oct 16, 2020 at 10:23

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