Dear Matthew,
I would like to ask a few questions to understand you better:
MW: Someone mentioned that an individual is something that does not have members (in the sense of a set having members) and that is close to what I would mean, but that would make the null set an individual, so it is not quite adequate. My definition of individual is something that exists in space and time. I am not a set (or class or type or kind or sort etc) nor is my car or this email. Nor is Sherlock Holmes to give a more difficult example. All these things can be placed in space and time (even if it is imaginary space and time) . On the other hand, sets/classes/types are generally considered to exist outside space and time.
I understand that a 'main dichotomy' between an individual and a set/class/type is - existence in space and time (rather than having or not having members).
MW: On the other hand, sets/classes/types are generally considered to exist outside space and time.
Can we consider opposite - sets/classes/types do exist within space and time as well? For example, as a collection/set of space and time extensions of all their members?
MW: There already is an object that is the collection of all the space-time extensions, it is their mereological sum, and that is an individual but not a set.
MW: I think both these objects (the set and the mereological sum) are useful, but for different things. When I think about the set, I think about the properties that are common to each of its members, when I think about the mereological sum I think about the properties of the whole. So if I am interested in saying that each member has a certain weight, I use set, if I want the weight of all the collection I use the mereological sum.
What will happen if the criteria is joined: 'does not have members' and 'exists in space and time'? Not sure if it is better... We have now another (at least three) cases to think about...
MW: Yes, something that exists in space and time would not have members (if you use the distinction I have made above).
Regards
Matthew West
Information Junction
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