ardentsonata:

sets are just counts. mathematics is the study of an activity: the study of counting. what is the crucial result of russell’s paradox? we cannot define a set qua set. that is, there can be no concept (predicate) of “set” as such. a set is defined solely by what elements it succeeds in counting as one. spetharrific’s invocation of the sartrean motto — that existence precedes essence — is entirely appropriate. a set draws lines in that which is already; it can never be held responsible for what is , only how what is is counted.

to say a set is empty/void — which we do say of { }, the null set — is simply to say that this set has failed to count anything. and to say that every set includes the null set is just to say that every set contains a subset which practices this failure. note: the null set itself includes the null set. this is not particularly mysterious, for it is just to say that every set fails to count something that is within the bounds of its own situation — the null set cannot count itself, since it counts nothing. its universal inclusion means that no set counts everything, that every set misses something.

before the community chose to recognize her — that is, made the decision to count, to declare, her belonging — derpy could’ve been said to inhabit this void. her now essential character, the in/famous ‘derped’ eyes, could easily been dismissed as an animation error. that is, the actuality — the what is — of her “derped” eyes could easily have been ignored: remained unaccounted for, passed over as invisible, described as negligible, dismissed as nothing. this is just what we mean by the active nature of the count. a count is always a positive decision: a risk, a wager, a line in the sand.

it was never necessary for us to count derpy, lyra, bon bon, berry punch, carrot top, octavia, vinyl scratch, or the now many other background ponies as actual characters despite their actual readiness-to-hand (uh, we might also say “potential”) within the show. keep in mind, it is only now — after the count — that we may properly apply the term “presence,” since our initial experience of the background ponies before their inauguration by the community as characters is precisely an experience which denies them presence as such. if it had not been for the active decision of the community, instead of appearing to us, they would have tended to disappear into the background, becoming invisible, ancillary — more akin to the functioning of sky, dwellings, or landscapes. { }