How does the redundancy definition of abstractions account for numbers, e.g., the number three? It doesn’t seem like “threeness” is redundantly encoded in, for example, the three objects on the floor of my room (rug, sweater, bottle of water) as rotation is in the gear example, since you wouldn’t be able to uncover information about “three” from any one object in particular.
I could imagine some definition based on redundancy capturing “threeness” by looking at a bunch of sets containing three things. But I think the reason the abstraction “three” feels a little strange on this account is that it is both highly natural (math!) but also can be highly “arbitrary,” e.g., “threeness” is wherever a mind can count three distinct objects (and those objects can be maximally unrelated!).
Perhaps counting the three objects on the floor of my room is a non-natural use case of the abstraction “three,” but if so, why? And where is the natural abstraction “three” in the world?
How does the redundancy definition of abstractions account for numbers, e.g., the number three? It doesn’t seem like “threeness” is redundantly encoded in, for example, the three objects on the floor of my room (rug, sweater, bottle of water) as rotation is in the gear example, since you wouldn’t be able to uncover information about “three” from any one object in particular.
I could imagine some definition based on redundancy capturing “threeness” by looking at a bunch of sets containing three things. But I think the reason the abstraction “three” feels a little strange on this account is that it is both highly natural (math!) but also can be highly “arbitrary,” e.g., “threeness” is wherever a mind can count three distinct objects (and those objects can be maximally unrelated!).
Perhaps counting the three objects on the floor of my room is a non-natural use case of the abstraction “three,” but if so, why? And where is the natural abstraction “three” in the world?