Well, to obtain integer spin one actually does not need any physics knowledge. All of the possible integer spins map one-to-one on the group representations of

Well, to obtain integer spin one actually does not need any physics knowledge. All of the possible integer spins map one-to-one on the group representations of the rotation group. It is pure mathematics. One thing with half-integer spin is that if an object transforms according to a half-integer representation and one rotates the object by 360 degrees the state function acquires a minus sign. This is difficult to imagine coming from a spatial object, though, because one would be inclined to say that rotating by 360 degrees is the no-op. So, these half-integer spin objects are actually kind of strange and one would probably not have imagined them if one would just take mathematics as the starting point.