Retrieving a property of a JSON object by index?

Assuming this JSON object:

var obj = {
    "set1": [1, 2, 3],
    "set2": [4, 5, 6, 7, 8],
    "set3": [9, 10, 11, 12]
};

The "set2" property may be retrieved like so:

obj["set2"]

Is there a way to retrieve the "set2" property by index? It is the second property of the JSON object. This does not work (of course):

obj[1]  

So, let's say that I want to retrieve the second property of the JSON object, but I don't know its name - how would I do it then?

Update: Yes, I understand that objects are collections of unordered properties. But I don't think that the browsers mess with the "original" order defined by the JSON literal / string.