Ordinals as indexicals

Are ordinary language ordinals, 'first', 'second', 'third', etc., indexicals? (They don't seem to be included in standard lists of indexicals.) If you relate six individuals, say, all different in height, on the basis of 'between in height', you'll get an ordering with no first, and no last, just a shortest, a next taller, through to tallest, and equally, a tallest, a next shorter, through to shortest. Under the sequence from shortest to tallest, the shortest is first, but under the sequence from tallest to shortest, the tallest is first. Since 'first' here varies with the context - namely, which sequence - shouldn't it be classified as an indexical? So, as a general conclusion, aren't all ordinals indexicals?