[oh_my_goodness]

True, and it's a great example of how this whole drama is about a practical trade-off, not about a unique Right Answer. If you play piano, the second is the second finger; the fifth is the fifth finger, and it all makes sense. No problem. On the other hand trying to actually count that way (two thirds make a fifth and so forth) is maddening.

[qu4z-2]

Clearly the solution is we need to start numbering fingers from 0.

[kazinator]

No, just use subtraction for the intervals. Third finger minus first finger = 3 - 1 = 2.

The floors of a building might start at 1, but you go up 1 flight of stairs from the 5th to the 6th floor, not two.

[oh_my_goodness]

Maybe that would do it. The only problem is that I'd have four fingers on each hand.