[MysticCat]

The bamboo stick of righteousness. I love it! I gotta get me one of those.

If you are swearing by something sacred to you, that is what matters in swearing an oath, since that is evidence of the seriousness and reverence with which you make your solemn promise. (Harking back to Tom Earp's comments, think of the Boy Scout Oath, which is made "On my honor.")

Think of wacko Shane in the last season of Survivor. He kept swearing by his son -- appropriate (in a creepy sort of way) because his son was so important to him. But he asked others to swear on his son, too, in essence asking others to make a meaningless oath because his son was just another kid to them. What was sacred to him, and therefore adequate to demonstrate the seriouness with which he would take his promise, was not the same as what was sacred to others.

Or think of Lord of the Rings -- when Frodo and Sam need to to extract a promise from Gollum that he will not harm them, Frodo asks Gollum "On what will you swear?" (I.e., how can you assure us that we can trust you?) Gollum swears on the Ring, which Frodo knows is everything to Gollum. Frodo knows that swearing by the Ring will bind Gollum's conscience.

Swearing an oath and making an affirmation are both forms a solemn promises. The difference is in the form, not the effect.