Originally posted by whodey
The concept is to swear on a book you deem to be a moral authority to which you live your life by. Therefore, the text that you elevate as being a moral authority would be the only text in which it would make sense to swear upon. You could use the Constitution as a document to swear upon, however, only if you respected it as the basis for your morality. Otherwise you might as well swear upon the latest addition of Newsweek.
Interestingly, some Christian sects like the Quakers, refuse to swear oaths based on Jesus' words in Matthew 5: 33-37:
33 Again, ye have heard that it was said to them of old time, Thou shalt not forswear thyself, but shalt perform unto the Lord thine oaths:
34
but I say unto you, swear not at all; neither by the heaven, for it is the throne of God;
35 nor by the earth, for it is the footstool of his feet; nor by Jerusalem, for it is the city of the great King.
36 Neither shalt thou swear by thy head, for thou canst not make one hair white or black.
37 But let your speech be, Yea, yea; Nay, nay: and whatsoever is more than these is of the evil one.
EDIT: And James 5:12:
12 But above all things, my brethren, swear not, neither by the heaven, nor by the earth, nor by any other oath: but let your yea be yea, and your nay, nay; that ye fall not under judgment.