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The important thing, Jesus is saying (in Matthew 5:33-37), is to tell the truth and keep one's pledges without insisting that a certain form of words must be used if it is to be binding. No oath is necessary for the truthful person... Their word is so reliable that nothing more than a statement is needed from them.

The important thing, Jesus is saying (in Matthew 5:33-37), is to tell the truth and keep one's pledges without insisting that a certain form of words must be used if it is to be binding. No oath is necessary for the