So the only potential liar in this case is the receiver of funds (who knows he's lying), and he's lying to a particular audience.
The sender can prove to this audience that the payment took place (and has to sacrifice anonymity for this transaction in that case).
You should become an architect. With such elaborate philosophical meanderings I'm sure you could successfully argue that since "most buildings are rectangular" therefore "most rectangular structures will stand up".

(It'll also be easier for you than trying to convince anyone who understands money and 'audits').