We investigate the consequences of the principle of Spectrum Exchangeability m inductive logic over the polyadic fragment of first order logic. This principle roughly states that the probability of a possible world should only depend on how the inhabitants of this world behave with respect to indistinguishability. This principle is a natural generahzation of exchangeability principles that have long been investigated over the monadic predicate fragment of first order logic. It is grounded in our deep conviction that in the state of total ignorance all possible worlds that can be obtained from each other by basic symmetric transformations should have the same a priori probability.