Reading more on isonomia, I can see this as the under-pinning logic that gets us from one observed world, to many conjectured worlds, as one example. In that case, it is a species of inductive argument: "the inference of a general law from particular instances".
There's a quote in one of Arthur Conan Doyle's stories where Sherlock Holmes says that if a logician were presented for the first time with a drop of water, he could infer the existence of a Pacific Ocean and a Niagara Falls without ever having seen either.
Isonomia would be an even more direct line of argument; someone presented for the first time with a Niagara Falls could very reasonably infer the existence of a Victoria Falls.
If you hold as a premise that "nature never furnishes only one thing of a kind", then the argument becomes deductive and the conclusion stands or falls exclusively on the merit of that premise.
So the obvious question that imposes is this; do we accept or reject the premise? Does nature ever furnish only one thing of a kind? Bearing in mind, of course, that each kind of atom always occurs in refulgent quantity.
(Some atoms are unstable and do not, evidently, occur in nature. It requires a particle accelerator to produce them and they only "survive" for a fraction of a nanosecond. But the potential to produce them is always there.)