Peirce's cosmology, or "mathematical metaphysics" (CP 6.213) aims to show "how law is developed out of pure chance, irregularity, and indeterminacy" (CP 1.407). The account, outlined in the accompanying chart, unfolds as follows.
“If we are to proceed in a logical and scientific manner, we must, in order to account for the whole universe, suppose an initial condition in which the whole universe was non-existent, and therefore a state of absolute nothing.. . .But this is not the nothing of negation. . . . The nothing of negation is the nothing of death, which comes second to, or after, everything. But this pure zero is the nothing of not having been born. There is no individual thing, no compulsion, outward nor inward, no law. It is the germinal nothing, in which the whole universe is involved or foreshadowed. As such, it is absolutely undefined and unlimited possibility -- boundless possibility. There is no compulsion and no law. It is boundless freedom.”
Now the question arises, what necessarily resulted from that state of things? But the only sane answer is that where freedom was boundless nothing in particular necessarily resulted.
“ . .I say that nothing necessarily resulted from the Nothing of boundless freedom. That is, nothing according to deductive logic. But such is not the logic of freedom or possibility. The logic of freedom, or potentiality, is that it shall annul itself. For if it does not annul itself, it remains a completely idle and do-nothing potentiality; and a completely idle potentiality is annulled by its complete idleness. (CP 6.215-219)”
Thus the principle that the logic of the universe is at least as sophisticated as our own -- that it therefore includes retroduction or abduction, the spontaneous form of inference that initiates a stream of inference -- leads us to an account of the first stirrings of determination in the utter indeterminacy of Nothing. This is the first appearance of a mode of positive possibility, different from the mere absence of determination that characterizes the initial zero-state.
“I do not mean that potentiality immediately results in actuality. Mediately perhaps it does; but what immediately resulted was that unbounded potentiality became potentiality of this or that sort -- that is, of some quality. Thus the zero of bare possibility, by evolutionary logic, leapt into the unit of some quality. (CP 6.220)”
The potentiality of a quality, in Peirce's metaphysics, is analogous to the Platonic Form or Idea, in that it is a timeless, self-subsisting possibility that serves as the metaphysical ground of the world of actual existence.
“The evolutionary process is, therefore, not a mere evolution of the existing universe, but rather a process by which the very Platonic forms themselves have become or are becoming developed. (CP 6.194)”
http://agora.phi.gvsu.edu/kap/Neoplatonism/