And yet the traditional/classical conception of God is that He is absolutely simple; His attributes are not discrete in the way that you seem to be suggesting. — aleteiest
Which is exactly the problem with the traditional/classical God. There is no way an infinite of attributes can belong to such a being. Such a God is simple and empty. No thing belongs to them because it would mean owning the discrete. The continuum of God is left with other at all, merely an empty set that has nothing to do with the world.
Spinoza's point is both the continuum and it's members are discrete-- the former as
the continuum itself, the latter as each particular member. To be a continuum or category is discrete, not to lack identity or discintion. The infinite is its own discrete truth-- it's the infinite itself, a set which contains endless discrete members.
With all due respect, that seems rather ... vague to me. — aleteiest
Only because you don't recognise the infinite as its own thing. It seems "vague" because you are trying understand it though a finite lens. You want us to say what is in the world or what it does to the world, how does it manifests in our observations of the world.
The point is the infinite is not vague at all. It means a set without beginning nor end, a distinction and identity all of its own, which is never any member of itself.
This seems like a case where Peirce's attempt to use generic terminology for his categories may have been misleading. They are not called 1ns, 2ns, and 3ns because they always and only come about in that order; on the contrary, my interpretation of his cosmology is that in the hierarchy of being, 3ns is primordial relative to the other two. In any case, 1ns/possibility does not "end" where 2ns/actuality "begins," they are both - along with 3ns/necessity - indispensable and irreducible ingredients of ongoing existence. — aleteiest
A hierarchy is an order. No doubt he is talking about logical terms, but hierarchy or order is an inherently a conception of the finite and time. It results in a leakage into causality (as we see in apo's argument which treat "vagueness" as the origin of the states of our reality), where 2ns (actuality) is considered to be born of 3ns (semiotics, necessity) and 1ns (possibility).
Possibility is necessary. In Peirce's terms, it is
also 3ns, along with logical distinction forms (semiotics), possibility is necessary. The hierarchy collapses. Since possibility is necessary and infinite, it never begins or ceases. It is just as "primordial" as semiotics. Logical distinction has always been. Possibility has always been. Neither came first. Peirce's triad collapses into the necessary (semiotics, possibility) and the contingent (actual states).
Furthermore, the hierarchy between the necessary and contingent does not make sense. For a state to be actual, it takes more than the presence of either semiotic discintion(i.e. form, meaning) and possibility. If I say: "There is a logical form of me being the US president and the possibility of me being the US president," it doesn't birth the actual state of me as the US president. Only an actual state can do that. In terms of definition, actual state are self-defined, not given by the necessity of semiotic and possibility. Actuality becomes just as "primordial" as semiotics or possibility.
If I am to be president of the US, there can only be a concurrence of possibility, semiotics and actuality. Only when those are all at once, of themselves, am I US president. There can be no hierarchy.