Snails do not have access to a platonic reality. It's not some mystical or divine intervention, but a simple result of a snail adding calcium to the edge of it's shell. — Banno

Sure. I agree. Josh and I were talking about "constructive interaction" with the environment and how that might be the genesis of universals like numbers. He said:

It’s not that the world isn’t involved, it’s just that the world only reaches us through our constructive interactions with it. We are an intrinsic part of the world, and the Real is the effect of a two-way interaction. — Joshs

That led to a little discussion of how that actually works in individual cases. We didn't get very far tho.

We bring one and two into existence, by an intentional act - it's something we do. Some important aspects of this. First, its we who bring this about, collectively; this is not a private act nor something that is just going on in the mind of one individual. Hence there are right and wrong ways to count. — Banno

I agree with the emphasis on the collective creation of counting (if the non-Fregean story is correct). I'm not sure I'd go so far as to say that intersubjective agreement results in the idea of "being right about counting." One can imagine mistakes in math that are widely accepted, but then corrected by reference to some Popperian discovery in the 3rd world. Wouldn't we say that it was that discovery that now made us "right," rather than the fact that everyone now agrees? After all, we agreed before, too.

Next, the existence had here is that of being the subject of a quantification, as in "Two is an even number". — Banno

Extremely important. @Michael and I are having a related conversation about what role "existence" plays in descriptions of platonism, and it hinges on a similar point. In the case you describe later in your post, the moral of the story would be: "P" is brought into existence depending upon an interpretation of (ideal logical) language; there are no facts in the world that change as a result of that interpretation. If -- as I do -- I lean toward the quantificational interpretation that allows P to be a "new thing," and if you dispute it, we aren't offering arguments pro and con about the object of the concept "to exist". We are specifying that very concept, rather than assuming it, in our differing interpretations. Or so it seems to me. And I think it's the gist of your comment here:

the account I gave above indicates how stuff like numbers and property and so on are constructed, by modelling that construction in a higher order logic. — Banno

I'm not a best-friend of formalism, but this is the kind of case where formal models really excel.

Yes, these parallels with Augustine are good. Anyone who favors the idea of an intelligible realm is going to have to say whether there's anything populating it before we humans arrive; Plato, Augustine, and Frege opt for saying that it's full, and we encounter it as such.

Which leads to the passages from Peirce and Nagel. History of philosophy isn't my forte, and I defer to Nagel on this, though it does seem a little oversimplified? I suppose there is a generalized "fear of religion," especially in analytic phil., but anti-Platonists seem to be offering genuine justifications for their position, that have to be taken seriously in their own right. And though my own sympathies are with religious modes of life, I don't doubt for a minute that one can be an anti-Platonist and a non-believer without also subscribing to what you're calling "the relativization of reason." Nagel himself is a good example. So is Habermas. And really, so is (most of) analytic phil., which questions various points concerning reason but rarely abandons it to relativism; the questioning is itself usually done using entirely standard assumptions about reason and its grounding.

Which is maybe just to say that evolutionary explanations aren't the only game in town, if one is dubious about platonism.