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There seems to be an entirely objective, human-independent way in which specific physical objects relate/correspond to specific abstract objects.

Example, we don't think the abstract inverse cube law 1/r^3, and the gravity around a planet is a human/mind-dependent connection or coincidence.

This is not a question about epistemic access to abstract objects, e.g. how do we know of abstract objects or their connections. It's rather, how do modern platonists explain the specific connections. For ancient Platonism a la Plato, the connections would ultimately be explained through philosophy and the Good.

But, not requiring humans, what is the nature of the objective, specific connection between abstract entity X and physical happening Y?

It can't be something like understanding of Kant, because these connections exist without humans.

Is the resolution that in each case, some specific property of the physical and some specific property abstract entails the connection? Is this really agreeable to modern platonists? I want to say it's not agreeable because, the physical would appear to have some purchase or likeness to the abstract (other than raw existence). I don't think platonists would like that.

What's the connection? We can't just stop at humans know it.

(let's try to only worry about cases where abstract objects have strong physical connections for this question, not about abstract objects without obvious connections, we could always say the abstract object connects to the mental->written on paper form for these).

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    I don't understand your reasoning. Because gravity can be described by an inverse square equation, this implies that the arithmetic square function somehow interacts with gravity?
    – David Gudeman
    Commented Aug 4, 2023 at 19:23
  • @DavidGudeman, that's roughly it; remember, JKusin's opponent is a platonist here, their account of why maths is true is that mathematical sets actually exist.
    – Paul Ross
    Commented Aug 4, 2023 at 19:52
  • Abstractions formulated by minds are of a different category than the abstractions of the platonic realm. Platonists hold that abstractions exist but are neither physical nor mental. When our minds formulate abstractions to describe the world as we experience it, the connection is explicit and the abstraction is mental - i.e., not platonistic.
    – nwr
    Commented Aug 4, 2023 at 20:43
  • @PaulRoss, I assume he's talking about Fregean "platonists", not Platonic "Platonists" because there haven't been many Platonists since about 1300 AD. Big-P Platonism attributes causal powers to Forms; little-p platonism holds that abstract objects are causally inert. The question seems to be claiming that there is an argument that abstract objects cannot be causally inert, but I don't see the argument. I know a hill that looks like a camel. Does that mean that camelness was a cause of the hill?
    – David Gudeman
    Commented Aug 4, 2023 at 21:59
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    We can say "instantiations of possibilities" exactly because it is so massive, the concrete cannot miss it either. Any arrangement of it instantiates some abstracta, no causal connection needed. This is how he solves both epistemic access and concrete applicability problems without Plato's mysterium of active forms. More parsimonious platonists, like Gödel or Woodin, envision the same non-causal instantiational connection, but it is less clear why existing concrete, as we perceive it, happens to fall under existing abstracta. It may have to do with human cognitive faculties a la Husserl.
    – Conifold
    Commented Aug 5, 2023 at 21:09

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The usual way of this involves possible worlds as abstract objects (or, then, possible objects as abstract, for that matter). Since every permutation of possible properties is encoded by abstract objects in abstract worlds, there will be by "happenstance" (or something like mathematical occasionalism, so to say) corresponding concretely possible worlds matching the a priori descriptions of whichever objects.

So, since there's some abstract world with an object that encodes the inverse-cube law, there's a physical world that "happens to" exemplify that law (so long as said exemplification is itself possible: dialethicists or impossible-worlds proponents will be inclined to accept that round squares are exemplifiable as well as encodable, perhaps, but otherwise we will be thinking that abstract objects that encode contradictory properties are precisely the ones with no concrete, exemplary counterparts).

As I write this, I feel like the account sounds vacuous or circular; we might be left with a "brute fact" option, then (the correspondence between some abstracta and some concreta is even more "by happenstance" in the sense of us having the abstract property is-an-explanation-of-correspondence but there is no deeper possibility of explaining where this property itself "comes from"). (C.f. problems like Bradley's regress.)

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    Happenstance. I like it more than other suggestions so far, as it fits within how I understand platonism and physical objects. It avoids muddling the two. Muddling is fine but don't call it modern platonism (call it Platonism or something else). I don't know if it's ultimately satisfactory, but I don't find it vacuous or circular. I will probably accept this soon. You totally understood my question. Thank you
    – J Kusin
    Commented Aug 5, 2023 at 20:25
  • @JKusin you're welcome :) I should note I picked up on this option roughly from a MathOF or MathSE comment (I don't remember where more precisely) which went something like "possible mathematical worlds constitute the possibility of different physical worlds too." I guess it's also like Tegmark's conjecture with an allowance for the world-types to be more separated, still, though.
    – Kristian Berry
    Commented Aug 5, 2023 at 20:38

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