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If memory serves me right, no copies we have of Plato's writing include a clear statement of what the Form of the Good is supposed to be. We have descriptions like "greater in dignity and might" than even Truth or Knowledge or Existence. This ultimate Form is to the other Forms what the sun is to the rest of the solar system.

But beyond that...

I think G. E. Moore thought that goodness being irreducible was what Plato had in mind. The only other interpretation I've found was that some kind of unity is in question, with Plato's mathematical themes crystallized in that unity.

Other interpretations I've thought of:

Essential vs. effective mysterianism: either being mysterious is intrinsic to the FoG, like it's the Form of Mystery; or it's just difficult to describe and articulate the FoG.

Theism: Plato intuited a theistic model but couldn't understand his own intuition, so ended up with a vaguely transtheistic model. I've never seen this stated as such but the thesis seems implicit in some Christian readings of Platonism with which I am familiar (e.g. Anselm).

The Form of the City: resonates with the unitarianism model as well as Socrates' comparison of virtue and political stability: the unity is the stability. The knowledge of the FoG is symbolized not by specific reasons in THE REPUBLIC but the text as a whole: the FoG is the Form of the Republic.

Saudade: sometimes described as "premature nostalgia," saudade is an emotion that brings to mind Platonic anamnesis (abstract/spiritual deja vu, even). The singularity of the emotion resembles an indecomposable Moorean conceptual intuition, and its erotetic aspect mirrors essential mysterianism.

What other interpretations of the FoG are on offer, or is this list (close to) complete?

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All Plato's work assumes at least two separate realms of existence, the ordinary one we experience on a day-to-day basis, and another one, which is where the Form of the Good exists.

Plato's foundational assumption is that the things in the second realm can never be adequately explained, described or conveyed in the first realm. In the Meno he strongly suggests that the only way to access the things in the second realm is by "remembering" them--they can't be taught.

Given that, nearly all of Plato's work can best be understood as extended but inadequate metaphors for the things of the second realm. Plato doesn't view any of those metaphors as complete, comprehensive or entirely accurate. They are intended solely to "remind" us of the truth. Given that, let's re-examine your suggestions:

  • Essential vs. effective mysterianism: I think this is the closest to being correct. Not just the Form of the Good, but all the Forms, and in fact, anything outside the ordinary realm is essentially mysterious. However this is due to the limitations and corrupted nature of the ordinary realm rather than to special properties of the Forms.

  • Theism: This is the neo-Platonist read, which didn't develop until several centuries after Plato's death, but is perhaps the most influential form of Platonism, having had a formative impact on Christian and Islamic theology. I wouldn't say that Plato "didn't understand" this implication, it's fairly explicit in some of his more religious dialogs. It's definitely a very abstract and non-personified notion of God, however, one that contrasts with the anthropomorphic pantheist religious beliefs of his own times. The fact that it reads as clearly theistic to us now is a result of how deeply his ideas were absorbed into religion.

  • The Form of the City: This is Plato's most extended and elaborated metaphor for the Form of the Good, so it's perhaps the place where we can best see how he conceived of it. However, it's still just a metaphor.

  • Saudade: Yes, subject to the same caveats as the others.

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Well, Plato does leave us in the lurch, kinda like writing down "2/0. Left to the reader as an exercise".

For what it's worth, me two cents would amount to one word, the name of a rather intriguing contraption which is "treadmill".

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