[aebtebeten]

OK, so so far I think I can use a similar application of Galois Theory to relate Abelard's exstinctiva square of opposition and his separativa square.

I haven't quite figured out how Alberic's argument goes through in Abelard's logic. but can clearly see that as the latter denies ex impossibili quodlibet something has to break. (for eiq merely observes that if False is True, then everything at least as true as False —ie everything— is True. In other words you have a degenerate situation, in which False == True)

Have I understood his logic so far?

[jhanschoo]

Ok I think I see what you mean, you think these philosophers describe systems that partly capture a fully elaborated system, and you can draw imperfect correspondences between them. But I don't see why you want to shoehorn them into being Galois correspondences under... what exactly.

[aebtebeten]

The what exactly is under https://news.ycombinator.com/item?id=41258636

Does it make sense?

[almost all Galois correspondences are imperfect; they're just the "best" imperfect correspondence, in some sense. (the ones that actually are bijections are the perfect ones, in that not only are R=RLR and L=LRL, but RL=1=LR)]

> But I don't see why

For fun? Because "Algebraic Theology" is a grammatical english noun phrase that up until recently seems to have been uninhabited? To create a model in which Spinoza is not Pantheist? All of the above?

[jhanschoo]

A couple thoughts:

1. in your original statement, you just name-dropped philosophers' names assuming that I'd understand what aspect of their work you were thinking of. Similarly, you can't say "use Galois theory" when you are actually thinking of drawing Galois correspondences between lattice-like structures.

2. Don't forget that notions like and Galois connections are today well-defined notions in terms of modern-day mathematical objects in turn relying on first-order logic or similar... whereas they were just beginning to explicate parts of logic.

[aebtebeten]

Right, I'm not saying they should've come up with it; I'm just saying that knowing what we know now it's possible to reconcile them.

(in my original statement, I didn't want to go into detail in case you weren't interested; typing costs my time, and the last two times I've attempted to discuss this on HN it's been crickets)