[jhanschoo]

> Speaking of reconciliation, might I interest you in a reconciliation of Aquinas and Spinoza, by way of Galois Theory?

This is kind of bad faith.

> They developed a great deal of formal logic... it seems more like they were mostly slathering on the tech debt. How am I mistaken?

https://plato.stanford.edu/entries/abelard/

> Abelard was the greatest logician since Antiquity: he devised a purely truth-functional propositional logic, recognizing the distinction between force and content we associate with Frege, and worked out a complete theory of entailment as it functions in argument (which we now take as the theory of logical consequence). His logical system is flawed in its handling of topical inference, but that should not prevent our recognition of Abelard’s achievements.

and you might be more familiar with Ockham's Razor. There are others, but you can do your own research if you're interested. There was a lot of work that needed to be done in between Aristotle's incomplete Syllogisms and the incomplete understanding of propositional logic that Sophists used, that helped birth Frege's Begriffsschrift.

[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)

[aebtebeten]

> [Aquinas reconciled with Spinoza] is kind of bad faith.

How so? I'm dead serious; Algolia will confirm — and you sound like part of the small audience that would actually know what the differences to be reconciled are.

Be back after (making a few other replies and) reading up on Abelard. Is this the same Abelard as Sic et Non?

Thanks for the substantial reply!