OK, today I'm going to figure out once and for all whether or not the grounds's grounding the grounding could grounded the grounded. Don't wait up

So apparently part of the problem is a principle called "amalgamation", which says that if X and Y are each grounds for Z then X and Y together are a ground for Z. Maybe I've been spending too much time with relevant logic lately but amalgamation seems eminently giveupable to me

Though he says that giving up amalgamation is going to resolve the puzzle by saying the grounds's grounding the grounded *could* ground the grounded, which is the opposite of the result I'm pre-theoretically motivated to reason towards

OK so he's constructing a situation where the grounds's grounding the grounded ground the grounded now, and it involves self-reference! Buried the lede a bit there buddy

Ah right he's got an example that doesn't use self-reference too; it quantifies into sentence position but I'm mostly down with a bit of quantification into sentence position

One oddity going on is that there's a certain relevantist vibe to the logic of ground in that it's non-monotonic, but you're also not allowed to have things grounding themselves, whereas P->P is usually fine for relevantists

He's got a view that "P grounds P∨Q" should be true whenever it doesn't lead to "R grounds R" cycles, and the instances of P grounding P∨Q don't lead to cycles unless you keep the amalgamation principle, so we should lose amalgamation. I think he just doesn't like the >>

>> amalgamation principle. And to be fair he does basically admit that, and I don't like it either, so we're probably on pretty much the same team

He's also talking about how it seems like we should be able to define up a non-amalgamating disjunction and an amalgamating disjunction, but this seems quite wrong: if amalgamation is true that will stop us defining up a non-amalgamating disjunction unless we also redefine ground

OK he's actually made basically this response now, which is kind of annoying

Anyway I think that he's probably right that the grounds's grounding the grounded could ground the grounded, so it's a good job I didn't like amalgamation anyway. Avoiding his kind of examples would probably mean putting restrictions on what grounds what that are too spicy for me

Essentially you'll get a case like this whenever there's a proposition Y that's grounded in one way by a proposition X, and in another *separate* way by X's grounding Y. Easy enough if Y is disjunctive, unless reality isn't at all loopy. But I think reality is eminently loopy

Here's the paper this thread was about https://philpapers.org/rec/LITCTG 

And a new thread on the topic https://twitter.com/MikeBenchCapon/status/1247168062039527424?s=20