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Sep 25 at 19:47 comment added Kristian Berry For emphasizing what I did not, and for emphasizing the challenges an approach like the one suggested would take, and the possible superfluity of the appeal (for isn't Fine a scientist as much as a philosopher, if already a mathematician as much as a philosopher? or a logician, anyway), I think this answer is sufficient. I remain optimistic about my prospects but I will have a lot of work to do, incl. a lot more reading, anyway.
Sep 25 at 19:43 vote accept Kristian Berry
Sep 25 at 19:42 comment added Kristian Berry I'm not sure... I don't want to be so quick about it, Hamkins did just participate in a workshop on generative ontology, grounding, and real definition, which sounds promising... But also, from the standpoint of the foundation axiom and its thematic relationship to the issues, here, I feel like I can see a tension in some of the fundamental grounding proposition schemes I'm seeing. How that tension is resolved... there are a few options I've noticed, but I'm unsure which is best.
Sep 25 at 19:03 comment added user509184 @KristianBerry To put a sharper point on what I wrote: grounding in set-theoretic geology is almost certainly not a good framework for formalizing talk of metaphysical grounding. There is a history of philosophers (including Fine) who are mathematically quite competent and have developed good, rigorous, mathematically fruitful frameworks for various kinds of reasoning in philosophy. Very few mathematicians have taken an interest in metaphysical grounding. I would first see what formalisms for metaphysical grounding the philosophers have offered, before asking us (mathematicians) to do it.
Sep 25 at 18:52 history edited user509184 CC BY-SA 4.0
Fixed another typo
Sep 25 at 16:21 comment added Kristian Berry I should've anticipated the issue of what the grounding relata are, in framing my question, since it is exactly where I take set geology for my point of departure: having possible worlds be the primary bearers of grounding values. I've decided to edit my post to include a citation of an example of the direction I want that to go, but I'm still holding your answer in the "probably going to be accepted" slot for now.
Sep 25 at 14:42 history edited user509184 CC BY-SA 4.0
Fixed typo
Sep 25 at 13:51 history answered user509184 CC BY-SA 4.0