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Alice Vidrine
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This time, there can be only one danger, for love.
This time, there can be only one danger, for love.

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So I apologize if this is a question that's been discussed before, but I couldn't turn it up on a search. This is also going to get mildly long-winded; apologies in advance.

The short-form preview: the PCs in my game seem to have a lot of aspects that I'm not sure the players find very interesting, so I'm wondering what kind of conversation to have to make sure that they're getting the most out of their aspects.

The longer version: I've been running a Fate game for a few months, and I'm noticing that the PCs have a lot of aspects between them that aren't really getting invoked or compelled. Consequently, my characters rarely use up their initial Fate point pools, and if they do it's often hard to find organic reasons to compel them to replenish their FP.

There are a lot of factors that can play a part in this, but the main factor I want to address in this post is that I, as their GM, don't think their aspects are very meaty, and from the level of active engagement with their aspects that my players display, they may not think so either (each player seems to have one aspect that they've entirely forgotten about).

So the actual question: Have you ever needed to have a conversation about adjusting characters' aspects to have more substance in the story, and how did that conversation go? (Bonus question: how did you do this without it sounding like "you're playing Fate wrong"?) I'd like to phrase it mostly as an advertisement of the virtues of adjusting aspects at a milestone, but I'm not sure I know how to get it started...

I recognize there are some things I could do better during play to help with this as well, so I hope it doesn't sound like I'm placing the situation I've described squarely on the players. It's just that I sort of know how I need to suck less as a GM, but I'm less sure how to have the above conversation, which I think would also help everyone at the table.

I'm running a fantasy game in Fate Core where magic can either succeed, or it can succeed with potentially catastrophic side effects. Greater skill with magical things increases your chances of falling on the former side of things. All PCs are assumed to have access to magic by default, but it's intended to be risky and dramatic when they use it.

I've been using a modified form of the Doom Points mechanic from the Voidcallers system in the Toolkit, but I'm still not convinced this is the nicest way to do it, for reasons I can't really put my finger on.

I'm interested in hearing how other people have treated/would treat magic with this sort of flavor (high powered, high risk, and dramatic).

I may not be the person to study INF. No pun intended, but I find nothing more counterintuitive than intuitionistic logic. I actually love doing formal proofs, but I find myself hard pressed to prove even the most basic things in just the propositional fragment...

Category theory has its usual share of bad terminology and bad conventions, but by far the worst I think is "category of elements". It's not bad because it's a misleading name exactly, but because it refers to two related, but distinct, constructions. Tonight, Borceux in particular gets demerits for the "category of elements" terminology because he defines the category of elements for a covariant functor, but later uses the different version for a contravariant functor without ever mentioning the difference.

Dear mathemativerse,

Are "right exact functors" a thing? And are they, as one hopes, the dual of left exact functors?

Not enough of a question to go on Stackexchange, but enough that I had to put it out there.

Because I feel like throwing down...

Apparently there's now a name for the constructivist confusion between alethic logic and a theory of proof: "proof relevance." Because clearly anything that can be given the clothing of formal logic, is logic.

Okay, now I'm done being curmudgeonly.

My recent notes are pointing to a very intimate relationship between the non-Cantorian parts of NF, the failure of Cartesian closedness, and the failure of AC. They're all really entangled, and this entanglement only kind of depends on the fact that for some sets, NF's internal X^1 is not isomorphic to X. I'm still hoping to find some more positive aspect of this entanglement; probably some characterization of what NF's "exponentials" really do that leads to the automatic failure of real exponentiation and the Pi functors, which in my wild fancies I imagine will give us an account of what the "USC" functor does in categorical terms...

But for now, the concrete problems...

Whoa, wait, what? Olivier Esser's positive set theory can interpret MK?

Hm, I thought with type-level exponentiation that I'd be able to easily define, and prove the existence of, very large Beth numbers. It turns out I really don't get how to talk about cardinals in NF+Counting/ML+N.

For one, I don't even know how I'd define beth_omega, much less prove (as I would need to) that it is Tc for some cardinal c. I mean, outside of invoking it as a supremum that might not exist in these set theories. Forster explained part of the solution to this, but not enough that I can piece the details together.

I dislike feeling like I need my hand held on things like this.
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I seem to be dead set on creating a theory of ordinals for ML just so I can go on and do model theory in it. Why not just keep learning model theory in a ZF-like theory and worry about this later? Because it's insufficiently beautiful and that is NOT HOW I DO.
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