Insisting on a formal definition that would work across contexts is harmful. If someone comes up with one, that's nice (I doubt this). But even then, others might come up with "type systems" that fall outside of this definition and that's still perfectly fine.
The twist is that we do not need formal definition to talk about types across multiple contexts. I do not know what the best way to do this is, but the essay has some suggestions inspired by philosophy, which might be interesting precisely because they do not need clear formal definition.
Insisting on a formal definition that would work across contexts is harmful. If someone comes up with one, that's nice (I doubt this). But even then, others might come up with "type systems" that fall outside of this definition and that's still perfectly fine.
The twist is that we do not need formal definition to talk about types across multiple contexts. I do not know what the best way to do this is, but the essay has some suggestions inspired by philosophy, which might be interesting precisely because they do not need clear formal definition.