I think sigma-algebras are probably not the right algebra to base beliefs on. Something resembling linear logic might be better for reasons we’ve discussed privately; that’s very speculative of course. Ideally the right algebra should be derived from considerations arising in construction of the representation theorem, rather than attempting to force any outcome top-down.
Have you elaborated on this somewhere or can you link some resource about why linear logic is a better algebra for beliefs than sigma algebra?
Have you elaborated on this somewhere or can you link some resource about why linear logic is a better algebra for beliefs than sigma algebra?
I asked Abram about this live here https://youtu.be/zIC_YfLuzJ4?si=l5xbTCyXK9UhofIH&t=5546
Would you be able to share Abram’s answer in written form? I’d be keen to hear what he has to say.