This is insightful. The areas where strong evidence is common are largely those areas we don’t intuitively think of as governed by probability theory and where classic logic performs well.
It seems like someone could take this a little further even and show that the limiting case for strong evidence and huge likelihood ratios would just be logic. This might be fruitful to unpack. I could see it being the case that our instincts for seeking “certainty” make more sense than we give them credit for. Gathering enough evidence sometimes allows reasoning to be performed using propositional logic with acceptable results.
Such logic is many orders of magnitude cheaper to evaluate compute wise vs probabilistic reasoning, especially as we get into larger and larger causal networks. There’s an obvious tradeoff between the cost to obtain more evidence vs more compute – it’s not always a choice that’s available (e.g., spend time investigating vs. spend time thinking/tinkering with models) but is often enough.
When I think about how I’m using the reasoning skills I’ve picked up here that’s roughly what I’m having to do for real-world problems. Use probabilistic reasoning to resolve simpler more object level propositions into true/false/maybe, then propositional logic to follow the implications. Fail back to probabilistic reasoning whenever encountering a paradox or any of the other myriad problems with simple logic – Or just for periodic sanity checking.
The areas where strong evidence is common are largely those areas we don’t intuitively think of as governed by probability theory and where classic logic performs well.
I’m pretty sure that statistics (as mathematics) all assume ‘logic’ (first-order logic at least), so I think this is also technically correct!
Gathering enough evidence sometimes allows reasoning to be performed using propositional logic with acceptable results.
Yes! Being able to use logic can be a fantastic super-power (when it works). Sometimes the universe really is like a Sudoku puzzle!
Being able to use both probabilities and logical statements, and appropriately, is a significant part of what I think David Chapman is gesturing at with what he calls ‘meta-rationality’. And beyond both of those formal rational systems, there’s an entire Platonic universe of alternative ontologies that can also be useful in some contexts (and for some purposes).
This is insightful. The areas where strong evidence is common are largely those areas we don’t intuitively think of as governed by probability theory and where classic logic performs well.
It seems like someone could take this a little further even and show that the limiting case for strong evidence and huge likelihood ratios would just be logic. This might be fruitful to unpack. I could see it being the case that our instincts for seeking “certainty” make more sense than we give them credit for. Gathering enough evidence sometimes allows reasoning to be performed using propositional logic with acceptable results.
Such logic is many orders of magnitude cheaper to evaluate compute wise vs probabilistic reasoning, especially as we get into larger and larger causal networks. There’s an obvious tradeoff between the cost to obtain more evidence vs more compute – it’s not always a choice that’s available (e.g., spend time investigating vs. spend time thinking/tinkering with models) but is often enough.
When I think about how I’m using the reasoning skills I’ve picked up here that’s roughly what I’m having to do for real-world problems. Use probabilistic reasoning to resolve simpler more object level propositions into true/false/maybe, then propositional logic to follow the implications. Fail back to probabilistic reasoning whenever encountering a paradox or any of the other myriad problems with simple logic – Or just for periodic sanity checking.
This comment is insightful!
I’m pretty sure that statistics (as mathematics) all assume ‘logic’ (first-order logic at least), so I think this is also technically correct!
Yes! Being able to use logic can be a fantastic super-power (when it works). Sometimes the universe really is like a Sudoku puzzle!
Being able to use both probabilities and logical statements, and appropriately, is a significant part of what I think David Chapman is gesturing at with what he calls ‘meta-rationality’. And beyond both of those formal rational systems, there’s an entire Platonic universe of alternative ontologies that can also be useful in some contexts (and for some purposes).