If the credences you assign to your beliefs obey the logical induction criterion, then you will get such-and-such benefits.
In the case of logical induction, the benefits are things like coherence, convergence, timeliness, and unbiasedness[2]. But different from probability theory, these concepts are operationalized as properties of the evolution of your credences over time, rather than as properties of your credences at any particular point in time.
Emphasis added.
I had not realized this is how it is defined, but now it seems obvious, or necessary. When dealing with real world systems where cognition happens in time, the logical induction criterion talk about beliefs over time rather than beliefs at a single point in time. Very interesting.
Yeah, I agree, logical induction bakes in the concept of time in a way that probability theory does not. And yeah, it does seem necessary, and I find it very interesting when I squint at it.
Great post, I’m glad this is written up nicely.
One section was especially interesting to me:
Emphasis added.
I had not realized this is how it is defined, but now it seems obvious, or necessary. When dealing with real world systems where cognition happens in time, the logical induction criterion talk about beliefs over time rather than beliefs at a single point in time. Very interesting.
Yeah, I agree, logical induction bakes in the concept of time in a way that probability theory does not. And yeah, it does seem necessary, and I find it very interesting when I squint at it.