It seems that every mathematical structure (there are some technicalities as to how to define it) could metaphysically be the correct description of fundamental physical structure. This means that making Bayesianism be the whole story about epistemology—even for idealized agents—is a hopeless endeavor. For there is no hope for an epistemologically useful probability measure over the collection of all mathematical structures unless we rule out the vast majority of structures as having zero probability.
A natural law or divine command epistemology can solve this problem by requiring us to assign zero probability to some non-actual physical structures that are metaphysically possible but that our Creator wants us to be able to rule out a priori. In other words, our Creator can make us so that we only take epistemically seriously a small subset of the possibilia. This might help with the problem of scepticism, too.
5 comments:
Very neat idea, but I wonder ...
Since there are so many structures, each has zero probability already (there are not even infinitesimals small enough for all those structures to have the same numerical value). So, we just have to classify the structures somehow; and to begin with, we have to do that while knowing nothing.
We could begin with something that looks more like pre-formal logic (just as we do when we think logically about what is probably the case). (Basically, logic is like knowledge, in that we do not need a concept of it.) So, while Bayesianism may well not be the whole story for idealized agents, it can be the basic picture for us (much as knowledge is basically justified true belief) so that there is no real problem (as opposed to academic puzzle) for this epistemology to be a solution to ... ?
My basic thought is that there are real academic questions about what is really the case; that academics should pursue truth, that they should not be pursuing theories of truth.
If so, then we do not want to rule out, early on, possibilities that really might turn out to have been true. Of course, we might be naturally such that we rule out falsehoods. But we might be naturally such that we rule out truths. We might be fooled by a demon into ruling out the truth. So, there would be scepticism even with your epistemology ...
Martin Cooke
So, we just have to classify the structures somehow; and to begin with, we have to do that while knowing nothing.
Yes, however we can methodologically classify the structures.
The interesting thing is that "knowing nothing" IS the method that gives one the correct structures.
Marin Cooke
We might be fooled by a demon into ruling out the truth. So, there would be scepticism even with your epistemology
It is impossible for the demon to rule out truth. ALL the demon can do is minimise the TOTAL INTRINSIC truth.
I meant that the demon might fool us into ruling out some particular truth, Philip; I meant that if we find ourselves taking just a small subset of the possibilia seriously, then while that might be because God wants that, or because Nature has so fitted us to the world, it might be because a demon wants it, or because it is a side-effect of something else that was selected for, or indeed, because we have some random mutation to that effect.
Martin Cooke
In other words, our Creator can make us so that we only take epistemically seriously a small subset of the possibilia.
Let's concentrate on this part of the blog post.
First, question: Do numbers lie?
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