My guess is that you, in practice, actually are interested in finding decision-relevant information and relevant advice, in everyday decisions that you make. I could be wrong but that seems really unlikely.
Yes, if course I do, I cannot help it. But just because we do something doesn’t mean we have the free will to either do or not do it.
I do think that any particular microstate can only lead to one macrostate.
Right, I cannot imagine it being otherwise, and that is where my beef with “agents have freedom of choice” is.
An issue with imagining a possible world where 1+1=3 is that it’s not clear in what order to make logical inferences. If you make a certain sequence of logical inferences with the axiom 1+1=3, then you get 2=1+1=3; if you make a difference sequence of inferences, then you get 2=1+1=(1+1-1)+(1+1-1)=(3-1)+(3-1)=4.
Since possible worlds are in the observer’s mind (obviously, since math is a mental construction to begin with, no matter how much people keeps arguing whether mathematical laws are invented or discovered), different people may make a suboptimal inference in different places. We call those “mistakes”. Most times people don’t explicitly use axioms, though sometimes they do. Some axioms are more useful than others, of course. Starting with 1+1=3 in addition to the usual remaining set, we can prove that all numbers are equal. Or maybe we end up with a mathematical model where adding odd numbers only leads to odd numbers. In that sense, not knowing more about the world, we are indeed in a “low-fidelity” situation, with many possible (micro-)worlds where 1+1=3 is an axiom. Some of these worlds might even have a useful description of observations (imagine, for example, one where each couple requires a chaperone, there 1+1 is literally 3).
Yes, if course I do, I cannot help it. But just because we do something doesn’t mean we have the free will to either do or not do it.
Right, I cannot imagine it being otherwise, and that is where my beef with “agents have freedom of choice” is.
Since possible worlds are in the observer’s mind (obviously, since math is a mental construction to begin with, no matter how much people keeps arguing whether mathematical laws are invented or discovered), different people may make a suboptimal inference in different places. We call those “mistakes”. Most times people don’t explicitly use axioms, though sometimes they do. Some axioms are more useful than others, of course. Starting with 1+1=3 in addition to the usual remaining set, we can prove that all numbers are equal. Or maybe we end up with a mathematical model where adding odd numbers only leads to odd numbers. In that sense, not knowing more about the world, we are indeed in a “low-fidelity” situation, with many possible (micro-)worlds where 1+1=3 is an axiom. Some of these worlds might even have a useful description of observations (imagine, for example, one where each couple requires a chaperone, there 1+1 is literally 3).