If we have an ordering over logical sentences, such that we can look at two sentences and determine at most one of (A is simpler than B), (B is simpler than A), then it seems natural to privilege the counterfactual that keeps the simpler term constant (and likely that this ordering is such that you never have to choose between counterfactuals at the same level of simplicity).
This doesn’t fully solve the problem—now I have a concept of thickness that’s predicated on an ordering, and the ordering is (in some sense) arbitrary for the reasons noted elsewhere (I could define B = A xor C as the ground term, which makes A = B xor C now a composite term). But it seems (to me) like the important thing is being able to build a model that doesn’t allow cyclical behavior at all. Afterwards, one can check to see whether or not the ordering matters (and if so, try to figure out the criteria that make for a good ordering), or view it as arbitrary in approximately the way that axiom sets are arbitrary.
If we have an ordering over logical sentences, such that we can look at two sentences and determine at most one of (A is simpler than B), (B is simpler than A), then it seems natural to privilege the counterfactual that keeps the simpler term constant (and likely that this ordering is such that you never have to choose between counterfactuals at the same level of simplicity).
This doesn’t fully solve the problem—now I have a concept of thickness that’s predicated on an ordering, and the ordering is (in some sense) arbitrary for the reasons noted elsewhere (I could define B = A xor C as the ground term, which makes A = B xor C now a composite term). But it seems (to me) like the important thing is being able to build a model that doesn’t allow cyclical behavior at all. Afterwards, one can check to see whether or not the ordering matters (and if so, try to figure out the criteria that make for a good ordering), or view it as arbitrary in approximately the way that axiom sets are arbitrary.