In order for the predcitions to be combatible they must be silent about each other.
If the base cases are H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6
then it makes sense to say that HX (H1,H2,H3,H4,H5,H6) is 50% of XX
and that {X2,X4,X6} is 50% of XX
However if the base cases are H,T,1,2,3,4,5,6 then H would be 50% of {H,T} but not of X and {2,4,6} would be 50% of {1,2,3,4,5,6} but not X
The case where “everything works out” would like the OR to output a prediction scope of {H1,H2,H3,H4,H5,H6,T2,T4,T6}. But someone mean could argue that the OR outputs a prediction scope of {H,2,4,6}
If the claims are about separate universes then they are not predictions about the same thing. A heads claim doesn’t concern the dice world so it is not a prediction on it. Predictiontions should be alternative descriptions what happens in the world of concern. So the predictions should have the same amount of holes in them and at the root level all details shoudl be filled out ie 0 holes. An OR operation would need to produce an object that has more holes than the inputs if the inputs speak about the same universe. That is H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 are the base level hypotheses and {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6} and {} are prediction scopes neither which is found among the hypotheses. Applying a prediction OR would push towards the former object. But hypotheses are required to be firm in the details while scopes can be slippery. That is predction scopes {H1} and {H2} can be ored to {H1,H2} but the hypotheses H1 and H2 can’t be ored to produce a hypothesis.
In order for the predcitions to be combatible they must be silent about each other.
If the base cases are H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6
then it makes sense to say that HX (H1,H2,H3,H4,H5,H6) is 50% of XX
and that {X2,X4,X6} is 50% of XX
However if the base cases are H,T,1,2,3,4,5,6 then H would be 50% of {H,T} but not of X and {2,4,6} would be 50% of {1,2,3,4,5,6} but not X
The case where “everything works out” would like the OR to output a prediction scope of {H1,H2,H3,H4,H5,H6,T2,T4,T6}. But someone mean could argue that the OR outputs a prediction scope of {H,2,4,6}
If the claims are about separate universes then they are not predictions about the same thing. A heads claim doesn’t concern the dice world so it is not a prediction on it. Predictiontions should be alternative descriptions what happens in the world of concern. So the predictions should have the same amount of holes in them and at the root level all details shoudl be filled out ie 0 holes. An OR operation would need to produce an object that has more holes than the inputs if the inputs speak about the same universe. That is H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 are the base level hypotheses and {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6} and {} are prediction scopes neither which is found among the hypotheses. Applying a prediction OR would push towards the former object. But hypotheses are required to be firm in the details while scopes can be slippery. That is predction scopes {H1} and {H2} can be ored to {H1,H2} but the hypotheses H1 and H2 can’t be ored to produce a hypothesis.