Right, you’d need more than that one axiom before you could really say you had a formulation of Occam’s Razor. I’m just making a more specific point, that whatever formulation of complexity you come up with, so long as it satisfies the axiom above, will have the property that any probability distribution over discrete outcomes must assign diminishing probability to increasingly complex hypotheses in the limit.
EDIT: actually even without that axiom, so long as you consider only discrete hypotheses and your definition of complexity maps hypotheses to a real positive number representing complexity, you will have that the mass of probability given to hypotheses more complex than x falls to zero as x goes to infinity.
Right, you’d need more than that one axiom before you could really say you had a formulation of Occam’s Razor. I’m just making a more specific point, that whatever formulation of complexity you come up with, so long as it satisfies the axiom above, will have the property that any probability distribution over discrete outcomes must assign diminishing probability to increasingly complex hypotheses in the limit.
EDIT: actually even without that axiom, so long as you consider only discrete hypotheses and your definition of complexity maps hypotheses to a real positive number representing complexity, you will have that the mass of probability given to hypotheses more complex than x falls to zero as x goes to infinity.