I also agree that the standard model should be given more weight (due to its conceptual simplicity to pin down) than any particular nonstandard model, but I don’t see why it should be given more weight than all of them put together.
I’m not sure that it does deserve more weight than all of them put together. That largely rests on how complicated our needlessly complicated models have to be in order to recover the empirical world. If there are a lot of relatively simple ways to perfectly reproduce the empirical predictions of our standard models to date, then that will make a bigger difference than if there are an even greater number of fantastically gerrymandered, convoluted systems.
Even though there are more complicated universes that perfectly generate our observations to date than there are simple universes that do so, given proper subsets of our universe, assuming a structurally simple universe tends to yield more accurate predictions than does assuming a structurally complex universe.
Although in absolute terms there are so many more ways to be complicated than to be simple that given almost any data, most models predicting that data are exceedingly complicated and gerrymandered...
… and although it is not clear whether sentience exists in a larger proportion of complicated worlds than of simple ones (or vice versa)...
… nevertheless it seems clear that a larger proportion of the simple than of complex worlds that predict some of our experience predict all of it. That is, there are proportionally many more ways to complicatedly predict most of our observations and then spectacularly fail to predict the last few, than there are ways to complicatedly predict most of our observations and then predict the last few as well.
This, however, is still speaking very generally; the degree of complexity will make a huge difference here, and not all non-standard models are radically more complicated.
Even though there are more complicated universes that perfectly generate our observations to date than there are simple universes that do so, given proper subsets of our universe, assuming a structurally simple universe tends to yield more accurate predictions than does assuming a structurally complex universe.
But when we are talking about which model of set theory to use to model our experiences, all of the non-standard models give exactly the same predictions to date (and will continue to do so until we reach non-standard times). And not all of these models are horribly complicated. There’s the model of constructable set theory, where you only have the sets absolutely guaranteed you by the axioms. This gives you a countable model of set theory (and hence not the standard one), but it is still easily describable.
I’m not sure that it does deserve more weight than all of them put together. That largely rests on how complicated our needlessly complicated models have to be in order to recover the empirical world. If there are a lot of relatively simple ways to perfectly reproduce the empirical predictions of our standard models to date, then that will make a bigger difference than if there are an even greater number of fantastically gerrymandered, convoluted systems.
Even though there are more complicated universes that perfectly generate our observations to date than there are simple universes that do so, given proper subsets of our universe, assuming a structurally simple universe tends to yield more accurate predictions than does assuming a structurally complex universe.
Although in absolute terms there are so many more ways to be complicated than to be simple that given almost any data, most models predicting that data are exceedingly complicated and gerrymandered...
… and although it is not clear whether sentience exists in a larger proportion of complicated worlds than of simple ones (or vice versa)...
… nevertheless it seems clear that a larger proportion of the simple than of complex worlds that predict some of our experience predict all of it. That is, there are proportionally many more ways to complicatedly predict most of our observations and then spectacularly fail to predict the last few, than there are ways to complicatedly predict most of our observations and then predict the last few as well.
This, however, is still speaking very generally; the degree of complexity will make a huge difference here, and not all non-standard models are radically more complicated.
But when we are talking about which model of set theory to use to model our experiences, all of the non-standard models give exactly the same predictions to date (and will continue to do so until we reach non-standard times). And not all of these models are horribly complicated. There’s the model of constructable set theory, where you only have the sets absolutely guaranteed you by the axioms. This gives you a countable model of set theory (and hence not the standard one), but it is still easily describable.