Yes, simpler models out of several equivalent ones are preferable, no argument there. I never said otherwise, that would be silly. Here I define “simpler” instrumentally, those which require less work to make the same set of predictions. Please don’t strawman me,
Sorry! Any strawmanning was unintentional. However, I’m not so sure that there was strawmanning. I meant “simpler” in terms of some appropriately rigorous version of Occam’s razor. This seems different from your conception of “simpler”. A simpler theory in my sense need not involve less work to make the same predictions. The standard usage of “theoretical simplicity” on LW is more in line with my conception than yours, so I have good reason to believe that this is the way TheOtherDave was using the word.
Just to make sure: do you think simpler models (in my sense) are preferable? Or do you think our two senses are in fact equivalent?
It’s kind of entertaining watching this exchange interpreting my earlier comments, and I’m sort of reluctant to disturb it, but FWIW my usage of “simplicity” was reasonably well aligned with your conception, but I’m not convinced it isn’t well-aligned with shminux’s, as I’m not really sure what “work” refers to.
That said, if it refers to cognitive effort, I think my conception is anti-aligned with theirs, since I would (for example) expect it to be more cognitive effort to make a typical prediction starting from a smaller set of axioms than from a larger set of (mutually consistent) axioms, but would not consider the larger set simpler.
I would (for example) expect it to be more cognitive effort to make a typical prediction starting from a smaller set of axioms than from a larger set of (mutually consistent) axioms, but would not consider the larger set simpler.
My guess is that the larger set will have some redundancy, i.e. some of the axioms would be in fact theorems. But I don’t know enough about that part of math to make a definitive statement.
I agree that if it’s possible, within a single logical framework F, to derive proposition P1 from proposition P2, then P1 is a theorem in F and not an axiom of F… or, at the very least, that it can be a theorem and need not be an axiom.
That said, if it’s possible in F to derive some prediction P3 from either P1 or P2, it does not follow that it’s possible to derive P1 from P2.
I meant “simpler” in terms of some appropriately rigorous version of Occam’s razor.
I’m yet to see a workable version of it, something that does not include computing uncomputables and such. I’d appreciate f you point me to a couple of real-life (as real as I admit to it to be, anyway) examples where a rigorous version of Occam’s razor was successfully applied to differentiating between models. And no, the hand-waving about a photon and the cosmological horizon is not rigorous.
A simpler theory in my sense need not involve less work to make the same predictions.
Again, a (counter)example would be useful here.
Just to make sure: do you think simpler models (in my sense) are preferable? Or do you think our two senses are in fact equivalent?
That depends on whether simpler models in your sense can result in more work to get to all the same conclusions. I am not aware of any formalization that can prove or disprove this claim.
Yes, simpler models out of several equivalent ones are preferable, no argument there. I never said otherwise, that would be silly. Here I define “simpler” instrumentally, those which require less work to make the same set of predictions. Please don’t strawman me,
Sorry! Any strawmanning was unintentional. However, I’m not so sure that there was strawmanning. I meant “simpler” in terms of some appropriately rigorous version of Occam’s razor. This seems different from your conception of “simpler”. A simpler theory in my sense need not involve less work to make the same predictions. The standard usage of “theoretical simplicity” on LW is more in line with my conception than yours, so I have good reason to believe that this is the way TheOtherDave was using the word.
Just to make sure: do you think simpler models (in my sense) are preferable? Or do you think our two senses are in fact equivalent?
It’s kind of entertaining watching this exchange interpreting my earlier comments, and I’m sort of reluctant to disturb it, but FWIW my usage of “simplicity” was reasonably well aligned with your conception, but I’m not convinced it isn’t well-aligned with shminux’s, as I’m not really sure what “work” refers to.
That said, if it refers to cognitive effort, I think my conception is anti-aligned with theirs, since I would (for example) expect it to be more cognitive effort to make a typical prediction starting from a smaller set of axioms than from a larger set of (mutually consistent) axioms, but would not consider the larger set simpler.
My guess is that the larger set will have some redundancy, i.e. some of the axioms would be in fact theorems. But I don’t know enough about that part of math to make a definitive statement.
I agree that if it’s possible, within a single logical framework F, to derive proposition P1 from proposition P2, then P1 is a theorem in F and not an axiom of F… or, at the very least, that it can be a theorem and need not be an axiom.
That said, if it’s possible in F to derive some prediction P3 from either P1 or P2, it does not follow that it’s possible to derive P1 from P2.
I’m yet to see a workable version of it, something that does not include computing uncomputables and such. I’d appreciate f you point me to a couple of real-life (as real as I admit to it to be, anyway) examples where a rigorous version of Occam’s razor was successfully applied to differentiating between models. And no, the hand-waving about a photon and the cosmological horizon is not rigorous.
Again, a (counter)example would be useful here.
That depends on whether simpler models in your sense can result in more work to get to all the same conclusions. I am not aware of any formalization that can prove or disprove this claim.