The proof does allow for different Razors depending on your specific definition of complexity. It’s true that this makes the statement fairly weak. But it is also in a way a virtue, because it corresponds with our actual use of the Razor. There are in fact different definitions of complexity and we use different ones in different contexts; we learn from experience which contexts require which Razors. For example, if you want to describe the path of a ball moving through the air, you expect to be able to describe it with some fairly simple mathematics, and you think this more likely than complicated mathematical descriptions.
On the other hand, if you see a precise human-shaped footprint in the mud in your yard, saying “a human did it” is very complicated mathematically, since the mathematical description would include the description of a human being. So in this way, “Wind and weather did it” should be simpler, in the mathematical way. Nonetheless, you use a different Razor and say that with this Razor, it is simpler to say that a human being did it.
The last paragraph feels wrong to me. This is the explanation for that feeling that came to mind first, but I’m not positive it’s my true objection:
If your only observation were the footprint, sure—but your observations also include that you live on a planet with 7 billion people who leave footprints like that—so despite the comparitive algorithmic simplicity of the weather model, it doesn’t match the observations as well.
The proof does allow for different Razors depending on your specific definition of complexity. It’s true that this makes the statement fairly weak. But it is also in a way a virtue, because it corresponds with our actual use of the Razor. There are in fact different definitions of complexity and we use different ones in different contexts; we learn from experience which contexts require which Razors. For example, if you want to describe the path of a ball moving through the air, you expect to be able to describe it with some fairly simple mathematics, and you think this more likely than complicated mathematical descriptions.
On the other hand, if you see a precise human-shaped footprint in the mud in your yard, saying “a human did it” is very complicated mathematically, since the mathematical description would include the description of a human being. So in this way, “Wind and weather did it” should be simpler, in the mathematical way. Nonetheless, you use a different Razor and say that with this Razor, it is simpler to say that a human being did it.
The last paragraph feels wrong to me. This is the explanation for that feeling that came to mind first, but I’m not positive it’s my true objection:
If your only observation were the footprint, sure—but your observations also include that you live on a planet with 7 billion people who leave footprints like that—so despite the comparitive algorithmic simplicity of the weather model, it doesn’t match the observations as well.