There must be something we can whack them with to get this—maybe Kolmogorov complexity or stuff like that?
This is exactly how I responded to the problem of grue when hearing about it. I don’t see your post as invalidating that. Here’s why (and this may be equivalent to your own answer, I don’t know): you need to calculate the additional Kolmogorov complexity of concept X+”everything else you knew” over “everything else you know”.
For a simple example, if I see just the cover of a known book, considering the Kolmogorov complexity of the book in isolation should lead me to conclude that the inside of the book doesn’t exist. Surely the inside of the book containing a whole lot of data has far greater Kolmogorov complexity than an empty book with the same cover? The obvious answer is that once you include the rest of your knowledge, the marginal added complexity by assuming this book “matches” the cover is less than assuming it doesn’t.
In the same way, in our world, if something has attributes that fit both grue and green, the overall complexity of grue+”all my knowledge” will be greater than overall complexity of green+”all my knowledge”. Conversely, if “changing when the sun is out” is a real possibility, that compresses the space needed to express the grue concept, and lowers the marginal complexity.
You seem to be using “ease of learning X” as some kind of proxy for actual Kolmogorov complexity, or something.
This is exactly how I responded to the problem of grue when hearing about it. I don’t see your post as invalidating that. Here’s why (and this may be equivalent to your own answer, I don’t know): you need to calculate the additional Kolmogorov complexity of concept X+”everything else you knew” over “everything else you know”.
For a simple example, if I see just the cover of a known book, considering the Kolmogorov complexity of the book in isolation should lead me to conclude that the inside of the book doesn’t exist. Surely the inside of the book containing a whole lot of data has far greater Kolmogorov complexity than an empty book with the same cover? The obvious answer is that once you include the rest of your knowledge, the marginal added complexity by assuming this book “matches” the cover is less than assuming it doesn’t.
In the same way, in our world, if something has attributes that fit both grue and green, the overall complexity of grue+”all my knowledge” will be greater than overall complexity of green+”all my knowledge”. Conversely, if “changing when the sun is out” is a real possibility, that compresses the space needed to express the grue concept, and lowers the marginal complexity.
You seem to be using “ease of learning X” as some kind of proxy for actual Kolmogorov complexity, or something.
Yep. I didn’t go for Kolmogorov complexity because I had another mathematical definition I wanted to try out: http://lesswrong.com/r/discussion/lw/mbr/grue_bleen_and_natural_categories/