However, I expect that the space of abstractions is (approximately) discrete. A mind may use the tree-concept, or not use the tree-concept, but there is no natural abstraction arbitrarily-close-to-tree-but-not-the-same-as-tree. There is no continuum of tree-like abstractions.
This doesn’t seem likely to me. Language is optimized for communicating ideas, but let’s take a simpler example than language: transmitting a 256x256 image of a dog or something, with a palette of 100 colors, and minimizing L2 error. I think that
The palette will be slightly different when minimizing L2 error in RGB space rather than HSL space
The palette will be slightly different when using a suboptimal algorithm (e.g. greedily choosing colors)
The palette will be slightly different when the image is of a slightly different dog
The palette will be slightly different when the image is of the same dog from a different angle
By analogy, shouldn’t concepts vary continuously with small changes in the system’s values, cognitive algorithms, training environment, and perceptual channels?
Another analogy: consider this clustering problem.
Different clustering algorithms will indeed find slightly different parameterizations of the clusters, slightly different cluster membership probabilities, etc. But those differences will be slight differences. We still expect different algorithms to cluster things in one of a few discrete ways—e.g. identifying the six main clusters, or only two (top and bottom, projected onto y-axis), or three (left, middle, right, projected onto x-axis), maybe just finding one big cluster if it’s a pretty shitty algorithm, etc. We would not expect to see an entire continuum of different clusters found, where the continuum ranges from “all six separate” to “one big cluster”; we would expect a discrete difference between those two clusterings.
This doesn’t seem likely to me. Language is optimized for communicating ideas, but let’s take a simpler example than language: transmitting a 256x256 image of a dog or something, with a palette of 100 colors, and minimizing L2 error. I think that
The palette will be slightly different when minimizing L2 error in RGB space rather than HSL space
The palette will be slightly different when using a suboptimal algorithm (e.g. greedily choosing colors)
The palette will be slightly different when the image is of a slightly different dog
The palette will be slightly different when the image is of the same dog from a different angle
By analogy, shouldn’t concepts vary continuously with small changes in the system’s values, cognitive algorithms, training environment, and perceptual channels?
The key there is “slightly different”.
Another analogy: consider this clustering problem.
Different clustering algorithms will indeed find slightly different parameterizations of the clusters, slightly different cluster membership probabilities, etc. But those differences will be slight differences. We still expect different algorithms to cluster things in one of a few discrete ways—e.g. identifying the six main clusters, or only two (top and bottom, projected onto y-axis), or three (left, middle, right, projected onto x-axis), maybe just finding one big cluster if it’s a pretty shitty algorithm, etc. We would not expect to see an entire continuum of different clusters found, where the continuum ranges from “all six separate” to “one big cluster”; we would expect a discrete difference between those two clusterings.