I think there are some pretty knock-down cases where human concepts are continuous. E.g. if you want to cut a rose off of a rosebush, where can you cut to get a rose? (If this example seems insufficiently important, replace it with brain surgery.)
That said, we should be careful about arguments that we need to match human concepts to high precision, because humans don’t have concepts to high precision.
In the abstraction formalism I use, it can be ambiguous whether any particular thing “is a rose”, while still having a roughly-unambiguous concept of roses. It’s exactly like clustering: a cluster can have unambiguous parameters (mean, variance, etc), but it’s still ambiguous whether any particular data point is “in” that cluster.
Good point. I was more thinking that not only could it be ambiguous for a single observer, but different observers could systematically decide differently, and that would be okay.
Are there any concepts that don’t merely have continuous parameters, but are actually part of continuous families? Maybe the notion of “1 foot long”?
I think there are some pretty knock-down cases where human concepts are continuous. E.g. if you want to cut a rose off of a rosebush, where can you cut to get a rose? (If this example seems insufficiently important, replace it with brain surgery.)
That said, we should be careful about arguments that we need to match human concepts to high precision, because humans don’t have concepts to high precision.
In the abstraction formalism I use, it can be ambiguous whether any particular thing “is a rose”, while still having a roughly-unambiguous concept of roses. It’s exactly like clustering: a cluster can have unambiguous parameters (mean, variance, etc), but it’s still ambiguous whether any particular data point is “in” that cluster.
Good point. I was more thinking that not only could it be ambiguous for a single observer, but different observers could systematically decide differently, and that would be okay.
Are there any concepts that don’t merely have continuous parameters, but are actually part of continuous families? Maybe the notion of “1 foot long”?