I think that the necessary and sufficient conditions approach is great when you’re making things which fit a definition or working with a set of already known necessary and sufficient conditions, but really terrible when dealing with concepts that your brain formed implicitly without your supervision.
Basically, if I can build something, I might as well enforce a legible and easy to deal with set of sufficient and necessary conditions on it. Things are only in there because I put them there, and if I know the rules well enough then it should be easy to manipulate.
Looking at things that my brain already thinks, I would be surprised if they were anywhere near that legible. Math will catch up eventually to describing it, but it’s harder and less natural, and the mathematical descriptions of things that I think will look weird compared to what naive hierarchical data structures look like. (i.e. lots of things will be conditioned on things that I think should be irrelevant, but the halo effect happens.)
I think that the necessary and sufficient conditions approach is great when you’re making things which fit a definition or working with a set of already known necessary and sufficient conditions, but really terrible when dealing with concepts that your brain formed implicitly without your supervision.
Basically, if I can build something, I might as well enforce a legible and easy to deal with set of sufficient and necessary conditions on it. Things are only in there because I put them there, and if I know the rules well enough then it should be easy to manipulate.
Looking at things that my brain already thinks, I would be surprised if they were anywhere near that legible. Math will catch up eventually to describing it, but it’s harder and less natural, and the mathematical descriptions of things that I think will look weird compared to what naive hierarchical data structures look like. (i.e. lots of things will be conditioned on things that I think should be irrelevant, but the halo effect happens.)