For example, just what do we mean in talking about a ‘model’ of ZFC, when ZFC or something similar is exactly the raw material used to construct models in other fields?
Learning to distinguish different levels of formalism by training to follow mathematical arguments from formal set theory can help you lots in disentangling conceptual hurdles in decision theory (in its capacity as foundational study of goal-aware AI). It’s not a historical accident I included these kinds of math in my reading list on FAI.
Hmmm. JoshuaZ made a similar point. Even though the subject matter and the math itself may not be directly applicable to the problems we are interested in, the study of that subject matter can be useful by providing exercise in careful and rigorous thinking, analogies, conceptual structures, and ‘tricks’ that may well be applicable to the problems we are interested in.
I can agree with that. At least regarding the topics in mathematical logic we have been discussing. I am less convinced of the usefulness of studying the philosophy of mind. That branch of philosophy still strikes me as just a bunch of guys stumbling around in the dark.
I am less convinced of the usefulness of studying the philosophy of mind. That branch of philosophy still strikes me as just a bunch of guys stumbling around in the dark.
And I agree. The way Eliezer refers to p-zombie arguments is to draw attention to a particular error in reasoning, an important error one should learn to correct.
Learning to distinguish different levels of formalism by training to follow mathematical arguments from formal set theory can help you lots in disentangling conceptual hurdles in decision theory (in its capacity as foundational study of goal-aware AI). It’s not a historical accident I included these kinds of math in my reading list on FAI.
Hmmm. JoshuaZ made a similar point. Even though the subject matter and the math itself may not be directly applicable to the problems we are interested in, the study of that subject matter can be useful by providing exercise in careful and rigorous thinking, analogies, conceptual structures, and ‘tricks’ that may well be applicable to the problems we are interested in.
I can agree with that. At least regarding the topics in mathematical logic we have been discussing. I am less convinced of the usefulness of studying the philosophy of mind. That branch of philosophy still strikes me as just a bunch of guys stumbling around in the dark.
And I agree. The way Eliezer refers to p-zombie arguments is to draw attention to a particular error in reasoning, an important error one should learn to correct.