In FAI, the central question is what a program wants (which is a certain kind of question about what the program means), and not what a program does.
Computer science will tell lots about what which programs can do how, and how to construct a program that does what you need, but less about what a program means (the sort of computer science that does is already a fair distance towards mathematics). This is also a problem with statistics/machine learning, and the reason they are not particularly useful for FAI: they teach certain tools, and how these tools work, but understanding they provide isn’t portable enough.
Mathematical logic, on the other hand, contains lots of wisdom in the right direction: what kinds of mathematical structures can be defined how, which structures a given definition defines, what concepts are definable, and so on. And to understands the concepts themselves one needs to go further.
Unfortunately, I can’t give a good positive argument for the importance of math; that would require a useful insight (arrived at through use of mathematical tools). At the least, I can attest finding a lot of confusion in my past thinking about FAI as a result of each “level up” in understanding of mathematics, and that counts for something.
In FAI, the central question is what a program wants (which is a certain kind of question about what the program means), and not what a program does.
Computer science will tell lots about what which programs can do how, and how to construct a program that does what you need, but less about what a program means (the sort of computer science that does is already a fair distance towards mathematics). This is also a problem with statistics/machine learning, and the reason they are not particularly useful for FAI: they teach certain tools, and how these tools work, but understanding they provide isn’t portable enough.
Mathematical logic, on the other hand, contains lots of wisdom in the right direction: what kinds of mathematical structures can be defined how, which structures a given definition defines, what concepts are definable, and so on. And to understands the concepts themselves one needs to go further.
Unfortunately, I can’t give a good positive argument for the importance of math; that would require a useful insight (arrived at through use of mathematical tools). At the least, I can attest finding a lot of confusion in my past thinking about FAI as a result of each “level up” in understanding of mathematics, and that counts for something.