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There always are shenanigans if you pass a certain threshold of expressive power. Can we do most or all useful /interesting stuff below that threshold though?
by naasking 3y ago
There always are shenanigans if you pass a certain threshold of expressive power. Can we do most or all useful /interesting stuff below that threshold though?
- H8crilA 3y agoExcessive power has been proven to be just addition and multiplication over the natural numbers. So - no, we can't.
- naasking 3y agoYes, addition and multiplication over the infinite naturals. I don't think it's obvious that all three of these are needed together for all interesting applications. For instance, various types of finitism eliminate the infinities.