A definition doesn't change: The prime numbers or Turing Machines are the same set regardless of who Putin invades next or what law Biden decides to veto.
But the set of inputs that an oracle implicitly defines, could change if the oracle changes. And you could change your mind or die tomorrow.
So you would need a very large number of definitions of bread, indexed by (time, person). Any one of them could be a valid definition - it's theoretically possible to make you look at 1000 pictures of bread so your brain is encouraged to make a bread-detector neuron, and then scan your brain and calculate its response on any input - but you don't know which one is correct to use for any purpose.
i.e. If I want to start a bakery, should I use your current bread-oracle to define "marketable bread", your bread-oracle as of 5 years ago, should I take a statistical ensemble of brain scans from millions of people, or should I use my own?
It seems like just having a function that returns true on some inputs and false on others doesn't tell you much, whereas traditional mathematical definitions have strict relations to other things.
But the set of inputs that an oracle implicitly defines, could change if the oracle changes. And you could change your mind or die tomorrow.
So you would need a very large number of definitions of bread, indexed by (time, person). Any one of them could be a valid definition - it's theoretically possible to make you look at 1000 pictures of bread so your brain is encouraged to make a bread-detector neuron, and then scan your brain and calculate its response on any input - but you don't know which one is correct to use for any purpose.
i.e. If I want to start a bakery, should I use your current bread-oracle to define "marketable bread", your bread-oracle as of 5 years ago, should I take a statistical ensemble of brain scans from millions of people, or should I use my own?
It seems like just having a function that returns true on some inputs and false on others doesn't tell you much, whereas traditional mathematical definitions have strict relations to other things.