If induction has worked in the past, it is a simpler theory that it will continue to work, than it will stop working at precisely midnight, because the theory that it will stop working has to contain additional information specifying when it will stop working.
Marcus Hutter, in 2005, demonstrated that simpler theories are (all other things being equal) more likely to be true.
This gives us the bootstrap we need to have as least a minimal reason to trust induction that doesn’t require inductive reasoning.
If induction has worked in the past, it is a simpler theory that it will continue to work, than it will stop working at precisely midnight, because the theory that it will stop working has to contain additional information specifying when it will stop working.
Marcus Hutter, in 2005, demonstrated that simpler theories are (all other things being equal) more likely to be true.
This gives us the bootstrap we need to have as least a minimal reason to trust induction that doesn’t require inductive reasoning.
See also ReaysLemma