But I haven’t yet sat down and formalized the exact difference—my reflective theory is something I’m trying to work out, not something I have in hand.
“The principle of induction is true” is a statement that cannot be justified. “You should use the principle of induction when thinking about the future” can be justified along the lines of Pascal’s wager. Assuming that it works in a universe where it does in fact work, one will make predictions that are more accurate than predictions chosen at random. Assuming that it works in a universe where it doesn’t work, one will not make predictions that are less accurate than predictions chosen at random. But I don’t think you can construct a Pascal-style argument in favor of “you should use induction when thinking about induction.” It would be interesting if you came up with something.
But I haven’t yet sat down and formalized the exact difference—my reflective theory is something I’m trying to work out, not something I have in hand.
“The principle of induction is true” is a statement that cannot be justified. “You should use the principle of induction when thinking about the future” can be justified along the lines of Pascal’s wager. Assuming that it works in a universe where it does in fact work, one will make predictions that are more accurate than predictions chosen at random. Assuming that it works in a universe where it doesn’t work, one will not make predictions that are less accurate than predictions chosen at random. But I don’t think you can construct a Pascal-style argument in favor of “you should use induction when thinking about induction.” It would be interesting if you came up with something.