The starting point here is not “things that have worked in the past will continue to work in the future”. The starting point is induction: when we see a pattern, the we expect it is likely to continue. For instance, if we take a random sampling of 10 balls from an urn and they are all blue, I predict the next one is blue with some probability around 95% (I’m not sure what theory says my confidence should be). That’s induction.
And the more reliable the pattern is, the more we expect it to continue. In this case the pattern holds over all the Ns we have information about, therefore we expect it to hold for larger N too, especially because we have no reason to think there is anything special about N > 13.8 billion as compared to N < 13.8 billion.
“Empirical” results are inductive by definition, and while we can see that induction works by induction, I’m not arguing that induction proves itself to work, just that “things that have worked in the past will continue to work in the future” is an ordinary inductive result like any other.
The starting point here is not “things that have worked in the past will continue to work in the future”. The starting point is induction: when we see a pattern, the we expect it is likely to continue. For instance, if we take a random sampling of 10 balls from an urn and they are all blue, I predict the next one is blue with some probability around 95% (I’m not sure what theory says my confidence should be). That’s induction.
And the more reliable the pattern is, the more we expect it to continue. In this case the pattern holds over all the Ns we have information about, therefore we expect it to hold for larger N too, especially because we have no reason to think there is anything special about N > 13.8 billion as compared to N < 13.8 billion.
“Empirical” results are inductive by definition, and while we can see that induction works by induction, I’m not arguing that induction proves itself to work, just that “things that have worked in the past will continue to work in the future” is an ordinary inductive result like any other.