Insight doesn’t exactly “count as evidence”. Rather, when you acquire insight, you improve the evidence-strength of the best algorithm available for assigning hypothesis probabilities.
Initially, your best hypothesis-weighting algorithms are “ask an expert” and “use intuition”.
If I give you the insight to prove some conclusion mathematically, then the increased evidence comes from the fact that you can now use the “find a proof” algorithm. And that algorithm is more entangled with the problem structure than anything else you had before.
Insight doesn’t exactly “count as evidence”. Rather, when you acquire insight, you improve the evidence-strength of the best algorithm available for assigning hypothesis probabilities.
Initially, your best hypothesis-weighting algorithms are “ask an expert” and “use intuition”.
If I give you the insight to prove some conclusion mathematically, then the increased evidence comes from the fact that you can now use the “find a proof” algorithm. And that algorithm is more entangled with the problem structure than anything else you had before.