“For a true Bayesian, it is impossible to seek evidence that confirms a theory”
The important part of the sentence here is seek. The isn’t about falsificationism, but the fact that no experiment you can do can confirm a theory without having some chance of falsifying it too. So any observation can only provide evidence for a hypothesis if a different outcome could have provided the opposite evidence.
For instance, suppose that you flip a coin. You can seek to test the theory that the result was HEADS, by simply looking at the coin with your eyes. There’s a 50% chance that the outcome of this test would be “you see the HEADS side”, confirming your theory (p(HEADS | you see HEADS) ~ 1). But this only works because there’s also a 50% chance that the outcome of the test would have shown the result to be TAILS, falsifying your theory (P(HEADS | you see TAILS) ~ 0). And in fact there’s no way to measure the coin so that one outcome would be evidence in favour of HEADS (P(HEADS | measurement) > 0.5), without the opposite result being evidence against HEADS (P(HEADS | ¬measurement) < 0.5).
The important part of the sentence here is seek. The isn’t about falsificationism, but the fact that no experiment you can do can confirm a theory without having some chance of falsifying it too. So any observation can only provide evidence for a hypothesis if a different outcome could have provided the opposite evidence.
For instance, suppose that you flip a coin. You can seek to test the theory that the result was
HEADS, by simply looking at the coin with your eyes. There’s a 50% chance that the outcome of this test would be “you see theHEADSside”, confirming your theory (p(HEADS | you see HEADS) ~ 1). But this only works because there’s also a 50% chance that the outcome of the test would have shown the result to beTAILS, falsifying your theory (P(HEADS | you see TAILS) ~ 0). And in fact there’s no way to measure the coin so that one outcome would be evidence in favour ofHEADS(P(HEADS | measurement) > 0.5), without the opposite result being evidence againstHEADS(P(HEADS | ¬measurement) < 0.5).