I think your first example could be even simpler. Imagine you have a coin that’s either fair, all-heads, or all-tails. If your prior is “fair or all-heads with probability 1⁄2 each”, then seeing heads is evidence against “fair”. But if your prior is “fair or all-tails with probability 1⁄2 each”, then seeing heads is evidence for “fair”. Even though “fair” started as 1⁄2 in both cases. So the moral of the story is that there’s no such thing as evidence for or against a hypothesis, only evidence that favors one hypothesis over another.
That’s a great explanation. Evidence may also be compatible or incompatible with a hypothesis. For instance, if I get a die (without the dots on the sides that indicate 1-6), and I instead label* it:
Red, 4, Life, X-Wing, Int, path through a tree
Then finding out I rolled a 4, without knowing what die I used, is compatible with the regular dice hypothesis, but any of the other rolls, is not.
I think your first example could be even simpler. Imagine you have a coin that’s either fair, all-heads, or all-tails. If your prior is “fair or all-heads with probability 1⁄2 each”, then seeing heads is evidence against “fair”. But if your prior is “fair or all-tails with probability 1⁄2 each”, then seeing heads is evidence for “fair”. Even though “fair” started as 1⁄2 in both cases. So the moral of the story is that there’s no such thing as evidence for or against a hypothesis, only evidence that favors one hypothesis over another.
That’s a great explanation. Evidence may also be compatible or incompatible with a hypothesis. For instance, if I get a die (without the dots on the sides that indicate 1-6), and I instead label* it:
Red, 4, Life, X-Wing, Int, path through a tree
Then finding out I rolled a 4, without knowing what die I used, is compatible with the regular dice hypothesis, but any of the other rolls, is not.
*(likely using symbols, for space reasons)