Jaynes discusses Hempel’s Paradox on pages 143 to 144 of Probability Theory: the Logic of Science. I take away a broad lesson: one must always know what alternative hypotheses are available. Failing to be clear about your alternative hypotheses is my first candidate for what you are doing wrong.
My second candidate comes from rule IIIb for plausible reasoning (page 9).
… always take into account all the evidence relevant to the question …
One conspicuous feature of the world is the presence of rival faiths, each well attested by miracles about which the faithful will admit no doubts. This occurs both between religions (Muslim, Christian, Jew) and within religions (Orthodox, Catholic, Protestant).
It is tempting at this point to rush ahead down a well-worn path to atheism. “Since the rivals are mutually exclusive and the situation symmetrical they must all be wrong.” I’ve put the argument in quotes because I’m suggesting that we hold off and pause for reflection. Since we can see what is coming, we face a choice. We can either leave out the existence of rival religions because, for many people, it settles the issue, and we feel that including them therefore prejudges the issue. Or we can include the existence of rival religions and wonder whether the situation really is symmetrical.
Rule IIIb requires us to ask whether the existence of rival religions (with well attested miracles …) is relevant. We know that it is highly relevant. We even feel an itch to leave it out to avoid it over powering other considerations.
Rule IIIb then instructs us to take them into account. Ouch! The probability calculation has already gone badly wrong, just because it left out the rival religions and before we ever get to thinking about what the existence of rival religions implies for the issue we are considering.
Jaynes discusses Hempel’s Paradox on pages 143 to 144 of Probability Theory: the Logic of Science. I take away a broad lesson: one must always know what alternative hypotheses are available. Failing to be clear about your alternative hypotheses is my first candidate for what you are doing wrong.
My second candidate comes from rule IIIb for plausible reasoning (page 9).
One conspicuous feature of the world is the presence of rival faiths, each well attested by miracles about which the faithful will admit no doubts. This occurs both between religions (Muslim, Christian, Jew) and within religions (Orthodox, Catholic, Protestant).
It is tempting at this point to rush ahead down a well-worn path to atheism. “Since the rivals are mutually exclusive and the situation symmetrical they must all be wrong.” I’ve put the argument in quotes because I’m suggesting that we hold off and pause for reflection. Since we can see what is coming, we face a choice. We can either leave out the existence of rival religions because, for many people, it settles the issue, and we feel that including them therefore prejudges the issue. Or we can include the existence of rival religions and wonder whether the situation really is symmetrical.
Rule IIIb requires us to ask whether the existence of rival religions (with well attested miracles …) is relevant. We know that it is highly relevant. We even feel an itch to leave it out to avoid it over powering other considerations.
Rule IIIb then instructs us to take them into account. Ouch! The probability calculation has already gone badly wrong, just because it left out the rival religions and before we ever get to thinking about what the existence of rival religions implies for the issue we are considering.