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jimrandomh comments on [link] I Was Wrong, and So Are You - Less Wrong Discussion
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No. "A implies B" means either A&B, ~A&B, or ~A&~B. "A is an interpretation of B" means either A&B or ~A&~B, but excludes ~A&B. Let the statements be
(X) “A dollar means more to a poor person than it does to a rich person”
(Y) "A poor person is more likely to base his self-worth on how many dollars he owns than a rich person is likely to base his self-worth on how many dollars he owns."
You argued that Y implies X, but you didn't do anything to argue against X&~Y. I happen to believe X&~Y, which makes these statements definitely not mere rephrasings of each other.
Here's your error. There's a (Z).
(Z) "A poor person will suffer more for the lack of one dollar than a rich person will suffer for the lack of one dollar."
Here's what I originally said, broken into symbolic logic for you:
At no time did I say, however, that Y ⊃ Z. That assertion would be a direct contradiction of my last line in the comment: