jimrandomh comments on [link] I Was Wrong, and So Are You

jimrandomh 9 Nov 2011 19:53 UTC
0 points

You are saying that your interpretation implies the original question.

I’m saying it’s an interpretation of the original question, yes.

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.
- Logos01 9 Nov 2011 20:24 UTC
  −1 points
  Parent
  “A is an interpretation of B” means either A&B or ~A&~B, but excludes ~A&B
  
  Let the statements be (X) [...] (Y)
  
  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:
  - X ⊃ Z
  - X ⊃ Y
  - Y = ¬Z & Z = ¬Y
  At no time did I say, however, that Y ⊃ Z. That assertion would be a direct contradiction of my last line in the comment:
  
  Both of these rephrasings are potential “effectively synonymous” statements to the original question, but I hope that their answers are quite obviously inverted from each other.