You are saying that your interpretation implies the original question. But that leaves the possibility of your question being a stronger statement than the original question. If a libertarian denies your interpretation that does not necessarily mean they deny the original question.
In other words, it is possible that if “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” is false that “it stands that n+1 is a higher increase in self-worth for the ‘arbitrary’ poor person (compared to n) than is n+1 an increase compared to n for the ‘arbitrary’ rich person.” is also false.
In other words, just because poor people are not more likely to base their self-worth on dollars-owned than rich people, it does not mean that they necessarily do not value a dollar more than a rich person.
For example, a poor person may value the dollar more because it increases the amount of food they can buy to be enough to feed all their children. Perhaps they attach most of their self-worth to the ability to feed their children.
If your interpretation includes indirectly valuing dollars then the answer changes anyway.
You are saying that your interpretation implies the original question.
I’m saying it’s an interpretation of the original question, yes.
But that leaves the possibility of your question being a stronger statement than the original question.
… my question, as I have proposed it, IS the original question. Or, rather, it’s informational value is a subset of the informational value range available to the original question. Any assertions as to the potential strength of the original question, then, must include the rephrasing.
It’s definitionally impossible for “what that statement means to me” to be “a stronger statement than that statement”. It can be stronger than you intended—but communication requires two participants.
If a libertarian denies your interpretation that does not necessarily mean they deny the original question.
I in fact offered up two mutually exclusive intrepretations of the question. The fact remains that they are re-expressions of the same original question, however.
In other words, it is possible that [...] is also false.
I agree unequivocably.
In other words, just because a poor people are not more likely to base their self-worth on dollars-owned than rich people, it does not mean that they necessarily do not value a dollar more than a rich person.
Again, I agree unequivocably.
For example [...]
Sure, no problem, absolutely.
Now please explain to me why any of this is relevant to the conversation at hand. :)
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.
“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.
You are saying that your interpretation implies the original question. But that leaves the possibility of your question being a stronger statement than the original question. If a libertarian denies your interpretation that does not necessarily mean they deny the original question.
In other words, it is possible that if “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” is false that “it stands that n+1 is a higher increase in self-worth for the ‘arbitrary’ poor person (compared to n) than is n+1 an increase compared to n for the ‘arbitrary’ rich person.” is also false.
In other words, just because poor people are not more likely to base their self-worth on dollars-owned than rich people, it does not mean that they necessarily do not value a dollar more than a rich person.
For example, a poor person may value the dollar more because it increases the amount of food they can buy to be enough to feed all their children. Perhaps they attach most of their self-worth to the ability to feed their children.
If your interpretation includes indirectly valuing dollars then the answer changes anyway.
I’m saying it’s an interpretation of the original question, yes.
… my question, as I have proposed it, IS the original question. Or, rather, it’s informational value is a subset of the informational value range available to the original question. Any assertions as to the potential strength of the original question, then, must include the rephrasing.
It’s definitionally impossible for “what that statement means to me” to be “a stronger statement than that statement”. It can be stronger than you intended—but communication requires two participants.
I in fact offered up two mutually exclusive intrepretations of the question. The fact remains that they are re-expressions of the same original question, however.
I agree unequivocably.
Again, I agree unequivocably.
Sure, no problem, absolutely.
Now please explain to me why any of this is relevant to the conversation at hand. :)
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:
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: