I think you’re right. I was using prior knowledge to interpret the argument correctly. The ambiguity in the language definitely makes my example weaker. I tried empathizing with the commenter as an intuition thinker to try figuring out what the most likely mistake caused the confusion. I still think the commenter most likely didn’t pay attention to those words, but it’s also quite likely he understood the technically correct alternative interpretation.
In his situation, I’d probably read ‘any’ in the second sense simply because as a non-mathematician I can imagine the second sense being a practical test: (I give you a number, you show me that the difference between A and B is smaller, we reach a conclusion) whereas the first seems esoteric (you test every conceivable small number...)
On the other hand, the first reading is so blatantly wrong, the commenter really should have stepped back and thought ‘could this sentence be saying something that wasn’t obviously incorrect?’ Principle of charity and all that.
I think you’re right. I was using prior knowledge to interpret the argument correctly. The ambiguity in the language definitely makes my example weaker. I tried empathizing with the commenter as an intuition thinker to try figuring out what the most likely mistake caused the confusion. I still think the commenter most likely didn’t pay attention to those words, but it’s also quite likely he understood the technically correct alternative interpretation.
In his situation, I’d probably read ‘any’ in the second sense simply because as a non-mathematician I can imagine the second sense being a practical test: (I give you a number, you show me that the difference between A and B is smaller, we reach a conclusion) whereas the first seems esoteric (you test every conceivable small number...)
On the other hand, the first reading is so blatantly wrong, the commenter really should have stepped back and thought ‘could this sentence be saying something that wasn’t obviously incorrect?’ Principle of charity and all that.