Exactly. But, why do you think I'm saying that I ate vegetables when clearly what I'm saying is, "I ate every vegetable on my plate?" The answer is because you think the latter implies the former. You, you, you. Not me. You are taking what I am saying and failing to realize that what I'm saying equates to: If there were any vegetables on my plate, then I ate every one of them.
Slow down. In logic, you have to be very careful what you are saying. Now you are saying if
there were any vegetables on my plate, then
I at every vegetable on my plate. The former can be true while the latter is false. But the truth of the latter contradicts the falsity of the former since the latter logically implies there were vegetables on your plate that you did, in fact, eat...since if "I ate every vegetable on my plate" is true, then "I ate at least one vegetable on my plate" is true. In logic, the former does
imply the latter. You and Ken are mistaking "I ate every vegetable on my plate" as a universal generalization of the form of "All P are Q." But it is not. "I ate every vegetable on my plate" is a RELATION between a person and every vegetable on the plate.
In logic, It is saying,
"There is someone who ate each and every vegetable on his plate." The "all" or "every" takes a distributive
reading, not a general
This is the ambiguity of natural language I was telling you that you have to watch out for. Logic trains you to recognize these things.
Take this example: "Someone loves everybody."
R=loves. Logic tells you to translate this as,
So suppose Bob loves Jane, Susie, and Heather. Then the following is true for each loving relation that Bob stands to Jane, Susie, and Heather.
And suppose Bob, Jane, Susie, and Heather are the only people who exist. So Bob loves everyone implies,
Bob loves Bob, Bob loves Jane, Bob loves Susie, Bob loves Heather...
Bob would not stand in the loving relation to Jane if Jane did not exist. The same is true for the others. And Bob would not stand in the loving relation to everyone if he did not love someone or other. The same is true for eating each and every vegetable.