Based on the passage, it can be concluded that the author and Broyles-González hold essentially the same attitude toward

Nicole on March 4, 2020

Recap of 'ALL' 'NOT ALL' Quantifiers

I just wanted to understand a bit more how it turns into Some, then for Not All it turns into Some A, ~B. Could I just have a recap please?

Replies

on March 4, 2020

Hello @nicolebet,

Let's start with "all." The example Mehran uses is "All carrots are vegetables."
C - - - - - -> V

We have information about carrots. We know for certain that every single carrot is a vegetable. But we do not have as much information about vegetables. The statement above leaves room for a number of possibilities:

1. All vegetables are carrots.
2. Most vegetables are carrots.
3. Some vegetables are carrots.

But only one of these is a valid conclusion based on the information we have. I like to use the term "overlap." We know that the two categories overlap because all carrots are vegetables. The overlap group is 100% of the carrot population, but we don't know how it relates to the vegetable population. It could be 10%, 60%, or 100%, but we know that it is not 0% because there is some overlap. This is why "some" is the only valid conclusion.
C - - - - - - -> V
V - - some - - C

I'll make a new example for "not all."
"Not all mammals are primates."
There is some similar reasoning to the other example. "Not all" includes multiple possibilities:

1. Most mammals are primates.
2. Some mammals are primates.
3. No mammals are primates.

We don't know which, but they all have something in common: Some mammals are not primates. This is the only thing that we can say for certain.

Nicole on March 6, 2020

Thank you so much... using 'overlap' really helped it click.

Ravi on March 20, 2020

@nicolebet, great! Let us know if you have any other questions!