There Exists vs. For All – Math and Racism

I make generalizations by accident sometimes. I think everyone does. It’s just a habit we have of not being accurate when talking about other people.

One of the most basic principles of mathematics – logic, specifically – is the difference between “there exists” and “for all/every.” For example,

1. There exists a solution to the equation x+2=5

2. Every natural number is either even or odd.

The first statement tells us that something exists – but we only know of one number with that property. It would be silly to say that every number solves the equation. The second statement tells us something about all the natural numbers in the world – that even if we go on to infinity, we will never find a number which is neither even nor odd, or both at the same time.

I understand that logic theory is not a perfect analogy for our world since there is little room for grey areas. However, it still has a lot to teach us about our environment and society. The idea of political correctness is all about defining our statements in a more exact way. Often in everyday life we confuse “there exists” with “every,” and I want to argue that this miscalculation leads us to racism.

Here are some examples:

1. All Israelis are racist
2. All Arabs are terrorists
3. All Americans are rich (we have a big problem with that one here)
4. All Ethiopians are illiterate

All of These statements are wrong.

The four statements above are sentences which people have said to me. As sad as it is, I’m not making these up out of my own head. Let’s take a moment and look at some other ways to write the above statements

1. “There exist Israelis which are not racist.” (logical inverse) This is already a much more accurate statement, because we know there are Israelis which are not racist. Instead of saying “all” we should have said “there exist.” On the other hand, saying “There exist Israelis which are racist” gives the most accurate, much more intelligent sounding and much less judgmental statement, and it says the same thing as the original one: There’s racism in Israel, and I think it’s not cool.

2. “There exist Arabs which are not terrorists.” This one should be modified even further to the statement “There exist terrorists which are Arabs.” It’s deeper than “Not all Arabs are terrorists” – being a terrorist has nothing to do with being Arab! There are also terrorists which are Japanese and American. It’s terrible but it doesn’t mean that if you are American you have an increased chance of becoming a terrorist.

3. “There exist Americans that are not rich.” Sadly, most of the way Israelis are exposed to American culture is through television (similar to how Americans mostly see Israeli society through CNN). They watch shows like How I Met Your Mother, Glee and (God forbid) the Disney channel, and let’s face it – there’s not a lot of poverty on TV. It’s easy to look around and see that some people walked here from Ethiopia with the shirt on their back while Americans mostly take a 12 hour flight with two suitcases each. Regardless, the statement should still be “There exist Americans that are rich.” Because we know nothing about how many will be rich once we get infinity of them.

4.

“There exist Ethiopians that can read.” I sincerely thought we were done discriminating based on skin color, but it turns out the problem is still deep within us. Lots of people immigrate to Israel from Ethiopia, and just as with any group of new immigrants, the people who already live here find them strange, different, and “uneducated,” which just means they are culturally different. The statement is false because there are enough Ethiopians who are literate that if you meet one, it is wrong to assume they aren’t. Some have grown up here, served in the IDF and attended universities. Frankly, making a generalization based on skin color makes you look like the one who’s illiterate.

Everywhere we go there are people who are afraid of someone who’s different. But even that statement only implies the existence of two of these people. It is crucial to be exact when we speak of others, not to confuse “alls” with “exists” because we don’t have the ability to know what goes on when there is an infinite amount of people. Only then will it be perfectly okay to say “All.”