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.”

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Bridges, Walls, and Leadership

“There was a large crowd of people…They were throwing things and shouting…”

This is not a quote from the Women of the Wall, but it might as well be. I was killing time on Facebook yesterday when I read this status update:

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and it reminded me of something from a children’s book I used to love when I was a little girl, “The Story of Ruby Bridges” by Robert Coles . In the book, he describes how Ruby Bridges,  six year old African American girl was volunteered to be one of the first children to attend a white school. In the quote she describes walking to school, escorted by police men, through the crowds of protesters shouting and throwing things. One morning, her teacher watches through the window while Ruby stops in the middle of the crowd and refuses to move for several minutes. “I saw you talking,” Mrs. Henry told her later when Ruby finally agreed to enter the school building. “I wasn’t talking,” said Ruby, “I was praying.”

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Ruby was six years old at the time. She was the only black girl in a school full of white children with angry parents, and somehow she found it inside her to pray for the people who crowded around and shouted and threw things at her. And thank goodness that she did that. Thank goodness that she kept going with the police men every day even though so many people tried to silence her. In the end, she paved the road for integration in schools. Eventually she was able to go to school without being accompanied by police.

I loved The Story of Ruby Bridges. She was like a hero to me. I even used her character once in a project in ceramics, because to me she was proof that great leadership can come in any size or color. And that is what the Women of the Wall show young girls all over the world.

Thank goodness that the Women of the Wall refuse to be silenced. Thank goodness that despite all the people who try to discourage them, they keep fighting. I hope that soon we can see them going to pray at the Wall without being escorted by the police. The Story of Ruby Bridges teaches us that equality and tolerance will triumph in the end. And boy will that be awkward for the people on the other side.

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