{"id":3184,"date":"2015-06-01T10:33:19","date_gmt":"2015-06-01T14:33:19","guid":{"rendered":"http:\/\/www.goodmath.org\/blog\/?p=3184"},"modified":"2016-12-14T14:28:59","modified_gmt":"2016-12-14T19:28:59","slug":"the-bad-logic-of-good-people-cant-be-sexists","status":"publish","type":"post","link":"http:\/\/www.goodmath.org\/blog\/2015\/06\/01\/the-bad-logic-of-good-people-cant-be-sexists\/","title":{"rendered":"The Bad Logic of Good People Can’t be Sexists"},"content":{"rendered":"

One of my constant off-topic rants around here is about racism and sexism. This is going to be a nice little post that straddles the line. It’s one of those off-topic-ish rants about sexism in our society, but it’s built around a core of bad logic – so there is a tiny little bit of on-topicness.<\/p>\n

We live in a culture that embodies a basic conflict. On one hand, racism and sexism are a deeply integrated part of our worldview. But on the other wand, we’ve come to believe that racism and sexism are bad. This puts us into an awkward situation. We don’t want to admit to saying or doing racist things. But there’s so much of it embedded in every facet of our society that it takes a lot of effort and awareness to even begin to avoid saying and doing racist things.<\/p>\n

The problem there is that we can’t stop being racist\/sexist until we admit that we are. We can’t stop doing sexist and racist things until we admit that we do sexist and racist things.<\/p>\n

And here’s where we hit the logic piece. The problem is easiest to explain by looking at it in formal logical terms. We’ll look at it from the viewpoint of sexism, but the same argument applies for racism.<\/p>\n

    \n
  1. We’ll say \\text{Sexist}(x) to mean that “x” is sexist.<\/li>\n
  2. We’ll say \\text{Bad}(x) to mean that x is bad, and \\text{Good}(x) to mean that x is good.<\/li>\n
  3. We’ll have an axiom that bad and good are logical opposites: \\text{Bad}(x) \\Leftrightarrow \\lnot \\text{Good}(x).<\/li>\n
  4. We’ll have another axiom that sexism is bad: \\forall x: \\text{Sexist}(x) \\Rightarrow \\text{Bad}(x).<\/li>\n
  5. We’ll say \\text{Does}(p, x) means that person p does an action x.<\/li>\n<\/ol>\n

    The key statement that I want to get to is: We believe that people who do bad things are bad people: \\forall p, x: \\text{Does}(p, x) \\land \\text{Bad}(x) \\Rightarrow \\text{Bad}(p).<\/p>\n

    That means that if you do something sexist, you are a bad person:<\/p>\n