I was trying to explain to my (non-mathematical) girlfriend why it might be interesting to see what could be proved using constructive logic/why constructive proofs are stronger than classical ones. I came up with an analogy to a court situation where you can't be sentenced even if it can be proved that last night you either commited crime A or crime B but it is not clear which one. You can only be sentenced if there is a proof that you committed crime A or there is a proof that you committed crime B. (Does anyone know if such a scenario ever occurred in reality?)

Anyway, the talk didn't exactly go as I had anticipated, because the law of excluded middle didn't seem intuitive to her at all. »Wait, claiming that everything always has to be either this way or the other, isn't this a very right wing thing to say? It's like saying that there can only be two genders, that doesn't make sense to me at all!« So in the end I was trying to make plausible why some people would be convinced that either there is at least one unicorn or there are no unicorns at all, but I don't think she was convinced.

So I guess I have a constructive girlfriend.