Post #1030544

2026-04-08 11:22 UTC

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&#39;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&#39;t exactly go as I had anticipated, because the law of excluded middle didn&#39;t seem intuitive to her at all. »Wait, claiming that everything always has to be either this way or the other, isn&#39;t this a very right wing thing to say? It&#39;s like saying that there can only be two genders, that doesn&#39;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&#39;t think she was convinced. So I guess I have a constructive girlfriend.

Replies (5)

@jonmsterling@mathstodon.xyz 2026-04-08 11:25

@jdw Heh… if truth values are genders, though, she may not be happy to learn that even constructively there can be no truth values that is neither true nor false, and likewise no truth values that is both true and false ;-)

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@leah@blahaj.social 2026-04-08 11:27

@jdw Yes, see http://blog.sigfpe.com/2008/06/drugs-kate-moss-and-intuitionistic.html

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@glocq@mathstodon.xyz 2026-04-08 11:31

@jdw Your example/analogy is a great one :)

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@atif@mathstodon.xyz 2026-04-08 13:44

@jdw I knew I saw it somewhere the other day ! https://mathstodon.xyz/@dpiponi/116321689626319702

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@corvid19@c.im 2026-04-08 14:50

@jdw it looks like she looked at your binary logic example and applied it to a situation where fuzzy logic would be more applicable (if we accept that one can be, say, 42% man, 58% non-man). A similar issue occurs when people try to use binary logic when talking whether something is alive or dead and then argue for hours whether e.g. viruses are alive. I think that it makes sense that aliveness is likewise a spectrum that depends on the system itself, it's environment, timescales we consider, etc. Here's an interesting paper on this topic: https://link.springer.com/article/10.1007/s11084-010-9192-3 As for your question, IDK, but I came up with another analogy: let's take a 6-sided die. 4 of them are black, 2 of them are coloured with different colours A and B, such that when illuminated with some monochromatic light, A and B are indistinguishable. So when looking at the die under white light, you can always say which colour is up. But under the monochromatic light, if the coloured side is up, you can say it was either A or B, but not one of the black sides.

Open ##1368991