Jakob

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.

Apr 8 at 11:22amWeb
Show threadJon Sterling1d ago
@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 ;-)
Show threadJakob1d ago
@jonmsterling Internally, that is :)
Show threadJon Sterling1d ago
@jdw yes
Show threadLeah Neukirchen1d ago
@jdw Yes, see http://blog.sigfpe.com/2008/06/drugs-kate-moss-and-intuitionistic.html
A Neighborhood of Infinity: Drugs, Kate Moss, and Intuitionistic Logic

Show threadGrégoire Locqueville1d ago
@jdw Your example/analogy is a great one :)
Show threadAtif1d ago
@jdw I knew I saw it somewhere the other day ! https://mathstodon.xyz/@dpiponi/116321689626319702
Show threadMr. ZER017h ago

@atif @jdw
This shit is too stupid for it to be real. Someone got bribed or this is just plain out biases at play. I have to see the court documents to actually believe that. I think this might be her first offense and the court decided to forgive her or there wasn't enough evidence. Or just plain out racism/classism/halo effect/sexism or whatever ism... cause even a child wouldn't make such poor judgment.

I think this is probably twisting of facts for views/profit/("enter some incentive")

Show threadCorvid1923h ago

@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.

Is it Useful to Have a Clear-cut Definition of Life? On the Use of Fuzzy Logic in Prebiotic Chemistry - Discover Life

Many scientists, including one of the authors of the present paper, have devoted time to try to find a definition for life (Bersini and Reisse 2007). It is clear that a consensus will never be reached but, more importantly, it seems that the issue itself could be without major interest. It is indeed impossible to define a “natural” frontier between non-living and living systems and therefore also impossible to define dichotomic criteria which could be used in order to classify systems in one of these two classes (living or non-living). Fuzzy logic provides a natural way to deal with problems where class membership lacks sharply defined criteria. It also offers the possibility to avoid losing time with unnecessary controversies such as deciding whether a virus is, or is not, a living system.

SpringerLink