Before make the post I promised I'd make I thought I'd make a digression to point out a connection between Intuitionistic Logic and a recent news story.
Intuitionistic logic is what we get when we take ordinary everyday classical logic and drop the Law of the Excluded Middle (LEM), in other words, we drop the law that says that for any proposition, either it or its negation is true. This is such an ingrained notion that it's hard to imagine giving it up. For example, it seems obvious that either it's raining or it's not raining. But there are good reasons for not taking it for granted in mathematics. The main issue is that sometimes when we use LEM we find that we can prove the existence of something, but have no way of constructing it. Mathematics is full of such proofs. The best known example is probably the proof that an irrational number raised to the power of an irrational number can be rational. Some mathematicians (and many computer scientists) only like constructive proofs, ie. proofs that actually exhibit the thing whose existence is being proved. Using intuitionistic logic is a good way to always force this to be true. So, for example, in classical logic, you might find you have proved "A or B", but not have a proof of A or a proof of B. But in intuitionistic logic, if you prove "A or B", then you must have proved A or you must have proved B.
Now (British) criminal law is more lax than mathematical logic when it comes to proof. You only need to prove something beyond reasonable doubt, rather than providing a rigorous derivation from axioms. (Though admittedly mathematicians rarely do this in practice.) But criminal law does have one place where it has higher standards of proof than classical logic: you can't necessarily convict someone of "A or B" unless you have a proof of A or a proof of B. A proof of "A or B" will not do.
It seems that there is enough evidence to show that Kate Moss recently used a controlled substance of class A or class B. Unfortunately, the law requires either a proof that she had been using a class A drug, or a proof that she had been using a class B drug. A proof that she had been using one or the other will not do. And hence Kate Moss cannot be prosecuted. In this regard, the law is Intuitionistic. If you're going to have a legal system that doesn't recognise LEM then you really need to carve up crime-space as a semilattice so you can charge people with the join of two crimes :-)
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