Skip to main content

Skolem's paradox

By
I was cruising the net looking for information about skolemization when I stumbled on a paradox that I'd never seen before. Skolem's paradox is one of the most astounding paradoxes that I've ever seen. Here are a few links I dug up on the subject: The Löwenheim-Skolem Theorem MOORE ON SKOLEM'S PARADOX Reflections on Skolem's Paradox I'm don't totally understand all the implications of the paradox, but I do understand some of them and I find it both fascinating, and in some ways disheartening.

Comments

Post a Comment

Popular posts from this blog

Decidable Equality in Agda

By
So I've been playing with typing various things in System-F which previously I had left with auxiliary well-formedness conditions. This includes substitutions and contexts, both of which are interesting to have well typed versions of. Since I've been learning Agda, it seemed sensible to carry out this work in that language, as there is nothing like a problem to help you learn a language. In the course of proving properties, I ran into the age old problem of showing that equivalence is decidable between two objects. In this particular case, I need to be able to show the decidability of equality over types in System F in order to have formation rules for variable contexts. We'd like a context Γ to have (x:A) only if (x:B) does not occur in Γ when (A ≠ B). For us to have statements about whether two types are equal or not, we're going to need to be able to decide if that's true using a terminating procedure. And so we arrive at our story. In Coq, equality is ...
2 comments
Read more

Total Functional Programming

By
Recently on Lambda the Ultimate there was a post called "Total Functional Programming".  The title didn't catch my eye particularly, but I tend to read the abstract of any paper that is posted there that doesn't sound terribly boring.  I've found that this is a fairly good strategy since I tend to get very few false positives this way and I'm too busy for false negatives. The paper touches directly and indirectly on subjects I've posted about here before.  The idea is basically to eschew the current dogma that programming languages should be Turing-complete, and run with the alternative to the end of supplying "Total Functional Programming" .  At first glance this might seem to be a paper aimed at "hair-shirt" wearing functional programming weenies.  My reading was somewhat different. Most hobbiest mathematicians have some passing familiarity with "Turing's Halting Problem" and the related "Goedel's Inco...
Post a Comment
Read more

Teagrey

By
I was ironing my shirt today, which I almost never do. Because of this I don't have an ironing board so I tried to make a make-shift ironing board on my floor using a towel and some books. I grabbed the heaviest books on the nearest shelf, which happened to be Organic Chemistry, Stalingrad and an annotated study bible containing the old and new testament. As I pulled out the bible, a flower fell out which had been there for over 17 years now. I know that because it was put there by my first wife, Daniel, who killed herself in April about 17 years ago. It fell from Thessalonians to which it had been opened partially. Highlighted was the passage: "Ye are all sons of the light and sons of the day." I guess the passage gave her solace. Daniel was a complicated woman. She had serious mental health issues which plagued her for her entire life. None of them were her fault. She was dealt an absolutely awful hand in life, some truly nasty cards. She had some considerable c...
1 comment
Read more