How many distinct paradigms of programming are there?

I learned a few styles of programming in school. At least, I heard of them somewhere in passing.

• Procedural
• Object-oriented
• Functional
• Logical

Then, I come across a thread on Hacker News asking Ask HN: Do you recognize this approach to programming?. The answer seems to be something called functional reactive programming. So, I started wondering, "How many distinct styles or paradigms of programming are there?"

That led me to Peter Van Roy's The principal programming paradigms and Programming Paradigms for Dummies. PVR is a co-author of Concepts, Techniques, and Models of Computer Programming, which I've heard described as, "If you liked SICP, you'll like this."