Roy's Fortnightly Puzzle: Introduction

Okay, I am starting a new feature on M-Phi, and will attempt to keep it going as long as I have ideas.

I will post a simple puzzle involving logic or the philosophy of mathematics that is either a little to 'cute' to actually publish, or which is something I thought about but didn't make any substantial progress on.

A new puzzle will be posted every two weeks (roughly), as the title suggests.

The hope, of course, is that these simple puzzles will motivate us to think about issues in a new way. Of course, if that doesn't happen, and they are merely fun, then that works too.