There are probably many HN readers who would find this a congenial approach, since there are so many programmers here, and logic is so close to math and programming.

I also can't deny that studying it does make one's thinking more rigorous, and it's useful for working with other philosophy (and with math and programming).

However, I am concerned that someone who starts off with logic might get the impression that that's what all philosophy is about, or that's what it builds on, and just stop there. While that's true for some types of philosophy, it's not true for the majority of philosophy.

Also, for those people who aren't in to math, logic, puzzles, or programming, I'm not sure this approach would be particularly engaging for them.

When starting from the Socratic dialogues, I think pretty much everyone gets engaged, since they deal with questions which are of universal concern. They are also questions and themes that run throughout the whole course of Western philosophy (and many in Eastern philosophy too, though from a different direction).

People who start with Socrates instead of logic might not have the tools to analyze his arguments rigorously (though if that's even possible is debatable), but they'd get a much better feel for what philosophy was about.