Here is a more personal reflection on what I love in working in philosophical logic.
I love the “aha!” moment of recognition. This is the relief of a proof completed, or a counterexample found. It is the delight of gaining clarity into something that you had only dimly understood, or the dawning realisation that an assumption you had made is in fact false and a whole new vista of possibilities opens up to you.
The particular kind of “aha” that I mean is the kind where you’re working out of the consequences of something you already know. This can be understood as a kind of mastery that is gained when you become familiar with the conceptual tools you’re using. It is the acquisition of greater skill.
This is the “aha” that students in my second year logic class experienced when they figured out for themselves that not all symmetric and transitive relations must be reflexive. In one sense, they already knew the definitions of these concepts (at least, most of them did) and this fact was implicit in what they already knew, but now they had figured this out for themselves — they saw it for themselves. They understood something new about how these concepts fit together, how they relate.
There is a lot of scope for this when working in philosophical logic. We’re pushing concepts to their limits, finding the boundaries of conceptual space. We map out its topography. Sometimes you think that things hang together in some way (say, your examples of symmetric and transitive relations all happened to be reflexive, too) and then you suddenly see that they’re not. That moment of recognition is the dawning of new light, the opening up of new territory, the acquisition of new conceptual capacities, and moments like these are to something to be treasured.
The Moment of Recognition is the fifth of twelve things that I love about philosophical logic.