Many have voted for a deep problem being one that touches on something fundamental. (
,
,
indirectly -- if metaphysics is fundamental,
indirectly, maybe -- if that explains why the impact of an answer would be so great).
@Banno and
@Hermeticus both note that questions we never quite answer are the deep ones.
@T Clark and
@TheMadFool make related points, that there can be problems or tasks where we feel we are out of our depth, or in over our heads, either unable to answer or at least finding that our usual ways of solving a problem don't work.
@Joshs is the only one to suggest that depth may not be a very helpful way of classifying problems, and suggests "intimacy" instead.
I am genuinely surprised no Wittgensteinians showed up to say that there are no deep problems.
@Joshs answer I don't quite have a handle on, but I have a bad interpretation of it that might be useful: if we set out to
define what we mean by "fundamental" we might naturally arrive at something like a dependency tree.
*(The way computer science handles trees, the root is depth 0, and the nodes are of varying depths, with leaves representing maximal depth of a subtree. Ordinary usage reverses that, just as it puts the root at the bottom, not the top.)
But what are the nodes in this tree? Concepts? Issues? Beliefs? Problems?
It can't be problems (or questions) because that would suggest a dependency like "to answer b, you need first to answer a"; if answering simple questions is dependent on answering deep, hard questions, the simpler questions are at least slightly more unanswerable than the deeper ones. Maybe that's wrong though. Maybe it's only that if you had an answer for
a then
b would take care of itself. Unclear.
Concepts might be a better candidate, but then we're not saying a question is deep if answering it requires the most fundamental concepts, because everything does, everything is dependent on them; instead we might say depth is not dealing with a lot of dependent concepts, but passing right by those nodes on the tree and heading for questions the answer to which only uses nodes close to the root.
Which brings me to my bad interpretation of
@Joshs. The tree image suggests there are a lot of steps between where we start, out here at the leaves, perhaps, and the answers we seek, near the root;
@Joshs's idea of intimacy actually does look like a claim that we can instead do valuable work right here within a step or two of where we are. He could even say, maybe there is hierarchical tree structure here, but we needn't peg value to depth, to distance from where we are.
I also want to come back to this:
I think what we mean with deep philosophical problems are questions, with no definite answer, which would have an enormous impact on how we perceive and think about the world. — Hermeticus
Sometimes mathematicians will speak of "deep" results, theorems that show connections that are surprising and illuminating. I remember being entranced as a youngster when I first saw
. How could
and
be related like that? It was mind-boggling. The proof of Fermat's last theorem pulled together several branches of mathematics that as an undergrad you might not expect to be related. That's a deep result. It might change the way you think about mathematics.
I also want to make one more nod to the experience of depth. We all know the joke about looking where the light is best. As you move farther from the available light, you might begin to experience depth, the depth of shadow and obscurity. As you go deeper into a cave, the light coming in from the cave's mouth is less and less helpful in finding your way around. It's always Wittgenstein: the general form of a philosophical problem is, "I don't know my way around here." What's more, my usual way of
finding my way around here -- sight -- isn't working; I not only need to find my way, I need first to find a way to find my way. Is that depth? (And to pull these two paragraphs together: deep in the cave, you might discover that this cave actually connects to another cave you know, the mouth of which is miles away.)
(Bring a torch! My limited experience with real math matches that. To prove a theorem in topology, say, you build some really specialized sort of set or space or transformation -- your torch -- and then you send it down into the cave and it lights up your surroundings for you, shows you exactly how things stand. That suggests that philosophical problems might be solvable with a sort of Deleuzean, or at least pragmatic, concept craftsmanship.)