Every serious thinker should read Sylvain Bromberger’s On What We Know We Don’t Know cover to cover. It’s a short book – nine essays, some written decades apart – but it does something almost no other book on scientific method does: it treats the question itself, not the answer, as the thing worth studying.
Most writing about how science works starts with answers. What makes a good theory? What counts as evidence? What makes an explanation convincing? Bromberger starts one step earlier. He asks a simpler question: what does it actually mean to be stuck on a question? And his answer is that “being stuck” isn’t one thing. There are at least two very different ways to be stuck, and mixing them up leads to a lot of confused thinking about progress — in science, and really in any field.
Two ways to be stuck
The first he calls a p-predicament. Here, you understand the question perfectly, you’re confident it has a real answer, but every answer you can come up with is one you have to throw out. You’re not short of answers — you’re drowning in wrong ones.
Think of a detective story. You know someone left a locked room. You know it’s possible. But every way out — the door, the window, the chimney — turns out to be blocked or too small. You keep generating answers and rejecting them, one by one. That’s a p-predicament: too many bad answers, no good one yet.
The second, sharper condition is a b-predicament. Here you can’t even imagine the answer. Not “I’ve thought of it and rejected it” — you literally cannot conceive of what the answer would look like. Bromberger’s own example is a kettle: he doesn’t know why it hums right before the water boils, and — before learning any physics — he can’t even picture a candidate explanation. It’s not “I don’t know X.” It’s “I don’t know what kind of thing would even count as knowing X.”
That distinction matters more than it sounds. In the detective story above, the fix eventually turns out to be simple: the murderer was a child, small enough to fit through the chimney nobody thought to check. Once you hear it, you realize you could have imagined it — you just didn’t. That’s escaping a p-predicament. But sometimes the fix isn’t “you missed an option.” Sometimes nobody, however clever, could have pictured the answer without a genuinely new idea. Newton didn’t just find the right answer to “why do tides happen” sitting among the wrong ones – the very idea of gravity as a force acting across empty space had to be invented first. That’s escaping a b-predicament.
Why this is useful, not just clever
This gives you a real diagnostic. When a debate in your field feels endless, ask which kind of stuck you’re in. If people are trading answers and shooting each other down, that’s a p-predicament – it will likely resolve with more evidence and better arguments. But if the same question keeps circling back unresolved, decade after decade, that’s often a sign of a b-predicament: the field lacks a concept it needs, and no amount of arguing inside the current frame will produce it. What’s needed instead is something closer to invention than deduction.
Read the book slowly – it’s dense, though each essay stands on its own. But it leaves you with a genuinely practical habit of mind: before assuming a hard problem just needs more work, ask whether it needs a different way of thinking altogether.
It’s freely available online — worth the time.
