Infinity on the Table
Why some thinkers insist we’re bounded—and why I’m betting we’re not
Some thinkers believe we’ll always have blind spots—realms of understanding sealed off by the architecture of our brains. Noam Chomsky calls these mysteries rather than problems. They're not unsolved puzzles waiting for insight; they’re un-solvable, full stop. Like asking a cat to do calculus. Some truths, Chomsky suggests, may simply lie beyond the reach of human cognition.
And then there’s David Deutsch, who calmly drops the epistemological equivalent of a mic: all problems are solvable—at least in principle. Knowledge, he argues, has no upper bound. We may never finish learning, but there’s no reason we must ever stop.
These are not small disagreements. They go to the root of what kind of creatures we are—and what kind of future is available to us.
Where do you stand—mystery or problem?
Let me know in the comments.
The Claim
Let’s state it cleanly:
There are no known limits to the growth of knowledge.
That’s not a claim that we know everything. It’s not even a prediction that we’ll figure everything out. It’s a wager: that there’s no physical law, no structural inevitability, that prevents us from explaining anything that can be explained.
In other words: if something can be understood, it can be understood by us—or at least by minds not fundamentally different from ours.
This belief is not a certainty. It’s a posture. An attitude toward problems. A way of saying: keep going.
II. The Case for Limits (The Chomsky Position)
In What Kind of Creatures Are We?, Noam Chomsky offers a thoughtful, even humbling caution: human intelligence is not general intelligence. It’s an evolved tool, forged for survival on the African Savannah. Why should we assume it can grasp quantum gravity, or the origin of consciousness?
He draws a biological analogy: rats can’t be trained to understand the concept of “prime number.” Not because they’re lazy or irrational—but because their mental hardware lacks the necessary abstractions. Why wouldn’t the same apply to us?
Chomsky doesn’t argue that everything is beyond us—just that some things might be. He calls them mysteries: cognitive dead ends, where our tools simply fail.
His position is cautious, even elegant. It defends scientific realism1 while preserving intellectual humility. It’s a way of saying: maybe we should stop pretending we’re gods.
III. The Case for Unbounded Growth (Deutsch Position)
Deutsch, however, comes at this from the other direction.
In The Beginning of Infinity, he argues that all problems are solvable, unless explicitly forbidden by the laws of physics. That’s a powerful constraint. And the laws of physics, as we know them, contain no provision against understanding.
His core move is philosophical: he treats knowledge not as a pile of facts, but as a process of generating better explanations. And explanations are subject to refinement, recursion, and growth. We don’t need omniscience—we need progress.
To Deutsch, what matters isn’t how limited our minds currently are, but whether those limitations are fixed. If we can build instruments, institutions, or even new minds that extend our reach, the boundary keeps moving.
More provocatively: Deutsch treats human beings not just as problem-solvers, but as universal explainers. We’re not the endpoint of cognition. We’re the beginning of something that doesn’t have one.
IV. But Isn’t That a Contradiction?
This is where things get juicy. Deutsch also claims that we’ll never run out of problems. There will always be new questions to ask.
So… doesn’t that mean there will always be things we don’t know? Isn’t that a kind of limit?
Not quite. Here’s the distinction:
A limit to knowledge means something is in principle unknowable—a wall we can’t breach.
Endless problems, by contrast, mean there’s no final wall—just an infinite hallway.
We’ll always have more to learn not because we’re permanently stunted, but because new problems emerge as consequences of our progress. Solve one puzzle, and it reveals three more.
It’s a feature, not a bug.
To Deutsch, the presence of ignorance isn’t proof of limitation—it’s proof of movement. We don’t need to fear the unknown. The unknown is the raw material of all insight.
V. Why I Side with Deutsch (For Now)
Chomsky makes a compelling case for caution. And he’s not wrong to remind us of our biological constraints. But his view risks a kind of elegant fatalism—there are some things we just weren’t meant to know.
That posture can harden into epistemic surrender.2
Deutsch, by contrast, offers an orientation. Not just optimism, but agency. His claim isn’t that we’re guaranteed to understand everything—but that we should proceed as if no road is closed until we hit a locked gate. And so far, every locked gate has turned out to be a puzzle.
I find that more generative. More useful. More aligned with how progress actually happens: a series of impossibilities that suddenly become obvious.
VI. So What?
This isn’t just metaphysical banter.
If knowledge is fundamentally bounded, we must ration our curiosity. If it’s unbounded, then our responsibility is to build the scaffolds—education, ethics, systems—that let more people reach more understanding.
The idea that there are no known limits to the growth of knowledge doesn’t mean we’re limitless. It means we don’t yet know what the limits are—and until we do, we should act as if we can go further.
That’s not arrogance. That’s hope, weaponized.
If Deutsch is wrong, we’ll never know it. That’s the irony. The limits, if they exist, will never raise their hand and say “Here I am.” They’ll just keep us in the dark—and we’ll mistake it for nightfall.
But if he’s right, then this moment—whatever confusion, chaos, or ignorance surrounds it—isn’t the end of something. It’s just another beginning.
An invitation to keep asking. To keep thinking.
To treat each mystery not as a wall, but as a door we haven’t opened yet.
Scientific realism is the view that well-supported scientific theories aim to describe the world as it actually is—including unobservable entities like electrons or black holes. Realists argue that the success of science would be a miracle if our best theories weren’t at least approximately true. Critics, like instrumentalists or constructive empiricists, contend that theories are useful tools, not necessarily mirrors of reality.
Epistemic surrender refers to the conscious act of relinquishing certainty—accepting that some questions may remain unresolved, and that understanding often requires openness rather than control. It is not the rejection of reason, but the humility to let reality revise your beliefs. The phrase appears in spiritual, philosophical, and psychological contexts, often linked to trust, transformation, or the limits of analytical grasp.