What Can You Know Without Looking?

Imagine you’re sitting at your desk, and you try to figure out something without getting up, without looking out the window, without asking anyone, and without checking your phone. Just by thinking. Here are some things you might be able to know:

• All bachelors are unmarried.
• 2 + 2 = 4.
• If A is taller than B, and B is taller than C, then A is taller than C.
• It’s wrong to torture children just for fun.

Now compare those to:

• All bachelors in the U.S. pay different taxes than married men.
• Two quarts of water plus two quarts of gasoline makes four quarts of liquid.
• Kevin Durant is taller than LeBron James.
• Torture often produces unreliable testimony.

The first group feels different. You don’t need to do research or check any facts. You just understand them, and you know they’re true. The second group requires you to actually look something up, measure something, or trust someone who did.

Philosophers have a name for this difference. Knowledge that comes just from thinking, from understanding the ideas involved, is called a priori (a Latin phrase that means “from what comes before” — before experience). Knowledge that comes from the senses — from looking, listening, touching, measuring — is called a posteriori (meaning “from what comes after” — after experience). The question this article explores is: what exactly is a priori knowledge, where does it come from, and can we really trust it?

What Kinds of Things Can We Know a Priori?

The simplest examples are things like “all squares are rectangles” or “green is a color.” You don’t need to go check a bunch of squares to know they’re all rectangles — you understand what “square” and “rectangle” mean, and you can see that one is just a special version of the other. Same with “all vixens are female”: a vixen is defined as a female fox, so if you know that definition, you already know that all vixens are female.

But some philosophers have pointed to trickier examples. Take the statement “water is H₂O.” Many scientists think this is necessarily true — water couldn’t be anything else and still be water. But you can’t figure out water’s chemical structure just by thinking about the concept of water. You had to discover that through experiments. So some necessary truths can only be known a posteriori.

And here’s where it gets even stranger. Some philosophers think there are contingent truths — things that could have been otherwise — that we can know a priori. Suppose someone decides that the standard meter stick in Paris will define what “one meter” means. Then you can know, just by understanding that definition, that the stick is one meter long — even though it’s a contingent fact (the stick could have been a different length, and then “one meter” would have referred to that different length). Similarly, “I am here now” is something you always know when you say it, even though you could have been somewhere else. You know it a priori.

Wait — Can We Ever Be Wrong?

This is where things get interesting. If a priori knowledge comes just from thinking, shouldn’t it be perfectly reliable? If you carefully think through a math proof, how could you end up believing something false?

But philosophers have noticed that a priori justification can be wrong. Maybe someone in the past was a priori justified in believing that every event has a cause — it just seemed obvious from thinking about what an “event” is. But modern physics suggests that some subatomic events are genuinely random. So that belief, though justified a priori, turned out false.

Here’s another example philosophers use. Imagine a heap of beans. If you take one bean away, you still have a heap. Take another, still a heap. If you keep going, you eventually reach one bean — which isn’t a heap. But each step seems obviously true! You’re justified in believing each step a priori, but they can’t all be true together. This is called the sorites paradox.

A priori justification can also be defeated. Suppose you work through a math proof and feel certain of your result. Then a trusted expert tells you that you made a mistake. That new evidence — empirical evidence, from testimony — can defeat your a priori justification. So a priori knowledge isn’t some magical, untouchable thing. It can be wrong, and it can be overridden by experience.

Where Does A Priori Justification Come From?

Now we get to the harder question. When you know a priori that all bachelors are unmarried, what actually gives you that justification? What’s going on in your mind?

View 1: There’s Nothing Special Here

Some philosophers, like Timothy Williamson, argue that the difference between a priori and a posteriori isn’t really that important. Think about how you might figure out whether nine inches is more or less than nineteen centimeters. You could learn that one inch equals 2.54 centimeters, do the math, and see that nine inches is about 23 centimeters. That seems a priori. But you could also form a mental image of two marks nine inches apart and two marks nineteen centimeters apart, and compare them in your imagination. That uses mental skills you developed from experience — you’ve seen inches and centimeters before.

Williamson says that both a priori and a posteriori knowledge rely on skills we develop through experience. The difference is like the difference between looking through a microscope versus looking through a telescope. There’s a difference, but it’s not a basic, fundamental difference.

View 2: Rational Intuition

Other philosophers think there’s something special going on. They think we have a mental capacity they call “rational intuition” or “intellectual seeing.” This isn’t the same as a gut feeling or a hunch. It’s more like when you just see that if A is taller than B and B is taller than C, then A is taller than C. You don’t work through steps; you just grasp it.

George Bealer describes a rational intuition as an “intellectual seeming” — it seems to you that a proposition is necessarily true, just from understanding it. Laurence BonJour calls it a “rational insight” — an immediate, non-inferential grasp that something must be so.

This is supposed to be different from physical intuition (like the intuition that a house undermined will fall). Physical intuition depends on your experience with physical objects. Rational intuition depends only on understanding the concepts involved.

Some philosophers think that this kind of intuition has a special “feel” to it — a distinctive phenomenology, like a special glow in your mind. Others disagree and think the intuition is just the judgment itself, without any special feeling.

View 3: You Don’t Need Evidence at All

A third view says that some beliefs are just “default reasonable” — you’re entitled to hold them without any evidence at all. This isn’t just about a priori knowledge; it applies to everything. On this view, all your beliefs are justified until you find a reason to doubt them.

But this seems too generous. If you start believing random things about life on other planets with no evidence — just because you feel like it — are you really justified? Most philosophers think not. Something has to give you that justification.

Another version of this view says we’re “entitled” to accept certain presuppositions — like the laws of logic, or that we’re not brains in vats being fed false experiences — because we couldn’t do science or reason at all without them. But critics ask: does being useful make something rational to believe? Wanting something to be true doesn’t make it true.

Should We Trust Rational Intuitions?

Even if rational intuitions exist, should we trust them? How could we check if they’re accurate? With vision, we can check against touch, or against other people. But if intuition is checked only against other intuitions, that’s like checking a crystal ball against itself.

Some defenders respond: perception can’t be fully checked either, except against other perceptions, and we still trust it. And we can sometimes correct mistaken intuitions by reflecting further, or by noticing that they conflict with other things we know.

Experimental philosophers have studied people’s responses to philosophical thought experiments — like the famous “trolley problem” where you have to decide whether to push someone off a bridge to save more people. They found that people’s answers vary based on culture, economic background, and even the order questions are asked. But defenders of intuition say these studies usually test quick, shallow reactions, not the careful, reflective intuitions that come from fully understanding a concept.

Can A Priori Knowledge Tell Us About the Real World?

Here’s a deeper worry. Even if a priori reasoning can tell you about relationships between concepts (like “all bachelors are unmarried”), can it tell you anything about the actual world? Maybe it just tells you about your own concepts, not about reality.

One philosopher, Carrie Jenkins, argues yes — but only because our concepts are grounded in experience. The concept “table” accurately represents tables in the world because we developed the concept through interacting with tables. If our concepts accurately represent reality, then exploring them a priori can tell us about reality. But this means a priori knowledge depends on empirical knowledge after all — which some philosophers find unsatisfying.

Others say this gets things backwards. We can know a priori that 2 + 2 = 4 even if we’re brains in v