People come to philosophical questions expecting puzzles: hard on the surface, solvable underneath, with an answer at the back of the book. That is not what these are. A genuine philosophical question is a place where two things you already believe turn out to be incompatible, and the work is deciding which one to give up. That is why they stay open. Nobody has found the trick, because there is no trick.
Twelve below, grouped by what they are actually testing. Each is a paragraph, because the point is to see the shape of the problem, not to settle it.
Questions about right and wrong
The trolley problem
A runaway trolley will kill five people. You can divert it to a track where it kills one. Do you pull the lever? Almost everyone says yes. Change it so that the only way to stop the trolley is to push a large stranger off a bridge, and almost everyone says no, even though the arithmetic is identical. The question is not which answer is right. It is why the arithmetic stops governing us the moment we have to touch someone. Our full explainer covers the variants and what the neuroscience found.
Is-ought: can you get a "should" from an "is"?
Hume noticed that moral arguments quietly change gear: three paragraphs about how the world is, and then, without warning, a sentence about what we ought to do. No purely factual premise seems to entail a moral conclusion. If he is right, every appeal to nature, science or tradition as a source of values has a missing step in it. If he is wrong, nobody has yet shown where.
The paradox of tolerance
Popper's version: unlimited tolerance leads to the disappearance of tolerance, because the intolerant will use the space it gives them to close it. So a tolerant society must be intolerant of something, which means the principle cannot be applied to itself without breaking. Every free society is somewhere on this gradient and pretending otherwise is the only position that is definitely wrong.
Questions about who you are
The ship of Theseus
Replace a ship's planks one at a time until none of the originals remain. Same ship? Now gather the discarded planks and rebuild them into a second ship. Which one is Theseus's? The question looks like word-play until you notice your body replaces most of its material over a lifetime, and that you are the ship.
The teleporter problem
A teleporter scans you, destroys the original, and assembles an exact copy on Mars. The copy has your memories and believes it walked in. Did you travel, or did you die and get replaced by someone who thinks they are you? Now notice that nothing in the machine's operation is different in kind from what sleep does to continuity, and the discomfort spreads backwards into ordinary life. This is Parfit's territory, and he concluded that identity matters less than we think.
The problem of other minds
You have direct access to exactly one consciousness. Everyone else is an inference from behaviour. The inference is overwhelming and it is still an inference, and there is no experiment that would settle it. Mostly this is a philosopher's amusement, until the question becomes practical, which it now has: we are building things that behave as if there is someone home.
Questions about knowledge
The brain in a vat
If your experiences were produced by a machine rather than a world, everything would seem exactly as it does. Descartes got there with a demon in 1641; the film version arrived in 1999. The interesting move is not the paranoia but the response: Descartes went looking for one thing that survives total doubt, and the something he found was the doubting itself.
Mary's room
Mary knows every physical fact about colour vision and has lived her whole life in a black-and-white room. She is released and sees a red tomato. Does she learn something new? If yes, then physical facts do not exhaust the facts, and there is something about experience that no complete science captures. If no, you have to explain away a very stubborn intuition.
Why is there something rather than nothing?
Leibniz's question, and the one most likely to be dismissed as unanswerable by people who have not sat with it. Every explanation of why something exists must itself be a something, so the question reappears one level up, forever. It is the clearest example of a question whose value is that it will not resolve.
Questions about how to live
The experience machine
Nozick's machine gives you any experience you choose, indistinguishable from real, for the rest of your life. Plug in? Most people refuse, which is evidence that we want more than pleasant experiences: we want the experiences to be of something, and we want to be the ones doing it. That refusal is a serious problem for any theory that says wellbeing is just feeling good.
Do we have free will?
Either your choices follow from prior causes, in which case they were going to happen anyway, or some of them do not, in which case they are random, and random is not freedom either. The compatibilist reply is that this is the wrong fork, and freedom means acting from your own reasons without external coercion, which is compatible with those reasons having causes. Whether that is a solution or a change of subject is itself the live argument.
What is a good life?
The oldest one, and the only one on this list where the schools give genuinely different practical answers rather than different analyses. Aristotle says a life of activity in accordance with virtue. The Stoics say a life spent on what is up to you. The Taoists say stop pushing the river. Epicurus, misquoted for two millennia, says friendship and a garden. This is where philosophy stops being a seminar.
Where to take these next
If you want the map rather than the highlights, the branches of philosophy lays out which department each question belongs to, and what philosophy is covers the discipline itself. For the people who asked them, the philosophers worth reading routes to each one. To read rather than browse, the beginner shelf is the honest starting point, and 365 Days of Philosophy (ours, flagged) takes 130-odd thinkers one page a day for a year.
Common questions
What are the big questions in philosophy?
Free will, personal identity, whether we can know anything for certain, whether moral facts exist, what consciousness is, and what a good life consists of. The famous thought experiments — the trolley problem, the ship of Theseus, Mary's room, the experience machine — are compact ways of getting at those six.
Why don't philosophical questions have answers?
Because they are not puzzles with hidden solutions. A real philosophical question is a place where two things you already believe contradict each other, so the work is deciding which belief to abandon. Different people abandon different ones, which is why the question stays open.
What is the hardest philosophical question?
Consciousness has the best claim, in the form Chalmers called the hard problem: why is there something it is like to be you, rather than all this processing happening in the dark? Every other question on the list has at least one respectable answer. That one has no agreed shape.
What is a good philosophical question to ask someone?
The experience machine, because it takes ten seconds to state and almost everyone answers instantly and then cannot justify the answer. Ask whether they would plug in for life, then ask why not.
Where should I start reading philosophy?
Not with the big systems. Start with a short original that argues rather than surveys — Plato's Apology, Marcus Aurelius, or Camus's The Myth of Sisyphus. Our beginner guide matches the starting point to how you actually read.
Is philosophy just opinions?
No. Opinions do not have to survive objections, and philosophical positions do. The subject is largely the record of positions that failed, which is why the arguments get sharper over time even though the questions do not close.