How do you know?

A candle and a table cost $38 in total. The table costs $30 more than the candle. How much does the candle cost? Seriously, stop reading until you have an answer in mind.

Did you think $8? Well, if the candle costs $8, the table must cost $38 to be $30 more expensive. That makes the total $46, not $38.

The answer is actually $4. The table costs $34 and thus together they cost $38, making the difference $30.

If you got it wrong, you are not alone. In a 2013 study, a similar question was asked to 1,750 US adults and only 13% of them got it right.¹

We can check the answer because the question gives us everything we need. This is usually not the case in real life. We form opinions, choose careers, put our faith in certain people with incomplete information. We have to decide what to believe and how sure to be, with uncertainity.

Truth

Truth is how things really are.

Given the conditions in our question, the candle costs $4. Your answer and how sure you are about it cannot change that.

Now suppose you measure a strip of paper and your ruler reads 10cm. Does that make “This paper strip is 10cm long” a true statement?

What if the ruler’s markings are incorrect? This can happen due to a factory defect, expansion/contraction due to temperature, or simply wear and tear.²

Regardless of what the ruler says, what you think, or whether the strip even gets measured or not - it has a certain length and that length is the truth. Our statement would only be true if the strip is actually 10cm.

Belief

In everyday life, when someone says “I believe X” instead of “I know X”, we assume that they are saying “believe” because they aren’t sure about it or it’s just an opinion. In formal language, a belief is what we accept to be true.

For example, if you believe that 2 + 2 = 4 is true, that’s a belief. If you believe that ghosts exist or your cat loves you, those are beliefs too. A belief is something you accept as true, it doesn’t matter whether it actually is.

Now imagine someone reads that paper strip example where the ruler itself is faulty and decides to never believe anything unless they are really really sure.

They hear an ambulance siren outside. Does that mean that there’s an ambulance? Well, the sound could be coming from someone’s speakers. To be really sure, they look out of the window and see an ambulance. But what if it is a vehicle modified to look like an ambulance by drug traffickers to avoid suspicion? That person can keep inventing such possibilities. How would they get even the simplest things done?

When you hear the siren, you have a reason to believe there’s an ambulance. When you see it through the window, you have one more reason, a more reliable one this time and thus you are now more justified in believing that it’s an ambulance.

Wait, what makes a reason “good” for having a belief anyway? Here are three questions you can ask yourself:

Did I see/hear/touch it? If you see an apple or think a cup is hot by touching, you have good reason for believing it.
Can I check it?: I haven’t measured Mount Everest myself but I believe it’s 8,848 meters. Why? Because multiple people have checked it throughout the history and I can too, using trignometry.
Is it the best explanation? You come home to see a vase knocked down. Nobody lives with you except your cat and there’s no sign of someone breaking in. The simplest explanation is that your cat knocked it over even though you didn’t see it happen. The explanation is a good reason to believe so.

This is a good starting point for keeping your beliefs in check but see what happens when we use them wrong:

I just saw a shadowy figure from the corner of my eye at 2 AM, must be a ghost! Seeing something unclear in poor lightning for a split second when you are sleep or sleepy deprived and you conclude that it’s a ghost?
I just found this study that says eating candies makes you happier, must be true! Could be true but did you check who funded the study or how it was done? Bogus studies are very common. It was probably funded by Candy Store Inc.
That person didn’t text back in an hour so they must be losing interest in me! Is that really the best explanation? Come on.

These conclusions probably felt reasonable to the person who came to them. That’s the thing, you can’t really “feel” how strong a reason is, you have to really think about it, ask questions. Such wrong conclusions are also often caused by finding reasons for a belief instead of forming a belief based on reasons.

Anyways, for now, lets come back to the paper strip measuring example and list the 4 aspects we have identified:

Truth: How long it is.
Belief: How long you think it is.
Reasons: Reasons to think that.
Justification: What makes those reasons good.

But, when can you say that you “know” the length?

Knowledge

Knowledge is a belief that’s both justified and true.

If you asked someone in 200 BCE if something is crawling in your eyelashes, they would look at them carefully and say no. If you ask, “Do you really know that?” and they would say, “Of course, I’m looking at them there’s nothing crawling there.”

We have microscopes now and thus can see the mites that live in the eyelashes of almost everyone. demodex mite under microscope

For roughly two centuries, scientists believed that Newton’s laws of motion and gravity can explain all physical reality. Then electromagnetism, quantum physics, relativity and speed of light made us realized things are not so simple, just like the microscope in our example. We now know that newton’s laws applied to many things but not everything.

We can be, have been, and will be wrong about things both in our everyday life and while doing science, that’s part of making progress towards that truth. Just keep in mind that our beliefs, even the ones so reliable that we call them knowledge, can be wrong.

You might be thinking, “If knowledge needs to be true and we usually can’t say for sure if something’s true, what does even qualify as knowledge?”

This is what “Epistemology” is all about, an entire field of study dedicated to nature and limits of knowledge.

Let me show you why “knowledge” is such a complex subject. We will start with our simple definition: knowledge is a belief that’s justified and true. In simple words:

It is justified: You have good reasons for believing it.
It is true: For a belief to count as knowledge, it needs to be true. Even in everyday language when something we “knew” turns out be wrong, we say “I thought/believed it was X” not “I knew it was X.”
It is believed: You actually believe it is true.

Sounds solid and even too cautious but is it really enough?

Let’s say, it’s a Sunday morning. You just woke up. You look at the clock on your wall and it says 7:00.

There’s a twist. The clock’s battery died at 7:00 last evening and its hands thus stopped at that time. You just happened to look at it at 7:00 this morning. So, do you know that the time is 7:00?

If we go by our proposed definition:

It is justified: The clock tells time and you know it’s morning by the sunlight coming through your window. That’s a good reason to believe it’s 7:00. If it showed 4, that would make you doubt.
It is true: Even if it is a coincidence, it really is 7:00 right now.
You believe it: You believe that it is 7:00.

Now, do you really know the time or did your belief just happen to be true? If you had looked at it at 7:30, the clock would still say 7:00. You just got lucky.³

As you can see, knowing things is hard but all such questioning and verification is how your medicines work and robots land on the moon. Scientists do an experiment many times to avoid getting lucky, like the clock example. Doing an experiment multiple times can produce wrong results when the equipment itself is faulty, so they calibrate and maintain it unlike the ruler in our example. They try to think of everything that can make a conclusion appear true while it isn’t and then take precautions to avoid that. Once they believe their conclusion is justified, they get other scientists to look at it.

Once the results and details of the experiment are published, anyone can check it and do it again to make sure they didn’t get anything wrong. Even after all this, we remain open to information that strengthens the conclusion or goes against it.

Okay, how does it help me?

Remember the four aspects of the paper strip example? Truth, belief, reasons, and justification.

There’s a fifth one I skipped because I wanted you to see how hard it is to know things “for sure”. The fifth aspect is confidence: how sure you are that the strip is 10cm long?

Earlier, I said that a belief is something you accept to be true. But you don’t just “believe” or “not believe” something. Maybe your belief in something is at like 80% because you have your doubts.

This is important because in many real life scenarios, we don’t even have the whole picture to decide what to believe. And even if we did have it, the “knowledge” section showed how we can still be wrong.

We also know from our experience and the examples that we love to jump to conclusions, especially when the conclusion favours what we already believe in.

So, what to do about it?
Instead of waiting until we know “for sure” or jumping to conclusion, we can hold each belief at the confidence its reasons deserve. And when reasons that support or challenge the belief come up, adjust that confidence accordingly.

Or if you want a simpler takeway: we can be wrong even when we are really really sure so we should always keep an open mind. Especially about the beliefs that you are really really sure about because your brain is protecting them really hard.

And don’t forget, you probably thought the candle was $8 and were pretty sure about it. There are many candles like that and we will find them all as we go ;)

Topics for further reading

Justified True Belief (Our definition of knowledge)
The Gettier problem (The clock example, and more like it)
Fallibilism (Philosophy principle that says human knowledge is never free from possibility of error.)
Skepticism (A stance that questions our ability to know.)