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.
Is your answer $8? 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 were able to correct our mistake because we had all the information needed to find the truth in the question itself and we checked it. This is usually not the case in real life. We form opinions, choose careers, put our faith in certain people with incomplete information. With this article, we will discuss how to decide what to believe when we have incomplete information and how sure we should be.
Truth
Truth is simply how things really are.
Given the conditions in our question, the candle costs $4. How certain you feel about a different answer cannot change that.
Now suppose I measure a strip of paper and my 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 temperatures, or simply wear and tear.2
Regardless of what the ruler says, what you think, or whether that strip ever gets measured - it has a certain length and that length is the truth.
Belief
A belief is what you accept to be true.
When you look at the ruler and think, “The paper strip is 10cm long”, that is a belief. Whether it is true depends on the strip’s actual length.
Now imagine someone reads that example 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, more concrete this time. You are more justified in believing that that’s an ambulance.
You can have different levels of confidence (e.g. 40% or 80%) in a belief. You can say, “I have good reasons to think this, but I could be wrong” and thus remain open to changing your mind when you learn more. For example, the $8 answer may have felt convincing before we checked it. Feeling sure and having good reasons to be sure are different things. New information can increase or decrease your confidence. How much it should change depends on how strongly that information supports or challenges your belief.
Coming back to the paper strip measuring example, we now know that there are 4 aspects to it:
- Truth: How long it is.
- Belief: How long you think it is.
- Justification: Reason to think that.
- Confidence: How sure you are.
But, when can you say that you “know” the length?
Knowledge
Let’s start with a simple definition: knowledge is a justified, true belief. That would mean:
- It is justified: You have good reasons for believing it. For example, “I saw it on the internet” isn’t a good reason by itself.
- It is true: If you think you “know” something and later it turns out to be false, you never knew it; you believed that you did. For a belief to count as knowledge, it needs to be true.
- It is believed: You actually believe it is true.
This definition is a good starting point but is it 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 it has been right every morning so far. You don’t have a good reason to believe it’s wrong. If it was showing 3 PM, that would make you look again.
- 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.