UNIT: Rationality CONCEPTS
GRADE LEVEL: 8
The goal of this lesson is to explore the concept of belief in detail. We will introduce the concepts of epistemology and epistemic belief, i.e., the kind of belief that is justified and connected with probability.
We will also discuss the connection between theories, facts, and truth.
- Develop vocabulary concerning beliefs
- Be able to distinguish between “belief that” and “belief in”.
- Connect belief with probability.
- Learn the word epistemic/epistemology.
- Learn to define rational belief.
The word belief is used in many ways in the English language. When we talk about rational belief, we are usually referring to epistemic beliefs.
The word epistemology means the study of how we know things. Epistemic belief is informed beliefs about the way things are, not beliefs about the way things ought to be. For example, if I say I believe it will rain tomorrow, I also mean that I judge it to be probable that it will rain tomorrow.
Non-epistemic belief is disconnected from expectation. “Belief in” something often denotes moral support, which is not an assessment of probability. For example, you can believe in your school team, even if you do not believe it is probable that they will win the game or win the tournament.
Beliefs about personal preferences can also be epistemic beliefs because they are beliefs about oneself. For example, if I believe I like chocolate, I am also saying that I think it is probable that I will usually enjoy eating a bar of chocolate.
A rational belief is a belief that is justified by reason and evidence.
Epistemic beliefs are about theories, i.e., about models that make predictions that relate to probability.
When we obtain enough justification for a theory that we believe it with high confidence, then we say we know the theory is true. If the justified confidence level is very high, then we say the theory is a fact.
In this lesson, we will be talking about kinds of belief.
Present a list of beliefs as examples, e.g.,
- I believe that the cheetah is the fastest land animal.
- I believe that the average distance between the Earth and the Moon is 238,856 miles.
- I believe that Birmingham is north of London.
- I believe that the DOW Jones Industrial average will go up tomorrow.
- I believe that 27 x 11 = 297
- I believe that all bachelors are unmarried.
- I believe that chocolate is more delicious than red velvet cake.
- I believe in the Chicago Bears football team. (For this example, pick a losing team)
What is different about the last belief on this list?
Anticipated answer: it is not a true belief that the Bears will likely win this year.
Actual answer: it is not a belief-that, but a belief-in. It shows support for something, or a moral conviction about something.
Under line the word “that” in the first 7 items.
Sometimes people omit the word “that” or “in” after the word belief, and it makes different senses of the word “belief” sound the same.
Cross out the last item on the list, and then ask what is different about belief number 7. (“I believe that chocolate is more delicious than red velvet cake.”)
Anticipated answer: it is subjective. It is an opinion.
Actual answer: True, but it is also a true belief about my own preferences.
When we have a “belief that”, we do it because we have justification – or, at least, we ought to.
What are some of the justifications I might have for these beliefs? Let’s go through the list.
Ask the students for possible justifications. (2-4 minutes) Examples:
- We can time how long it takes for a cheetah to cover a known distance. We can ask someone who we believe has performed this experiment.
- We can bounce a laser pulse off of the moon and time how long it takes to return.
- I can use a map, or make the journey myself.
- Maybe I lack justification for this one? Or maybe I can look at the futures market.
- I can do the arithmetic.
- This is true by definition! Definition is a justification.
- I know myself by tasting foods, and by introspection.
The study of how we justify beliefs is called epistemology. For this reason, “a belief that” is called an epistemic belief.
Epistemic beliefs are about theories or definitions:
- “the cheetah is the fastest land animal” is a theory about the fastest land animal.
- “the average distance between the Earth and the Moon is 238,856 miles” is a theory about how far away the moon is.
- “Birmingham is north of London” is a theory about the relative location of the two cities.
- “the DOW Jones Industrial average will go up tomorrow” is a theory about how the markets will behave tomorrow.
- “27 x 11 = 297” is a theory about what will happen when you multiple two numbers.
- “all bachelors are unmarried” is a definition.
- “chocolate is more delicious than red velvet cake” is a theory about my own preferences.
A theory is a model of the world that makes a prediction about the likelihood of experiences.
In our list of beliefs, what are the experiences that each theory predicts to be likely?
- “the cheetah is the fastest land animal” is a theory that predicts a cheetah is more likely to win a race with a lion or a gazelle.
- “the average distance between the Earth and the Moon is 238,856 miles” is a theory that predicts a light beam will take about 2.56 seconds to return to Earth after bouncing off of the moon.
- “Birmingham is north of London” is a theory that predicts that if we march from London, we will have to march mostly northward to reach Birmingham.
- “the DOW Jones Industrial average will go up tomorrow” is a theory that says the share prices of stocks in the DOW 100 are likely to rise on average tomorrow.
- “27 x 11 = 297” is a theory that predicts that multiplying 27 by 11 will likely compute to 297.
- “chocolate is more delicious than red velvet cake” is a theory that predicts I will more likely enjoy a chocolate bar than a red velvet cupcake.
We say we know a theory is true when we have enough justification for it to believe it with high confidence. If we have very good evidence for a theory, we may call it a fact.
Now we can introduce the idea of a rational belief. We say an epistemic belief is rational when its theory is better justified than its competitors. For example, our belief that cheetahs are the fastest land animals is rational when we have better justification for this than, say, the theory that lions are the fastest land animals.
At the end of the lesson, students will be given a list of beliefs, and asked whether the belief is epistemic or non-epistemic.
Which of the following beliefs are epistemic?
- I believe I will sell more cookies if I lower the price.
- I believe in the Loch Ness Monster.
- I believe Abraham Lincoln was the 16th president of the United States.
- I believe in spending time outdoors.
- I believe spending time outdoors is good for one’s health.