What is Probability?

Introduction

Welcome to this lecture series on reasoning with probabilities. I want to start off by acknowledging that studying probability theory isn’t high on most people’s “bucket lists” of things to do before they die, so we should probably spend some time talking about why this stuff is important from a critical thinking standpoint.

Here are **five reasons to study probability**.

- It’s an essential component of so-called “
**inductive logic**”, which is the branch of logic that deals with risky inferences. Inductive logic is arguably more important for critical thinking purposes than deductive logic. - It’s an essential component of
**scientific reasoning,**so if you want to understand scientific reasoning, you need to understand something about probability. - There are many interesting
**fallacies**associated with probabilistic reasoning, and critical thinkers should be aware of at least some of these fallacies. - Human beings suffer from what some have called
**“probability blindness”**. On our own, we’re very bad at reasoning with probabilities and uncertainty. Or to put it another way, we’re very susceptible to probabilistic fallacies. This fact about us is absolutely essential to understand if we’re going devise strategies for avoiding these fallacies. - Finally, probability is
**philosophically very interesting**, and a lot of important philosophical debates turn on the interpretation of probabilistic statements, so some grounding in the philosophy of probability can be very helpful in both understanding those debates and making informed critical judgments about those issues.

Just to give an example of the fifth point , the so-called “fine-tuning” argument for the existence of God is based on the premise that we live in a universe that is probabilistically very unlikely if it wasn’t the product of some kind of intelligent design, and therefore the best explanation for our existence in this universe is that it was, in fact, a product of intelligent design. But this kind of argument turns on what it means for something to be “probabilistically unlikely”, and whether it’s even meaningful to talk about the universe in this way. I won’t say any more about that here, but that’s just one example of an interesting philosophical debate where probability plays an important role.