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EAS-A193 Class Notes

An Introduction to
Critical Thinking

Critical Thinking

One of our natural tendencies is to believe what wish to be true. Unfortunately, our desires often conflict with the real situation. Spotting inconsistencies in our own and others arguments, ideas, and positions is important if you are interested in being fooled by neither yourself nor by others. Some people will try to fool you, and you will see others fooling themselves. But always remember that the purpose of critical thinking is to find the truth, not to ridicule others.

Some Thinking References

Although you must practice critical thinking to get good at it, an examination of the common pitfalls in non-critical thinking can help you along the way.

Several good, descriptions of faulty arguments and logic of the pitfalls can be found in the books

Bad Arguments - Avoiding the Burden of Proof

Bad Arguments - Avoiding the Issue

Another common characteristic of faulty thinking is to avoid the true issue. Some of the types of misguided thinking that fits this category are

Bad Arguments - Avoiding Responsibility

Also common are ways of passing on the responsibility your to investigate and find the truth

Bad Arguments - Faulty Logic

Some Common Problems With Pseudoscience Arguments

In pseudoscience, some problems are associated with

Some Common Problems in Scientific Thinking

Good Thinking Practices

The goal is not to come up with an idea we like, but one that follows from the starting premise and matches the evidence. Here's a list of some good thinking practices:

A Valuable Tool - Probability

Probability is a valuable tool to appreciate the occurrence of random events and to avoid begin fooled by coincidence. In many ways, probability is common sense quantified. Consider the possibility of an event, lets call it x, occurring

For example, suppose that you flip a coin twice. What is the probability of getting two heads?

To answer that question we must first identify all the possible outcomes

hh tt ht th

Then, compute the quotient defined above to find that the probability of hh is 1 / 4 = 0.25.

Combinations

To compute probabilities, we need to be able to compute the number of combinations we can construct out of objects.

If some choice can be made N different ways and another choice can be made M different ways, a total of MxN different choices can be made. For example, consider rolling two dice

Each die has six possible outcomes (the numbers 1 through 6)

We have two sets of six choices, so the possible outcomes are 6 x 6 = 36.

Suppose you flip a coin three times. Since each flip has two possible outcomes, we have 2 x 2 x 2 = 8 possible results. In this simple case we can list them all

hhh hht htt ttt tth thh tht hth

Probabilities

Suppose you flip a coin three times. Since each flip has two possible outcomes, we have 2 x 2 x 2 = 8 possible results.

hhh hht htt ttt tth thh tht hth

So what is the probability of getting two tails in three flips? There are three ways we can do that

hhh hht htt ttt tth thh tht hth

and eight possible choices, so the probability is

Probability of two tails in three flips = 3 / 8

What is the probability of having three tails out of three?

Probabilities with Two Dice

We have 6 numbers on each die, so 6 x 6 = 36 possible combinations.

What is the probability of rolling a twelve? There's only one way to do it, so 1 in 36.

What is the probability of getting doubles? There are 6 ways to get doubles, so its 1 in six.

What about rolling a seven? How many ways can we roll a seven?

1+6, 6+1, 2+5, 5+2, 3+4, 4+3

so the probability is 6/36, or 1 in 6.


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Prepared by: Chuck Ammon
August/September 1997