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

  • The Demon-Haunted World, Science as a Candle in the Dark by Carl Sagan
  • Why People Believe in Weird Things, Pseudoscience, Superstition, and Other Confusions of our Time by Michael Shermer
  • An Enquiry Concerning Human Understanding by David Hume.

Bad Arguments - Avoiding the Burden of Proof

  • Assuming the truth without evidence.
  • Drawing conclusions from inadequate evidence or making hasty judgments.
  • Post hoc, ergo propter hoc, which translates roughly as it happened after, so it must be caused by.
  • Related to the above is the tendency of people to have selective memories - in essence to forget the usual but remember the unusual.
  • Related to our selective memories is our over-interpretation of coincidence, which is rooted in our generally poor grasp of probability and chance.

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

  • Ad hominem - arguing against an individual, not the individuals position. Focus on the argument, not the arguer.
  • Ad Ignorantiam - support for an argument cannot be rooted in ignorance of the real answer. Or, just because you cant disprove something doesn't mean that it must be true.
  • Proving another position wrong does not make your position right.
  • Considering only the extreme cases - ignoring the middle ground. Not all problems have solutions that are extreme, often the middle ground is the best we can do.

Bad Arguments - Avoiding Responsibility

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

  • Over reliance on authority - authorities have been wrong positions must be supported by evidence.
  • We just dont understand - There are many things we dont understand, but just because we dont understand something doesnt mean that we can claim it must be supernatural intervention.

Bad Arguments - Faulty Logic

  • non-sequitir - it doesnt follow. You base your argument on an unrelated fact.
  • Carrying an argument to a ridiculous extreme.
  • Circular Reasoning - when your conclusion is nothing but a restatement of one of your assumptions.

Some Common Problems With Pseudoscience Arguments

In pseudoscience, some problems are associated with

  • Scientific language does not make science
  • Bold statements does not make truth
  • Heresy does not equal correctness
  • Unexplained is not Inexplicable
  • Anecdotes do not make science
  • Rumors do not equal reality

Some Common Problems in Scientific Thinking

  • Theory Influences Observations
  • The Observer Changes the Observed
  • Equipment Constructs Results

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:

  • Encourage debate and seek out alternative points of view
  • Construct more than one hypothesis to match the evidence. Beware untestable hypotheses - they cannot be used for the basis of critical reasoning.
  • Dont get overly attached to an idea because it is yours, be fair and keep an open mind.
  • Avoid vague statements and ideas, be specific and if possible quantify your hypotheses.
  • If an argument is sequential, make sure every step in the sequence is based on solid evidence and reasoning.
  • Remember that extraordinary claims demand extraordinary evidence. If several solutions are viable, and you have to choose just one, choose the simplest.

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

  • Probability = number of possibilities favoring the occurrence of "x" divided by the total number of possibilities

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.


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


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: Charles J. Ammon