We all engage in reasoning everyday. We engage in reasoning whenever we argue with each other, evaluate what we read and hear, and consider the evidence for and against views or ideas. So it is not something that’s foreign or alien. But reasoning is something that you can get better at doing. It is a skill or an art. Like any skill, it requires a bit of knowledge and practice. Lots and lots of practice.
Our aim in this course is to teach you the fundamentals of good reasoning. We will illustrate these fundamentals by looking at reasoning from newspapers, journals, advertisements, textbooks, and some philosophical works. By the end of the course you will know the difference between good reasoning and bad reasoning. You will be able to detect fallacies and bad reasoning in others. You will become more clear-headed and logical in your own thinking. The skills you acquire through doing this course will stand you in good stead whatever course you take at Macquarie and whatever career your pursue afterwards.
Even though reasoning is something we all do, it can be quite difficult at times to do correctly. We are all prone to making mistakes in reasoning. Indeed, there is an entire branch of psychology which is dedicated to examining the common patterns of illogical and fallacious thinking. To illustrate the difficulty of correct reasoning I want to consider two reasoning tasks that have been much discussed by psychologists. The two tasks show how easy it is to fall into the traps of fallacious reasoning.
2. EXERCISES IN CRITICAL THINKING
The card selection task
You are presented with four cards as below. One half of each card is masked. The other half is blank or has a circle. Your job is to work out which of the masked cards you need to see in order to answer the follow question decisively:
FOR THESE CARDS, IS IT TRUE THAT IF THERE IS A CIRCLE ON THE LEFT THERE IS A
Blackboard Learning System 2/03/09 2:35 PM http://learn.mq.edu.au/webct/cobaltMainFrame.dowebct Page 2 of 129
CIRCLE ON THE RIGHT?
You have only one opportunity to make this decision. You must not assume that you can inspect the cards one at a time. Name those cards which it is absolutely essential to see -- ie that you absolutely must see to answer the question.
Before you read any further, pause to consider what you think is the right answer.
What do most people say?
The most common answer is that you should see cards (a) and (c); the next most common answer is that you need only see (a).
The correct answer:
The correct answer is: you must see (a) and (d). Let’s consider each card in turn.
You must see (a) because if the right-hand side of (a) has no circle, the conditional is shown to be false.
You need not see (b) because it has no circle on the left-land side and so whatever is hidden on the right-hand side has no bearing on the truth of the conditional.
You need not see (c) because what is hidden on the left-hand side does not bear decisively on the truth of the conditional, does not have the potential to decisively show the truth or falsity of the conditional.
You must see (d) because if the left-hand side of (d) has a circle, the conditional is shown to be false.
The original experiment by the British psychologist Peter Wason is described in the article:
Wason, P. C. (1968). Reasoning about a rule. Quarterly Journal of Experimental Psychology, 20,
For a good review of the theoretical psychological discussions see:
Oaksford, M., & Chater, N. (1994). A rational analysis of the selection task as optimal data selection.
Psychological Review, 101, 608-631.
Blackboard Learning System 2/03/09 2:35 PM http://learn.mq.edu.au/webct/cobaltMainFrame.dowebct Page 3 of 129
The Monty Hall problem
This problem is named after the presenter on the American TV show Let’s Make a Deal.
On the table are three identical boxes, each with a lid and also a neat pile of ten dollar bills. This