Arguments consist of premises (statements) followed by a conclusion. To be valid, the premises must support the conclusion. The structure of the argument starts with the premises:
All A are B. All C are A.
The premises are followed by the conclusion:
Therefore, all C are B.
Let A = rainy days and B = cloudy days. Let C = Tuesday.
Here are the premises to the above example:
All rainy days (A) are cloudy days (B). Tuesday (C) is a rainy day (A).
The conclusion:
Therefore, Tuesday (C) is a cloudy day (B).
Switch A and B around and see how this becomes invalid:
This is not logical: Tuesday (C) is a cloudy day (B), therefore Tuesday (C) there is rain (A).
This is logical: Tuesday (C) is a rainy day (A), therefore, Tuesday (C) there are clouds (B).
Every graduate student (A) is highly intelligent (B), and every teacher (C) is a graduate student (A).
Therefore, every teacher (C) is highly intelligent (B).
Note: The premises do not need to be true for the argument to be valid.
Make the above argument invalid:
You might notice that a true statement may not be valid.
Check your response. Here you'll find several links to examples of invalid arguments and faulty reasoning.
The examples above are termed syllogisms, forms of deductive reasoning. We use syllogistic reasoning in its valid (and invalid) forms often. There are four valid forms we use.
Take a break and look through your Windows Accessories on your PC. You'll find a great logic game called Minesweeper! Learn it. Teach it to your students. It's a simple way to get kids going on logic problems in their spare time.
Write a simple, logical syllogism below. Be prepared to paste your statements into the Tapped In text area for others to test.
For example: All those receiving 93% or better in this course will receive a raise. Susan and Sam each got a 95%! Therefore, Susan and Sam will receive a raise.
Finally, this page provides only a review of the basics of simple logic. Take a look at the Blackboard.com web on Logic Games geared toward practicing for the GRE. The site is interactive and provides several logic problems with immediate feedback. The site can be used for your more advanced high school students to get them in shape for the SAT.
