One Logical Form: A Simple Syllogism

One syllogism that is often used has the following form (P1 is premise one, etc.): 

P1  If A Then B
P2  Affirm A
C   Conclude B
The premises in an argument of this form will always lead to the conclusion. This will be the case even when the premises are not true. This results in a valid or deductive argument. Since the first premise is conditional, this kind of argument is called a conditional argument.

Example: 

P1 If a person has blue eyes,
    then they have red teeth.
P2 I have blue eyes.
C  I have red teeth.
For any argument of this form, if the premises are true then the conclusion must be true.

When an argument is in this syllogistic form the premises will always lead to the conclusion, but the truthfulness of the premises will still be undetermined from an analysis of the argument form. Indeed the first premise in the example above is clearly in doubt since many examples exist where it is not true.

Arguments can also be shown to be bad if they don't properly use the form. A common error is to affirm B instead of A. Affirming B instead of A is so common that this fallacy has a name: fallacy of affirming the consequent.

Practice Homework #1: Which of the following examples are deductive? Explain.

Example #1 Example #2 Example #3
P1 If a car travels 30 mph for 10 hours, then the car will have gone 300 miles.
P2 The car went 300 miles.
C The car traveled 30 mph for 10 hours.
P1 If two opposing forces on an object are unbalanced, then the motion of the object will change.
P2 Two opposing forces on an object are unbalanced.
C The motion of the object will change.
P1 If objects tend to go in a straight line, then objects can never go along curved paths.
P2 Objects tend to go in a straight line.
C Objects can never go along curved paths.

Check your answers by clicking on the appropriate number (in some browsers you will need to delete the old box before a new one will appear):    #1,     #2,     #3.

Practice Homework #2: Do the arguments lead to the truthfulness of the conclusion. In other words, which of the arguments in the table above are sound arguments? Explain.

Make sure you understand your choices and then check your answers.

These conditional arguments are only one of many different types of argument that can be analyzed and evaluated from a consideration of their logical form. It is highly useful to become acquainted with the different forms of argument, not only the forms that are valid, but also the forms that are invalid. This course will emphasize the conditional syllogism.

However, other types of arguments are also commonly used in science, but not all of these can be evaluated solely by inspecting their logical form. For example, causal arguments (establishing a cause and effect relationship) and arguments using analogy (the more things that two objects are observed to have in common, the more likely they will have unobserved things in common) are especially useful.