Argument Forms
As noted previously, it is difficult to distinguish between bad deductive arguments and bad inductive arguments: the difference between a conclusion that is not certain and one that is not probable is slight. However, each type of reasoning has its own unique argument forms. If you can learn recognize these forms, it will aid you greatly in distinguishing between deductive and inductive arguments.

Deductive Argument Forms
Many deductive arguments have the form of a syllogism. A syllogism is a deductive argument that consists of two premises and a conclusion. All syllogisms must meet this requirement. There are three different types of syllogisms we will examine, each of which has additional characteristics.

The disjunctive syllogism is a syllogism that has a disjunction as one or both of its premises. A disjunction is a statement of the form "Either X or Y." A disjunctive syllogism commonly offers two choices as possibilities. The non-disjunctive premise then eliminates one of the choices, leaving the remaining choice as the only possibility:

Either the Cowboys or the 49ers will win the Superbowl. (This is the disjunctive premise.)
The 49ers will not win the Superbowl. (Second premise: One of the two alternatives is eliminated.)
Therefore, the Cowboys will win the Superbowl. (We conclude that the remaining alternative is true.)

The categorical syllogism is a syllogism that meets two added requirements (besides being a deductive argument with two premises and a conclusion):

1) All the statements in the argument begin with one of the words "all," "no," or "some." These three words are known as quantifiers. All statements in a categorical syllogism must begin with a quantifier. (Premise and conclusion indicators do not count when you are determining whether a statement begins with a quantifier. For example, if the conclusion of an argument reads "Thus, all dogs are mammals," that statement is considered to start with a quantifier. The word "thus" is not considered the beginning of the statement.)

2) The argument uses three terms, each of which occurs twice in the argument. A term is a word or phrase that names a group or class of objects. For example, "cats," "people who listen to Michael Bolton without gagging," "aquatic mammals," and "full-time students" are all terms. Here is an example of a categorical syllogism:

All Michael Bolton fans are lovers of insipid muzak.
Some lovers of insipid muzak are people who enjoy the musical stylings of Kenny G.
Therefore, no Michael Bolton fans are people who enjoy the musical stylings of Kenny G.

Note that the argument has two premises and a conclusion. Each statement begins with one of the words "all," "no," or "some." There are three terms used in the argument: "Michael Bolton fans," "lovers of insipid muzak," and "people who enjoy the musical stylings of Kenny G." Each of these terms occurs twice in the argument. Thus, the argument is a categorical syllogism.

The final type of syllogism we will examine is the hypothetical syllogism. This syllogism has a conditional statement as one or both of its premises. The argument may be composed entirely of conditional statements. Here are some examples of hypothetical syllogisms:

If Christina Aguilera sings like a warthog in heat, then people cannot stand her.
Christina Aguilera sings like a warthog in heat.
Therefore, people cannot stand her.

If Elvis is alive, then he was captured by aliens from planet Zog.
If Elvis was captured by aliens from planet Zog, then he now lives on Zog.
Therefore, if Elvis is alive, then he now lives on Zog.

Another type of deductive argument is the argument based on mathematics. This is any argument that relies on purely mathematical computation to support its conclusion. Arguing that since Peter has 5 oranges and Ted has 3 oranges, that together they have 8 oranges is an example of this type of argument. Note that even illegitimate mathematical reasoning will fall into this category. For example, arguing that since A + B = 7, and A = 3, that therefore B = 5 is an argument by mathematics. It is a bad argument, since B must actually equal 4, not 5, but that does not change the type of reasoning being employed. It just indicates that the reasoning was poorly done.

The argument from definition is a deductive argument that relies upon the definition of a word used in the argument to justify its conclusion. For example, I note that Bruce Wayne is a bachelor. I then conclude he is unmarried. This is an argument by definition because the conclusion, "Bruce Wayne is unmarried," depends upon the definition of the word "bachelor."

It is worth noting that while the argument from definition has a very distinct form, all deductive arguments rely upon definitions in some sense. For example, mathematical arguments rely upon the definitions of the rules of math and the definitions of terms such as "square" or "circle." Categorical syllogisms also rely upon definition. Consider the first premise of the categorical syllogism used as an example earlier:

All Michael Bolton fans are lovers of insipid muzak.

This premise defines Michael Bolton fans as lovers of insipid muzak. If you look at the remaining propositions in the argument, you will see similar definitional moves being made.

Disjunctive syllogisms also use definition. A typical disjunctive syllogism offers you two alternatives, then excludes one of those two choices. The disjunctive premise is a definition, for it defines what two choices are available to you. Hypothetical syllogisms also rely upon definition, for hypothetical syllogisms employ conditional statements, and every conditional statement defines both a necessary and a sufficient condition. To sum up, while the argument from definition is a type of deductive argument, all deductive arguments will rely on definition in some way.

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© 2003, David Arthur