Evaluating Deductive and Inductive Arguments

Validity and Invalidity

A deductive argument is valid if its logical structure is such that if the premises are true, the conclusion is necessarily true. It is impossible for a valid argument to have true premises and a false conclusion.

An invalid argument is one where the conclusion does not logically follow from the premises, even if the premises and conclusion happen to be true in the real world.

Soundness

Validity alone is not enough for a "good" argument. A sound argument is a deductively valid argument that also possesses true premises. If an argument is valid but contains even one false premise, it is considered unsound.

Common Mistake: Do not assume an argument is invalid just because a premise is false. Conversely, do not assume an argument is valid just because the conclusion is true. Validity is about the connection between premises and conclusion, not the content itself.

Evaluating Inductive Arguments: Strength and Cogency

Inductive arguments are evaluated on a spectrum of probability rather than absolute certainty.

Strength and Weakness

An inductive argument is strong if the premises provide high probability for the conclusion. If the premises do not provide sufficient support to make the conclusion probable, the argument is weak.

Cogency

A "good" inductive argument must be both strong and true. A cogent argument is a strong inductive argument that has true premises. If an argument is strong but relies on false premises, it is not cogent.

A Four-Step Evaluation Procedure

When faced with a complex argument, follow this systematic approach:

1. Identify the components: Find the conclusion and the premises.
2. Test for Deduction: Ask, "If the premises are true, must the conclusion be true?"
   • If Yes: It is deductive. Check for validity (form) and then soundness (truth of premises).
   • If No: Proceed to step 3.
3. Test for Induction: Ask, "If the premises are true, is the conclusion probably true?"
   • If Yes: It is inductive. Check for strength (probability) and then cogency (truth of premises).
   • If No: Proceed to step 4.
4. Identify Failure: If the answer to both is no, the argument is either an invalid deductive argument or a weak inductive argument.

Complex Structures: Diagramming and Missing Parts

As arguments grow in complexity, they may involve multiple premises that support each other in different ways.

Independent vs. Dependent Premises

• Independent Premises: Each premise provides its own separate support for the conclusion.
• Dependent Premises: Premises that must work together to provide joint support; if one is removed, the support for the conclusion is undermined.

The Enthymeme (Missing Premises)

Often, arguments leave out premises because they seem obvious or because the arguer wants to hide a controversial claim. These are called enthymemes. When evaluating these, use the "Principle of Charity": try to find the most plausible premise that would make the argument valid or strong.

Exam Tip: If you encounter an argument that seems to jump to a conclusion without enough evidence, look for the "unspoken" premise. If that premise is a stereotype or an unwarranted assumption, the argument is likely flawed.