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Basic Logical Concepts

Chapter Outline

Following are the main learning objectives from the chapter.

Deduction and Induction

(See pgs. 52-56)

In distinguishing deductive arguments from inductive arguments, students should . . .

A. understand that deductive arguments are those which claim to prove their conclusions with rigorous, inescapable logic;

B. understand that inductive arguments attempt to show their conclusions are plausible or likely;

C. be familiar with the key differences between deductive and inductive arguments described on pgs. 55-56.

How Can We Tell Whether an Argument is Deductive or Inductive?

(See pgs. 56-62)

A. Students should understand that distinguishing whether an argument is deductive or inductive depends on whether the author intends the argument to provide conclusive grounds for the truth of the conclusion.

B. Students should be familiar with and be able to apply the four tests for determining whether an argument is deductive. To this end, students should . . .

1. recognize deduction and induction indicator words;

a. be aware that many arguments do not contain indicator words;

b. be aware that some authors use indicator words loosely or improperly;

2. understand that all deductive arguments claim that their conclusions follow with strict necessity from their premises;

a. distinguish a logical contradiction from a physical impossibility;

b. be aware that there are exceptions to the strict necessity test;

1. recognize when the language or context makes clear an arguer's intention to offer a logically conclusive argument;

2. recognize when an argument follows a pattern of reasoning that is characteristically deductive;

3. understand that arguments often follow common patterns that can help one to distinguish whether an argument is either deductive or inductive;

4. understand when it is appropriate to apply the principle of charity in those cases where it is difficult to discern whether an argument is intended to be deductive or inductive;

5. become familiar with and be proficient in the application of the guidelines for distinguishing deductive from inductive arguments on pgs. 61-62.

Common Patterns of Deductive Reasoning

(See pgs. 62-67)

A. Students should be able to recognize common patterns of deductive argument and you should be able to distinguish those patterns which are logically reliable from those which are not. Students should be able to recognize . . .

1. common patterns of hypothetical syllogisms.

2. categorical syllogisms.

3. arguments by elimination.

4. arguments based on mathematics.

5. arguments from definition.

Common Patterns of Inductive Reasoning

(See pgs. 67-71)

A. Students should be able to recognize common patterns of inductive argument, including . . .

1. inductive generalizations.

2. predictive arguments.

3. arguments from authority.

4. causal arguments

5. statistical arguments.

6. arguments from analogy.

Deductive Validity

(See pgs. 74-78)

A. Students should grasp the concept of deductive validity. To this end, students should . . .

1. understand that a deductively valid argument is one in which it is impossible for the premises to be true and the conclusion false;

2. distinguish between the everyday sense of "valid" as "good" or "true" from its precise technical sense which is used in the context of critical thinking;

3. understand that the validity of an argument does not depend on whether the premises and conclusion are actually true;

4. understand that no valid argument can have true premises and a false conclusion;

5. understand that all deductive arguments are either completely valid or completely invalid.

B. Students should understand and be able to apply the basic test of deductive validity: If the premises were all true, would the conclusion also have to be true? Further, they should . . .

1. comprehend that an argument can be valid and have false premises and a false conclusion; or stated differently, "valid" does not mean "true;"

2. understand that an argument can have true premises and a true conclusion and yet still be invalid; or stated differently, "true" does not mean "valid;"

C. Students should understand that any deductive argument in which the conclusion does not follow necessarily from the premises is invalid. To this end, students should . . .

1. understand that if it is logically possible for the premises to be true and the conclusion false, then the argument is invalid;

2. note that an invalid argument can have any combination of truth or falsity in the premises and conclusion.

D. Students should understand that validity is important because validity preserves truth.

E. Students should understand the distinction between a sound argument and an unsound argument. Students should . . .

1. understand that sound arguments must be valid and have all true premises.

2. understand that unsound arguments are invalid, have one or more false premises, or both.

Inductive Strength

(See pgs. 78-83)

A. You should understand the concept of inductive strength. To this end, you should . . .

1. understand that a strong inductive argument is one in which the conclusion follows probably from the premises;

2. understand that a weak inductive argument is an argument in which the conclusion does not follow probably from the premises;

3. understand that the strength of an argument does not depend on whether the premises and conclusion are actually true;

4. understand that no strong inductive argument can have true premises and a probably false conclusion;

5. note that a weak inductive argument can have any combination of truth or falsity in the premises and conclusion.

B. Students should understand and be able to apply the basic test of inductive strength: If the premises were all true, would the conclusion be probably true? Students should . . .

1. understand that, unlike deductive validity, inductive strength admits of degrees;

2. understand that an inductive argument can be made stronger or weaker by adding a premise.

C. Students should grasp the distinction between a cogent argument and an uncogent argument. Students should understand that . . .

1. in a cogent argument, the premises must be true and the argument must be inductively strong;

2. in an uncogent argument, the premises are false, the argument is inductively weak, or both.

Testing for Validity

(See pgs. 88-93)

A. Students should understand and be able to apply the Three C's Test to determine whether an argument is deductively valid. When testing for validity, students should . . .

1. Check to see whether the premises are actually true and the conclusion is false. If so, then the argument is invalid.

2. Attempt to conceive of a possible scenario in which the premises would be true and the conclusion false.

3. Apply the counterexample method of proving invalidity.