1. Evaluating Deductive Arguments
Chapter Five
Evaluating Deductive Arguments

2. Validity Validity is one way to evaluate a deductive argument.
A deductive argument is valid if, and only if, its premises entail its conclusion.
There is entailment in an argument if, and only if, the truth of the argument’s premises guarantees the truth of its conclusion—in the sense that, if the premises are all true, the conclusion cannot be false.

3. Valid and Invalid Arguments
Arguments may be divided into two groups: those that are valid and those that are invalid.
Only valid arguments are truth-preserving; if their premises are true, then it is not possible for their conclusion to be false.
Only in a valid argument do the premises entail the conclusion.
A logical thinker who accepts the premises of a valid argument cannot reject its conclusion without contradiction. But this doesn’t happen in the case of an invalid argument.

4. Validity and Truth
The validity of an argument is determined solely by consideration of its form and not the actual truth of the premises or the conclusion.
Whether an argument is valid is entirely a matter of whether its conclusion follows necessarily from its premises. The truth of the premises and conclusion are irrelevant to validity.

5. Validity and Truth 1. All dogs are fish.
A valid argument could have one or more false premises and a true conclusion, as in:
1. All dogs are fish.
2. All fish are mammals.
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3. Therefore, all dogs are mammals.
A valid argument could also be made up entirely of false statements, as in:
1. All Democrats are vegetarians.
2. All vegetarians are Republicans.
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3. Therefore, all Democrats are Republicans.

6. Validity and Argument Form
An argument form is the type of logical pattern that a particular argument follows.
The following is a valid argument form and any argument following this form would be valid.
All A are B.
All B are C.
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3. Some A are C.
The following is an invalid argument form and any argument following this form would be invalid.
Some C are B.
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3. Some C are A.

7. Technical Meaning of Validity
The term valid can only apply to an argument whose premises necessitate or entail its conclusion.
Statement are either true or false, but cannot be valid or invalid.
Arguments cannot be true or false, but can be valid or invalid.

8. Propositional Argument Forms
A proposition is the content of a belief or statement, which has truth value.
Propositional Forms = arguments that have the characteristic of being truth-preserving because the statements that constitute their premises and conclusion form distinctive patterns of relationship that transfer the truth of the premises (if they are true) to the conclusion.

9. Valid Propositional Argument Forms

10. Categorical Argument Forms
Categorical Argument Forms = arguments that have the characteristic of being truth-preserving because, within the statements that constitute their premises and conclusions, there are some expressions, usually called terms, which bear certain relationships to each other that make the arguments’ conclusions true if the premises are true.

11. Valid Categorical Argument Forms

12. Propositional or Categorical?
Certain connections between propositions, such as “either or . . .” and “if then . . .” indicate that the argument is probably better constructed as propositional.
Certain words within the premises indicating quantity, such as “all,” “no,” and “some” suggest that the argument is probably better constructed as categorical.

13. Cash Value of Validity
It is not possible that the argument’s premises are true and its conclusion false.
The conclusion could be false, if at least one of its premises is false.
It is contradictory to accept a valid argument’s premises and reject its conclusion.

14. Soundness
Validity is the first criterion in argument evaluation. The second criterion is soundness.
An argument is sound if, and only if, it is valid and all of its premises are true.
An argument is unsound if it lacks either validity, true premises, or both.
Unsoundness is a reason to reject an argument even if it is valid.
The conclusion of a sound argument is true.
A sound argument’s conclusion cannot be rejected without saying something false.

15. Soundness

16. Cash Value of Soundness
The argument’s conclusion is true; to deny it is to say something false.
A logical thinker who recognizes an argument as sound must accept its conclusion.

17. Cogency
A proposed argument has deductive cogency (or persuasiveness) when three conditions are met:
recognizable validity
acceptable premises
premises that are more clearly acceptable than the conclusion

18. The Cash Value of Cogency
Any argument that satisfies the conditions of cogency is rationally compelling, in the sense that it would move the thinker to accept its conclusion (provided she accepts its premises and works out its entailment).
It would be irrational for a thinker to reject the conclusion of a cogent argument.