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Learn about deductive arguments, including their forms, validity, and types. Explore examples and counterexamples to understand the concept better.
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Arguments (p.43) • An argument is a complex discourse in which one or more statements, the premises, are taken as providing evidence for the truth of another statement, the conclusion. • Arguments occur only in language. • Every argument is either a valid deductive argument or an inductive argument.
Examples of Arguments All humans are mortals. Premises Socrates is a human. Socrates is a mortal. Conclusion If this chapter is easy, I’ll finish it today. This chapter is easy. Premises I’ll finish it today. Conclusion
Another Example of an Argument Amelia is a member of ΑΨΩ and is helpful. Kurt is a member of ΑΨΩ and is helpful. Premises Luis is a member of ΑΨΩ and is helpful. Kay is a member of ΑΨΩ and is helpful. All members of ΑΨΩ are helpful. Conclusion • The arguments on the previous slide are deductive. The argument above is inductive.
Deduction: Validity (p. 44) • Validity is a property of an argument form. Regardless of the argument’s content, an argument form is valid if it is impossible for all the premises to be true and the conclusion false. • The form of an argument is the argument pattern. Many arguments have the same form.
Argument Forms (pp. 44-45) • The following two arguments have the same form: All dogs are mammals. All dachshunds are dogs. All dachshunds are mammals. All cats are reptiles All collies are cats. All collies are reptiles.
Argument Forms (pp. 44-45) • We can represent the form of an argument by replacing words or statements with variables. The form of the arguments on the previous slide may be represented thusly: All M are P. All S are M. All S are P.
Validity and Soundness (p. 45) • Validity has nothing to do with the content of an argument. • Validity is only a property of the argument form: All arguments with the same form are either valid or invalid. • A sound argument is a valid argument with true premises, so the conclusion of a sound argument must be true as well.
Deductive Counterexamples (p. 46) • You can show that an argument form is invalid by means of a deductive counterexample. • A deductive counterexample to a given argument is an argument of the same form in which all the premises are true and the conclusion is false.
Deductive Counterexamples (p. 46) Consider the argument: All people with advanced degrees are well-educated. All professors are well-educated. All professors are people with advanced degrees. The form is: All P are M. All S are M. All S are P.
Deductive Counterexamples (p. 46) Replace the variables with terms so that the premises are true and the conclusion is false, and you have constructed a deductive counterexample to the original argument: All cats are mammals. All dogs are mammals. All dogs are cats.
Kinds of Deductive Arguments (pp. 46-47) • Categorical Syllogisms • Categorical syllogisms show relationships among sets or classes of things. • The dogs-mammals-dachshunds and cats-reptiles-collies arguments above, and the counterexample arguments above are examples of categorical syllogisms. (See Chapters 13-19.)
Kinds of Deductive Arguments (pp. 46-47) • Propositional Arguments • Propositional arguments show relations among statements. • The argument concerning the ease of this chapter is an example of one kind of propositional argument. There are many distinct propositional argument forms. (See Chapters 20-24.) • Most of the deductive arguments you are likely to encounter on a day-to-day basis are propositional arguments.
