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- 1. Chapter 8 Deductive Arguments The aim of this tutorial is to help you learn to recognize, analyze, and evaluate deductive arguments. Copyright © 2021 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
- 2. 2 © McGraw-Hill. How Can Learning about Deductive Logic Help Us Make Better-Informed Decisions? Zigy Kaluzny-Charles Thatcher/Stone/Getty Images
- 3. 3 © McGraw-Hill. Sherlock Holmes Alfred Gescheidt/The Image Bank/Getty Images "When you have eliminated the impossible, whatever remains, however improbable, must be the truth".
- 4. 4 © McGraw-Hill. Deductive Arguments • A deductive argument claims that its conclusion necessarily follows from the premises. • Certain words or phrases are commonly used in deductive arguments; these include "certainly, absolutely, definitely, conclusively, must be, and it necessarily follows that."
- 5. 5 © McGraw-Hill. Hot or Not? Are deductive arguments better than inductive arguments?
- 6. 6 © McGraw-Hill. Deductive Reasoning and Syllogisms Deductive arguments are often presented in the form of syllogisms, with two supporting premises and a conclusion. A deductive argument is valid if the form of the argument is such that the conclusion must be true if the premises are true. • The form of an argument is determined by its layout or pattern of reasoning. • An argument is sound if it is valid and the premises are true.
- 7. 7 © McGraw-Hill. Some Mammals Are Fish Chris Gould/Photographer’s Choice/Getty Images No fish are dogs. All dogs are mammals. Therefore, some mammals are fish.
- 8. 8 © McGraw-Hill. Types of Deductive Arguments There are three types of deductive arguments used in everyday reasoning: • Arguments by elimination rule out different possibilities until only one possibility remains. • Arguments based on mathematics depend on mathematical or geometric equations to generate conclusions. • In arguments from definition, the conclusion is true because it is based on a key term or essential attribute in a definition.
- 9. 9 © McGraw-Hill. "Top Cop" Bo Dietl Uses Deductive Logic in Solving Cases Lawrence Schwartzwald/ Sygma/Getty Images
- 10. 10 © McGraw-Hill. Deductive Process of Elimination Mike Kemp/Rubberball Images/Getty Images A mouse locates the prize at the end of a maze through the deductive process of elimination.
- 11. 11 © McGraw-Hill. Deductive Reasoning Skills Jet Propulsion Laboratory/NASA The smooth landing of the Mars Rovers was a result of the deductive reasoning skills of the NASA scientists.
- 12. 12 © McGraw-Hill. Same-Sex Marriage Justin Sullivan/Getty Images Marilyn and Jessica cannot be married, since a marriage is a union between a man and a woman.
- 13. 13 © McGraw-Hill. Hypothetical Syllogisms Hypothetical reasoning involves "if…then…" reasoning. A hypothetical syllogism is a form of deductive argument that contains two premises, at least one of which is a hypothetical or conditional "if…then" statement. There are three basic patterns of hypothetical syllogisms: • Modus ponens (affirming the antecedent). • Modus tollens (denying the consequent). • Chain arguments.
- 14. 14 © McGraw-Hill. Modus Ponens Arguments In a modus ponens argument, the following structure is used: • If A, (antecedent), then B (consequent). • A. • Therefore, B.
- 15. 15 © McGraw-Hill. Modus Tollens Arguments In a modus tollens argument, the following structure is used: • If A, (antecedent), then B (consequent). • Not B. • Therefore, not A.
- 16. 16 © McGraw-Hill. Chain Arguments In chain arguments, the following structure is used: • If A, then B. • If B, then C. • Therefore, if A, then C.
- 17. 17 © McGraw-Hill. Using Hypothetical Syllogisms • Not all valid arguments are sound. • Rewording arguments in ordinary language in the form of hypothetical syllogisms can help you expose faulty premises.
- 18. 18 © McGraw-Hill. Categorical Syllogisms A categorical syllogism is a type of deductive argument that sorts things into specific classes. • It is composed of a conclusion, two premises, and three terms, each of which occurs exactly twice in two of the three propositions. Categorical syllogisms can be written in any of 256 standard forms or combinations.
- 19. 19 © McGraw-Hill. Standard-Form Categorical Syllogisms A standard form for categorical syllogisms is shown here: • All P are M. (P = predicate, M = middle term) • Some S are not M. (S = minor term, M = middle term) • Some S are not P. (S = minor term, P = major term) As with hypothetical syllogisms, if the form of a categorical syllogism is valid, then the argument will be valid regardless of term substitutions.
- 20. 20 © McGraw-Hill. Quantity and Quality Each proposition in a standard-form categorical syllogism is written in one of four forms, determined based on its quantity (universal or particular) and qualifier (affirmative or negative). There are four forms of propositions. • Universal affirmative: All S are P. • Universal negative: No S are P. • Particular affirmative: Some S are P. • Particular negative: Some S are not P.
- 21. 21 © McGraw-Hill. Each Term in a Venn Diagram Is Represented by a Circle
- 22. 22 © McGraw-Hill. Venn Diagrams Venn diagrams are useful instruments for evaluating the validity of categorical syllogisms. • They directly engage our spatial reasoning ability and help us to visualize group relationships effectively.
- 23. 23 © McGraw-Hill. Representing Each of the Four Types of Propositions in a Venn Diagram
- 24. 24 © McGraw-Hill. Venn Diagrams Use Overlapping Circles to Represent the Terms in a Proposition P M No (dogs) are (cats). S M Some (mammals) are (cats). S P Therefore, some (mammals) are not (dogs.)
- 25. 25 © McGraw-Hill. Translating Ordinary Arguments into Standard Form • Rewrite each proposition in standard form, starting with the conclusion. • Use the context and grammar of the original argument to decide on which quantifier to use. • Identify the three terms in the argument. • Where necessary, rewrite each term as a noun or noun phrase. • Each proposition should use a form of the to be verb. • Put the syllogism in standard form: major premise, minor premise, and conclusion.
- 26. 26 © McGraw-Hill. Conclusions • Knowledge of deductive arguments—including arguments from definition, mathematical arguments, arguments by elimination, and hypothetical and categorical syllogisms—is essential for us to effectively function in the world. • As good critical thinkers, we must constantly identify and evaluate these types of arguments, both our own and those presented to us by others.
- 27. 27 © McGraw-Hill. Perspectives on the Death Penalty David Leeson/Dallas Morning News/The Image Works