DEDUCTIVE ARGUMENTS The aim of this tutorial is

2 “When you have eliminated the impossible, whatever remains, however improbable, must be the

Deductive arguments 3 A deductive argument claims that its conclusion necessarily follows from the

Hot or Not? 4 Are deductive arguments better than inductive arguments? © 2012, The

Deductive arguments and syllogisms 5 Deductive arguments are often presented in the form of

6 No fish are dogs. All dogs are mammals. Therefore, some mammals are fish.

Types of deductive arguments 7 There are several types of deductive arguments. Three types

8 A mouse locates the prize at the end of a maze through the

9 Bo Dietl © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

10 The smooth landing of the Mars rovers was a result of the deductive

11 “Marilyn and Jessica cannot be married, since a marriage is a union between

Hypothetical syllogisms 12 Hypothetical reasoning involves “If…then…” reasoning. A hypothetical syllogism is a form

Modus ponens arguments 13 In a modus ponens argument, the following structure is used:

Modus tollens arguments 14 In a modus tollens argument, the following structure is used:

Chain arguments 15 In chain arguments, the following structure is used: If A, then

Using hypothetical syllogisms 16 Not all valid arguments are sound. Rewording arguments in ordinary

Categorical syllogisms 17 A categorical syllogism is a type of deductive argument that sorts

Standard-form categorical syllogisms 18 A standard form for categorical syllogisms is shown here: All

Quality and qualifier 19 Each proposition in a standard-form categorical syllogism is written in

Venn diagrams 20 Venn diagrams are useful instruments for diagramming and evaluating categorical syllogisms.

P M No (dogs) are (cats). 21 S M Some (mammals) are (cats). S

Translating arguments into standard categorical form 22 Rewrite each proposition in standard form, starting

Conclusions 23 Knowledge of deductive arguments—including arguments from definition, mathematical arguments, arguments by elimination,

24 How can learning about deductive logic help us make better-informed decisions? © 2012,

25 Perspectives on the death penalty © 2012, The Mc. Graw-Hill Companies, Inc. All

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DEDUCTIVE ARGUMENTS The aim of this tutorial is to help you learn to recognize, analyze, and evaluate deductive arguments.

Deductive arguments 3 A deductive argument claims that its conclusion necessarily follows from the premises. Certain words and phrases are commonly used in deductive arguments; these include certainly, absolutely, definitely, conclusively, must be, and it necessarily follows that. However, not all deductive arguments contain indicator words. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Deductive arguments and syllogisms 5 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 both (1) it is valid, and (2) the premises are true. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Types of deductive arguments 7 There are several types of deductive arguments. Three types are 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 an argument from definition, the conclusion is true because it is based on a key term or essential attribute in a definition. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

11 “Marilyn and Jessica cannot be married, since a marriage is a union between a man and a woman. ” This argument may no longer be sound because the legal definition of marriage is undergoing change. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Hypothetical syllogisms 12 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 © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Using hypothetical syllogisms 16 Not all valid arguments are sound. Rewording arguments in ordinary language in the form of hypothetical syllogisms can help you expose faulty premises. They are also useful as clarification tools, and as decision-making aids. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Categorical syllogisms 17 A categorical syllogism is a type of deductive argument that sorts things into specific classes or groups. 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. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Standard-form categorical syllogisms 18 A standard form for categorical syllogisms is shown here: All P are/are not M. Some S are/are not P. (P=predicate, M=middle term) (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. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Quality and qualifier 19 Each proposition in a standard-form categorical syllogism is written in one of four forms based on quality (universal or particular) and qualifier (affirmative or negative). Three forms predominate. Universal affirmative: Universal negative: Particular affirmative: All S are P. No S are P. Some S are P. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Venn diagrams 20 Venn diagrams are useful instruments for diagramming and evaluating categorical syllogisms. They directly engage our spatial reasoning ability and help us to visualize group relationships effectively. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Translating arguments into standard categorical form 22 Rewrite each proposition in standard form, starting with the conclusion. Use the context and grammar of the original argument to decide on which qualifier to use. Identify the three terms in the argument. Where necessary, rewrite each term as a noun or noun phrase. Each proposition uses a form of the to be verb. Assemble in standard form: major premise, minor premise, conclusion. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.

Conclusions 23 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. © 2012, The Mc. Graw-Hill Companies, Inc. All Rights Reserved.