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

Deductive arguments  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. 2 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Deductive arguments 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 both it is (1) valid, and (2) the premises are true. 3 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Types of deductive arguments  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. 4 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

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 5 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Modus ponens arguments  In a modus ponens argument, the following structure is used: If A, then B. A. Therefore, B. 6 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Modus tollens arguments  In a modus tollens argument, the following structure is used: If A, then B. Not B. Therefore, not A. 7 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Chain arguments  In chain arguments, the following structure is used: If A, then B. If B, then C. Therefore, If A, then C. 8 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

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. They are also useful as clarification tools, and as decision-making aids. 9 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Categorical syllogisms  Categorical syllogisms are 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. 10 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Standard form categorical syllogisms  A standard form for categorical syllogisms is shown here:  All P are/are not M.(P=predicate, M=middle term)  Some S are/are not M.(S=minor term, M=middle term)  Some S are/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. 11 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Quality and qualifier  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:All S are P  Universal negative:No S are P  Particular affirmative:Some S are P 12 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Venn diagrams  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. 13 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

Translating arguments into standard categorical form  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. 14 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.

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. 15 © 2010, The McGraw-Hill Companies, Inc. All Rights Reserved.