Students

In Chapter 2 you will learn to identify and analyze arguments. You will learn how to use premise-indicators and conclusion-indicators to decode the relationships between the propositions in an argument that is given in natural language. You will also learn two other techniques for analyzing the structures of arguments and understanding the relationships between the propositions in arguments: diagramming and paraphrasing. Finally, you will learn to use the context of an argument to help to identify and fill in premises that are not expressed in declarative form, hidden premises, and hidden conclusions.

Important concepts:

• diagramming arguments
• paraphrasing arguments
• conclusion-indicators and premise-indicators
• unstated propositions, propositions not in declarative form

The "Languages and Definitions" part of Chapter 3 focuses on how an understanding of the functions of language itself is important to logicians. Language is a complex tool; as a logician, you have to ensure that you are not led astray by words or discursive forms.

After reading this chapter, you should be able to:

1. Understand the three basic functions of language: informing, expressing, and directing.
2. Recognize that language can perform more than one function at a time.
3. Distinguish between grammatical form and logical function.
4. Understand how emotive language can inhibit logical argument.
5. Make distinctions between disagreements in belief and disagreements in attitude.

The "Definition" part of Chapter 3 describes how definitions are created and how to critique them. You will need to be able to apply the technique of definition to the analysis of disputes.

After reading this chapter, you should be able to:

1. Distinguish between genuine disputes and merely verbal disputes.
2. Understand the five kinds of definitions, and their uses.
3. Know how to construct denotative definitions and connotative definitions.
4. Identify the varieties of definitions.
5. Apply the five traditional rules of definition by genus and species.

In chapter 4, you are introduced to the concept of logical fallacies. To fully understand logic, you need to be able to distinguish fallacies from sound reasoning. The text discusses three major types of fallacies: fallacies of relevance, fallacies of presumption, and fallacies of ambiguity.

• In fallacies of relevance, arguments rely on premises that may seem relevant, but, in fact, are not. Such arguments are fallacies because they distract attention away from relevant facts and attempt to prove the truth of their conclusions based on irrelevant information.
• Fallacies of presumption contain dubious or untrue premises that are simply assumed to be true. You need to be able to see why these assumptions are made, and how to avoid making them—or being taken in by them.
• In fallacies of ambiguity, reasoning goes wrong because words or phrases within arguments mislead.

The chapter describes seventeen of the most common logical fallacies falling within these three categories. You should be able to detect them in arguments and explain what is wrong with them.

Chapter 5 presents the basic elements of classical deductive logic (also called Aristotelian logic). It discusses the four basic standard-form (A, E, I, and O) categorical propositions, the "square of opposition" they engender, and the problems which modern logicians have discovered with this type of logic. It then presents one response to this problem: Boolean logic.

After reading this chapter, you should be able to:

1. Use the terms distributed, undistributed, quality, and quantity as they apply to logic.
2. Understand the meanings of contraries, contradictories, subcontraries, subalterns, and superalterns.
3. Show how these relations are exhibited in the "square of opposition."
4. Understand the immediate inferences that can be drawn from the square of opposition.
5. Describe the issue of existential import, and explain how it makes Boolean logic necessary.
6. Symbolize categorical propositions with Venn diagrams.

Chapter 6 presents the basics of syllogistic logic. You will learn what standard form categorical syllogisms are, and how to identify their mood and figure. Once you can do this, you will be prepared to understand how, of the 256 possible syllogisms, only 15 are valid.

After reading this chapter, you should be able to:

1. Identify major, minor, and middle terms.
2. Describe what distribution is.
3. Use Venn diagrams to see if syllogisms are valid.
4. Use the six rules for testing syllogisms.
5. Give the names of the 15 valid syllogisms.
6. Describe how the 15 valid syllogisms can be deduced from the six rules.

Most arguments in the real world do not come in the rather stilted, standard form of categorical syllogism. Chapter 7 outlines how real arguments in ordinary language can be translated and converted into forms that make them closer to the standard form—and thus renders them analyzable with the tools you've already learned.

After reading this chapter, you should be able to:

1. Describe how regular syllogistic arguments differ from standard form categorical syllogisms.
2. Understand how arguments that appear to have more than three terms often really have only three.
3. Translate arguments into standard form to allow them to be tested with Venn diagrams or the rules of syllogisms.
4. Use parameters to translate difficult syllogistic arguments.
5. Identify enthymemes and know how to translate them.
6. Translate hypothetical and disjunctive syllogisms into standard form.
7. See how dilemmas can be used in argument.

Chapter 8 presents the fundamental concepts of modern symbolic logic. Since the analysis and appraisal of arguments is made difficult by the peculiarities of language, the system of modern symbolic logic was set up to be independent of language. Using a system of artificial symbols, modern symbolic logic attempts to move the analysis of argument directly to the issue of validity, bypassing the vagaries of any specific language.

After reading this chapter, you should be able to:

1. Use the special symbols: the dot, wedge, horseshoe, curl, and three bars.
2. Understand how these symbols are used to express negation, conjunction, disjunction, material implication, and material equivalence.
3. Use truth tables to test the validity of argument forms.
4. Deal with statement forms, including tautologous, contradictory, and contingent forms.
5. Use logical equivalence and De Morgan's theorems, as well as the principle of double negation.
6. Understand why the paradoxes of material implication are not really paradoxes after all.
7. Discuss the proper place of identity, non-contradiction, and excluded middle in logic.

This chapter explains the method of deduction in symbolic logic, which proves arguments valid or invalid more efficiently than truth tables. In addition, it introduces a simplified version of the truth table, which can be used to find an invalidating instance of an argument. If such an instance can be found, it is conclusive proof of the argument's invalidity.

After reading this chapter, you should be able to:

1. Construct a formal proof of validity using the nineteen rules of inference.
2. Understand the difference between the elementary valid argument forms and the logically true biconditionals.
3. Use "The Rule of Replacement" to substitute logical equivalences for each other within statements.
4. Discuss the strange situation that arises when no possible assignment of truth values permits the premises of an argument to be true at the same time, though such an argument must still be counted valid.

Chapter 10 presents an introduction to quantification theory, which offers a powerful method for dealing with deductive arguments whose constituents are not compound—which means that their validity depends on the inner logical structure of their propositions. The chapter introduces a new notation and a new concept: the propositional function.

After reading this chapter, you should be able to:

1. Understand the concept of a propositional function, and how a proposition may be obtained from a propositional function by instantiation.
2. Obtain propositions from propositional functions by means of generalization.
3. Use the universal quantifier (x) and the existential quantifier (õx).
4. Apply the four additional rules of inference: UI, UG, EI, and EG (universal instantiation and generalization, and existential instantiation and generalization).
5. Use the method of refutation by logical analogy to prove the invalidity of arguments involving quantifiers.
6. Symbolize and evaluate asyllogistic arguments (those not reducible to A, E, I, and O propositions, or singular propositions).

Chapter 11 moves from the analysis of deductive arguments, which are either valid or invalid, to the evaluation of inductive arguments, which can be highly probable but never absolutely certain. The most common type of inductive argument is argument by analogy. Every analogical argument can be determined to be more or less probable based on just six criteria. Analogies are also powerful tools for refuting both inductive and deductive arguments.

After reading this chapter, you should be able to:

1. Determine whether an analogy is used as an argument or for another purpose (such as an explanation).
2. Apply the six criteria for determining whether the premises of an analogical argument render its conclusion more or less probable.
3. Refute analogical arguments using logical analogies.

This chapter will introduce you to the reasons why this type of reasoning is so difficult to analyze and formalize. Central to the problematic nature of causal connections is the concept of causation itself. Most of the chapter concentrates on an explication of John Stuart Mill's five methods of experimental inquiry, which are:

• The method of agreement
• The method of difference
• The joint method of agreement and difference
• The method of residues
• The method of concomitant variation

After reading this chapter, you should be able to:

1. Discuss the various meanings of "cause."
2. Explain the nature of inductive generalization and the method of simple enumeration.
3. Understand Mill's five methods and apply them to causal relationships.
4. Appreciate the importance of these methods to inquiries of all kinds, including scientific hypotheses.
5. See the limitations in Mill's methods and understand their causes.

Chapter 13 will help you understand how scientific hypotheses are formulated and evaluated. Though even established laws of nature are somewhat hypothetical, there are still good ways to distinguish between fruitful and unhelpful hypotheses.

After reading this chapter, you should be able to:

1. Understand the practical and other values of scientific inquiry.
2. Distinguish between hypothetical, scientific explanations—which are empirically verifiable—and unscientific, dogmatic explanations.
3. Evaluate hypotheses using the five criteria: Relevance, Testability, Compatibility, Predictive power, and Simplicity. /li>
4. Identify the seven stages of scientific investigation.
5. Understand how crucial experiments are used.
6. Distinguish between different types of ad hoc hypothesis.
7. Recognize how classification is a valuable scientific instrument.

In chapter 14, you will learn that it is often possible to attach quantitative measures to conclusions about probable events. Probability can be conceived of in two alternative ways. When the outcome of an event is due to characteristics of the event being measured, then probability is an a priori conception. When we cannot know in advance what percentage of outcomes will be of a certain type, we take the relative frequency approach. If an event is complex, the probability of its occurrence may still be calculated, using a calculus of probability, as long as the probabilities of its component parts can be determined. You will also learn how to compute expected value, such as the return on investments. You will find that the expected outcomes for many intuitively "sound" bets are not worth it.

After reading this chapter, you should be able to:

1. Apply both the "relative frequency" and "a priori" theories of probability.
2. Use the calculus of probability, including the product theorem and the addition theorem.
3. Calculate probability based on joint occurrences and alternative occurrences.
4. Compute the expected value of an investment or wager.