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Unformatted text preview: sicC 1.1 Arguments, Premises, and Conclusions Logic may be defined as the organized body of knowledge, or science, that evaluates arguments. All of us encounter arguments in our day-to-day experience. We read them in books and newspapers, hear them on television, and formulate them when communicating with friends and associates. The aim of logic is to develop a system of methods and principles that we may use as criteria for evaluating the arguments of others and as guides in constructing arguments of our own. Among the benefits to be expected from the study oflogic is an increase in confidence that we are making sense when we criticize the arguments of others and when we advance arguments of our own. An argument, in its most basic form, is a group of statements, one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion). All arguments may be placed in one of two basic groups: those in which the premises really do support the conclusion and those in which they do not, even though they are claimed to. The former are said to be good arguments (at least to that extent), the latter bad arguments. The purpose oflogic, as the science that evaluates arguments, is thus to develop methods and techniques that allow us to distinguish good arguments from bad. As is apparent from the given definition, the term argument has a very specific meaning in logic. It does not mean, for example, a mere verbal fight, as one might have with one's parent, spouse, or friend. Let us examine the features of this definition in greater detail. First of all, an argument is a group of statements. A statement is a sentence that is either true or false-in other words, typically a declarative sentence or a sentence component that could stand as a declarative sentence. The following sentences are statements: Chocolate truffles are loaded with calories. Melatonin helps relieve jet lag. Political candidates always tell the complete truth. No wives ever cheat on their husbands. Tiger Woods plays golf and Maria Sharapova plays tennis. See information on our website: 1 The first two statements are true, the second two false. The last one expresses two statements, both of which are true. Truth and falsity are called the two possible truth values of a statement. Thus, the truth value of the first two statements is true, the truth value of the second two is false, and the truth value of the last statement, as well as that of its components, is true. Unlike statements, many sentences cannot be said to be either true or false. Questions, proposals, suggestions, commands, and exclamations usually cannot, and so are not usually classified as statements. The following sentences are not statements: Where is Khartoum? Let's go to a movie tonight. I suggest you get contact lenses. Turn off the TV right now. Fantastic! (question) (proposal) (suggestion) (command) (exclamation) The statements that make up an argument are divided into one or more premises and one and only one conclusion. The premises are the statements that set forth the reasons or evidence, and the conclusion is the statement that the evidence is claimed to support or imply. In other words, the conclusion is the statement that is claimed to follow from the premises. Here is an example of an argument: All film stars are celebrities. Halle Berry is a film star. Therefore, Halle Berry is a celebrity. The first two statements are the premises; the third is the conclusion. (The claim that the premises support or imply the conclusion is indicated by the word "therefore.") In this argument the premises really do support the conclusion, and so the argument is a good one. But consider this argument: Some film stars are men. Cameron Diaz is a film star. Therefore, Cameron Diaz is a man. In this argument the premises do not support the conclusion, even though they are claimed to, and so the argument is not a good one. One of the most important tasks in the analysis of arguments is being able to distinguish premises from conclusions. If what is thought to be a conclusion is really a premise, and vice versa, the subsequent analysis cannot possibly be correct. Many arguments contain indicator words that provide clues in identifying premises and conclusion. Some typical conclusion indicators are therefore wherefore thus consequently we may infer accordingly we may conclude it must be that for this reason so entails that hence it follows that implies that as a result Whenever a statement follows one of these indicators, it can usually be identified as the conclusion. By process of elimination the other statements in the argument are the premises. Example: 2 Chapter 1 Basic Concepts Tortured prisoners will say anything just to relieve the pain. Consequently, torture is not a reliable method of interrogation. The conclusion of this argument is "Torture is not a reliable method of interrogation;' and the premise is "Tortured prisoners will say anything just to relieve the pain." Claimed evidence Premises \; premises forth the What is claimed to follow from the evidence Conclusion If an argument does not contain a conclusion indicator, it may contain a premise indicator. Some typical premise indicators are In si nce as indicated by because for in that may be inferred from as given that seeing that for the reason t hat inasmuch as owing to Any statement following one of these indicators can usually be identified as a premise. Example: Expectant mothers should never use recreational drugs, since the use of these drugs can jeopardize the development of the fetus. they are as are the The premise of this argument is "The use of these drugs can jeopardize the development of the fetus," and the conclusion is "Expectant mothers should never use recreational drugs." In reviewing the list of indicators, note that "for this reason" is a conclusion indicator, whereas "for the reason that" is a premise indicator. "For this reason" (except when followed by a colon) means for the reason (premise) that was just given, so what follows is the conclusion. On the other hand, "for the reason that" announces that a premise is about to be stated. Sometimes a single indicator can be used to identify more than one premise. Consider the following argument: It is vitally important that wilderness areas be preserved, for wilderness provides essential habitat for wildlife, including endangered species, and it is a natural retreat from the stress of daily life. The premise indicator "for" goes with both "Wilderness provides essential habitat for wildlife, including endangered species," and "It is a natural retreat from the stress of Section 1.1 Arguments, Premises, and Conclusions 3 daily life." These are the premises. By method of elimination, "It is vitally importan11 that wilderness areas be preserved" is the conclusion. Some arguments contain no indicators. With these, the reader/listener must ask< such questions as: What single statement is claimed (implicitly) to follow from the; others? What is the arguer trying to prove? What is the main point in the passage? The; answers to these questions should point to the conclusion. Example: The space program deserves increased expenditures in the years ahead. Not only does the national defense depend on it, but the program will more than pay for itself in terms of technological spinoffs. Furthermore, at current funding levels the program cannot fulfill its anticipated potential. The conclusion of this argument is the first statement, and all of the other statements are premises. The argument illustrates the pattern found in most arguments: that lack indicator words: the intended conclusion is stated first, and the remaining statements are then offered in support of this first statement. When the argument is restructured according to logical principles, however, the conclusion is always listed after the premises: P1 : P2 : P3 : C: The national defense is dependent on the space program. The space program will more than pay for itself in terms of technological spinoffs. At current funding levels the space program cannot fulfill its anticipated potential. The space program deserves increased expenditures in the years ahead. When restructuring arguments such as this, one should remain as close as possible to the original version, while at the same time attending to the requirement that premises and conclusion be complete sentences that are meaningful in the order in which they are listed. Note that the first two premises are included within the scope of a single sentence in the original argument. For the purposes of this chapter, compound arrangements of statements in which the various components are all claimed to be true will be considered as separate statements. Passages that contain arguments sometimes contain statements that are neither premises nor conclusions. Only statements that are actually intended to support the conclusion should be included in the list of premises. If, for example, a statement serves merely to introduce the general topic, or merely makes a passing comment, it should not be taken as part of the argument. Examples: The claim is often made that malpractice lawsuits drive up the cost of health care. But if such suits were outlawed or severely restricted, then patients would have no means of recovery for injuries caused by negligent doctors. Hence, the availability of malpractice litigation should be maintained intact. Currently 47 million Americans are without health insurance. When these people go to a hospital, they are routinely charged two to three times the normal cost for treatment. This practice, which covers the cost of treating indigent patients, is clearly unfair. For these reasons, a national health insurance program should be adopted. Politicians who oppose this change should be ashamed of themselves. 4 Chapter 1 Basic Concepts In the first argument, the opening statement serves merely to introduce the topic, so it is not part of the argument. The premise is the second statement, and the conclusion is the last statement. In the second argument, the final statement merely makes a passing comment, so it is not part of the argument. The premises are the first three statements, and the statement following "for these reasons" is the conclusion. Closely related to the concepts of argument and statement are those of inference and proposition. An inference, in the narrow sense of the term, is the reasoning process expressed by an argument. In the broad sense of the term, "inference" is used interchangeably with "argument." Analogously, a proposition, in the narrow sense, is the meaning or information content of a statement. For the purposes of this book, however, "proposition" and "statement" are used interchangeably. Note on the History of Logic The person who is generally credited as the father of logic is the ancient Greek philosopher Aristotle (384-322 B.C.). Aristotle's predecessors had been interested in the art of constructing persuasive arguments and in techniques for refuting the arguments of others, but it was Aristotle who first devised systematic criteria for analyzing and evaluating arguments. Aristotle's chief accomplishment is called syllogistic logic, a kind of logic in which the fundamental elements are terms, and arguments are evaluated as good or bad depending on how the terms are arranged in the argument. Chapters 4 and 5 of this textbook are devoted mainly to syllogistic logic. But Aristotle also deserves credit for originating modal logic, a kind of logic that involves such concepts as possibility, necessity, belief, and doubt. In addition, Aristotle catalogued several informal fallacies, a topic treated in Chapter 3 of this book. After Aristotle's death, another Greek philosopher, Chrysippus (280-206 B.c.), one of the founders of the Stoic school, developed a logic in which the fundamental elements were whole propositions. Chrysippus treated every proposition as either true or false and developed rules for determining the truth or falsity of compound propositions from the truth or falsity of their components. In the course of doing so, he laid the foundation for the truth functional interpretation of the logical connectives presented in Chapter 6 of this book and introduced the notion of natural deduction, treated in Chapter 7. For thirteen hundred years after the death of Chrysippus, relatively little creative work was done in logic. The physician Galen (A.D. 129-ca. 199) developed the theory of the compound categorical syllogism, but for the most part philosophers confined themselves to writing commentaries on the works of Aristotle and Chrysippus. Boethius (ca. 480-524) is a noteworthy example. The first major logician of the Middle Ages was Peter Abelard ( 1079-1142). Abelard reconstructed and refined the logic of Aristotle and Chrysippus as communicated by Boethius, and he originated a theory of universals that traced the universal character of general terms to concepts in the mind rather than to "natures" existing outside the mind, as Aristotle had held. In addition, Abelard distinguished arguments that are valid because of their form from those that are valid because of their content, but he Section 1.1 Arguments, Premises, and Conclusions S ristotle was born in Stagira, a small Greek town situated on the northern coast of the Aegean sea. His father was a physician in the court of King Amyntas II of Macedonia, and the young Aristotle was a friend of the King's son Philip, who was later to become king himself and the father of Alexander the Great. When he was about seventeen, Aristotle was sent to Athens to further his education in Plato's Academy, the finest institution of higher learning in the Greek world. After Plato's death Aristotle left for Assos, a small town on the coast of Asia Minor, where he married the niece of the local ruler. Six years later Aristotle accepted an invitation to return to Macedonia to serve as tutor of the young Alexander. When Alexander ascended the throne following his father's assassination, Aristotle's tutorial job was finished, and he departed for Athens where he set up a school near the temple of Apollo Lyceus. The school came to be known as the Lyceum, and Alexander supported it with contributions of money and specimens of flora and fauna derived from his far-flung conquests. After Alexander's death, an antiMacedonian rebellion forced Aristotle to leave Athens for Chalcis, about thirty miles to the north, where he died one year later at the age of sixty-two. Aristotle is universally recognized as the originator of logic. He defined logic as the study of the process by which a statement follows by necessity from one or more other statements. The most fundamental kind of statement, he thought, is the categorical proposition, and he classified the four kinds of categorical propositions in terms of their being universal, particular, affirmative, and negative. He also developed the square of opposition, which shows how one such proposition implies the truth or falsity of another, and he identified the relations of conversion, obversion, and contraposition, which provide the basis for various immediate inferences. His crowning achievement is the theory of the categorical syllogism, a kind of argument consisting of three categorical propositions. He showed how categorical syllogisms can be catalogued in terms of mood and figure, and he developed a set of rules for determining the validity of categorical syllogisms. Also, he showed how the modal concepts of possibility and necessity apply to categorical propositions. In addition to the theory of the syllogism, Aristotle advanced the theory of definition by genus and difference, and he showed how arguments could be defective in terms of thirteen forms of informal fallacy. Aristotle made profound contributions to many areas of human learning including biology, physics, metaphysics, epistemology, psychology, aesthetics, ethics, and politics. However, his accomplishments in logic were so extensive and enduring that two thousand years after his death, the great philosopher Immanuel Kant said that Aristotle had discovered everything that could be known about logic. His logic was not superseded until the end of the nineteenth century when Frege, Whitehead, and Russell developed modern mathematical logic. 6 Chapter 1 Basic Concepts held that only formal validity is the "perfect" or conclusive variety. The present text follows Abelard on this point. After Abelard, the study of logic during the Middle Ages flourished through the work of numerous philosophers. A logical treatise by William of Sherwood (ca. 1200-1271) contains the first expression of the "Barbara, Celarent .. :'poem quoted in Section 5.1 of this book, and the Summulae Logicales of Peter of Spain (ca. 1205-1277) became the standard textbook in logic for three hundred years. However, the most original contributions from this period were made by William of Ockham (ca. 1285-134 7). Ockham extended the theory of modal logic, conducted an exhaustive study of the forms of valid and invalid syllogisms, and further developed the idea of a metalanguage, a higher-level language used to discuss linguistic entities such as words, terms, and propositions. Toward the middle of the fifteenth century, a reaction set in against the logic of the Middle Ages. Rhetoric largely displaced logic as the primary focus of attention; the logic of Chrysippus, which had already begun to lose its unique identity in the Middle Ages, was ignored altogether, and the logic of Aristotle was studied only in highly simplistic presentations. A reawakening did not occur until two hundred years later through the work of Gottfried Wilhelm Leibniz ( 1646-1716). Leibniz, a genius in numerous fields, attempted to develop a symbolic language or "calculus" that could be used to settle all forms of disputes, whether in theology, philosophy, or international relations. As a result of this work, Leibniz is sometimes credited with being the father of symbolic logic. Leibniz's efforts to symbolize logic were carried into the nineteenth century by Bernard Balzano ( 1781-1848). In the middle of the nineteenth century, logic commenced an extremely rapid period of development that has continued to this day. Work in symbolic logic was done by many philosophers and mathematicians, including Augustus De Morgan ( 18061871), George Boole (1815-1864), William Stanley Jevons (1835-1882), and John Venn (1834-1923 ). The rule bearing De Morgan's name is used in Chapter 7 of this book. Boole's interpretation of categorical propositions and Venn's method for diagramming them are covered in Chapters 4 and 5. At the same time a revival in inductive logic was initiated by the British philosopher John Stuart Mill (1806-1873 ), whose methods of induction are presented in Chapter 10. Across the Atlantic, the American philosopher Charles Sanders Peirce (1839-1914) developed a logic of relations, invented symbolic quantifiers, and suggested the truthtable method for formulas in propositional logic. These topics are covered in Chapters 6 and 8 of this book. The truth-table method was completed independently by Emile Post (1897-1954) and LudwigWittgenstein (1889-1951). Toward the end of the nineteenth century, the foundations of modern mathematicallogic were laid by Gottlob Frege ( 1848-1925). His Begriffsschrift sets forth the theory of quantification presented in Chapter 8 of this text. Frege's work was continued into the twentieth century by Alfred North Whitehead (1861-1947) and Bertrand Russell (1872-1970), whose monumental Principia Mathematica attempted to reduce the whole of pure mathematics to logic. The Principia is the source of much of the symbolism that appears in Chapters 6, 7, and 8 of this text. During the twentieth century, much of the work in logic has focused on the formalization of logical systems and on questions dealing with the completeness and Section 1.1 Arguments, Premises, and Conclusions 7 consistency of such systems. A now-famous theorem proved by Kurt Godel (19061978) states that in any formal system adequate for number theory there exists an undecidable formula-that is, a formula such that neither it nor its negation is derivable from the axioms of the system. Other developments include multivalued logics and the formalization of modal logic. Most recently, logic has made a major contribution to technology by providing the conceptual foundation for the electronic circuitry of digital computers. EXERCISE 1.1 I. Each of the following passages contains a single argument. Using the letters "P" and "c;"identify the premises and conclusion of each argument, writing premises first and conclusion last. List the premises in the order in which they make the most sense (usually the order in which they occur), and write both premises and conclusion in the form of separate declarative sentences. Indicator words may be eliminated once premises and conclusion have been appropriately labeled. The exercises marked with a star are answered in the back of the book. *1. Titanium combines readily with oxygen, nitrogen, and hydrogen, all of which have an adverse effect on its mechanical properties. As a result, titanium must be processed in their absence. (Illustrated World of Science Encyclopedia) 2. Since the good, according to Plato, is that which furthers a person's real interests, it follows that in any given case when the good is known, men will seek it. (Avrum Stroll and Richard Popkin, Philosophy and the Human Spirit) 3. As the denial or perversion of justice by the sentences of courts, as well as in any other manner, is with reason classed among the just causes of war, it will follow that the federal judiciary ought to have cognizance of all causes in which the citizens of other countries are concerned. (Alexander Hamilton, Federalist Papers, No. 80) *4. When individuals voluntarily abandon property, they forfeit any expectation of privacy in it that they might have had. Therefore, a warrantless search or seizure of abandoned property is not unreasonable under the Fourth Amendment. (Judge Stephanie Kulp Seymour, United States v.Jones) 5. Artists and poets look at the world and seek relationships and order. But they translate their ideas to canvas, or to marble, or into poetic images. Scientists try to find relationships between different objects and events. To express the order they find, they create hypotheses and theories. Thus the great scientific theories are easily compared to great art and·great literature. (Douglas C. Giancoli, The Ideas of Physics, 3rd ed.) 6. The fact that there was never a land bridge between Australia and mainland Asia is evidenced by the fact that the animal species in the two areas are very different. Asian placental mammals and Australian marsupial mammals have not been in contact in the last several million years. (T. Douglas Price and Gary M. Feinman, Images of the Past) 8 Chapter 1 Basic Concepts exists an unis derivable logics and contribution circuitry of *7. Cuba's record on disaster prevention is impressive. After October 1963, when Hurricane Flora devastated the island and killed more than a thousand people, the Cuban government overhauled its civil defense system. It was so successful that when six powerful hurricanes thumped Cuba between1996 and 2002 only 16 people died. And when Hurricane Ivan struck Cuba in 2004 there was not a single casualty, but the same storm killed at least 70 people in other Caribbean countries. (Newspaper clipping) premises they make the premises and words maybe labeled. The 8. The classroom teacher is crucial to the development and academic success of the average student, and administrators simply are ancillary to this effort. For this reason, classroom teachers ought to be paid at least the equivalent of administrators at all levels, including the superintendent. (Peter F. Falstrup, letter to the editor) 9. An agreement cannot bind unless both parties to the agreement know what they are doing and freely choose to do it. This implies that the seller who intends to enter a contract with a customer has a duty to disclose exactly what the customer is buying and what the terms of the sale are. (Manuel G. Velasquez, "The Ethics of Consumer Production") * 10. Punishment, when speedy and specific, may suppress undesirable behavior, but it cannot teach or encourage desirable alternatives. Therefore, it is crucial to use positive techniques to model and reinforce appropriate behavior that the person can use in place of the unacceptable response that has to be suppressed. (Walter Mischel and Harriet Mischel, Essentials of Psychology) as well as in 11. Profit serves a very crucial function in a free enterprise economy, such as our own. High profits are the signal that consumers want more of the output of the industry. High profits provide the incentive for firms to expand output and for more firms to enter the industry in the long run. For a firm of aboveaverage efficiency, profits represent the reward for greater efficiency. (Dominic Salvatore, Managerial Economics, 3rd ed.) order. But they Scientists To express the great scientific 12. Cats can think circles around dogs! My cat regularly used to close and lock the door to my neighbor's doghouse, trapping their sleeping Doberman inside. Try telling a cat what to do, or putting a leash on him-he'll glare at you and say, "I don't think so. You should have gotten a dog." (Kevin Purkiser, letter to the editor) * 13. Since private property helps people define themselves, since it frees people from mundane cares of daily subsistence, and since it is finite, no individual should accumulate so much property that others are prevented from accumulating the necessities of life. (Leon P. Baradat, Political Ideologies, Their Origins and Impact) 14. To every existing thing God wills some good. Hence, since to love any thing is nothing else than to will good to that thing, it is manifest that God loves everything that exists. (Thomas Aquinas, Summa Theologica) Section 1.1 Arguments, Premises, and Conclusions 9 ...
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