Week 2

LOGICProf Roy Shaff Chapters 2-3

Key Terms for Ch 2-3 Diagramming Paraphrasing Matrix Retrograde analysis Brain teasers Authorial intent Informative discourse Expressive discourse Directive discourse Ceremonial Performative Declarative Interrogative Exclamatory Imperative Emotive language Disagreement in attitude Emotively neutral language Disagreement in belief Merely verbal disputes Apparently verbal disputes Obviously genuine disputes Lexical definitions Precising definitions Stipulative definitions Persuasive definitions Ostensive definition Theoretical definitions Intension Connotative definition Extension Denotative definition Operational definition Quasi-ostensive definition Synonymous definition Definition by example Definition by genus and difference

3 Objectives When you complete this lesson, you will be able to: Paraphrase arguments and diagram arguments Identify interwoven, complex arguments Solve reasoning problems List and describe the three different types of disputes Describe the five different types of definitions Differentiate between extension and intension Describe the six techniques for creating definitions List the five rules for definition by genus and difference

Analyzing Arguments Arguments can be analyzed, once recognized, by paraphrasing them or by diagramming them.

Paraphrasing Paraphrasing involves setting forth the argument in a clear and precise form.

Paraphrasing Exercises #1 Premise: The Detroit Pistons are an all-around better team than the San Antonio Spurs. Conclusion: The Pistons did not lose [the NBA finals, in 2005] because of lack of ability. Premise: The Pistons will beat the Spurs two out of every three times; and the Spurs will win one out of every three times. Premise: The Pistons had won the 5th and 6th games of the series — two in a row, so if they had won the final game they would have won three out of three. Conclusion: The Pistons lost because of the law of averages.

Paraphrasing Exercises #2 Premise: Universities have commonly offered strange literary theories, and assorted oddities, in place of the writing courses that ought to have been offered. Students have been unknowingly shortchanged. Conclusion: That is why vast numbers of students cannot express themselves well in writing.

Paraphrasing Exercises #3 Premise: People divided on ethnic lines tend not to adopt programs that will give mutual support. Conclusion: (and premise of the following argument): Therefore nations that are racially diverse tend to have lower levels of social support than nations that are racially homogenous. Conclusion: Therefore a welfare state is in tension with a racially diverse population; the more racially diverse a community is, the more difficult it is to maintain comprehensive welfare programs.

Paraphrasing Exercises #4 Premise: If freedom were a natural part of the human condition we could expect to find free societies spread throughout human history. Premise: We do not find that, but instead find every sort of tyrannical government, from time immemorial. Conclusion: it is simply false to say (as Orlando Patterson does) that freedom is a natural part of the human condition.

Paraphrasing Exercises #5 Premise: if future scientists find a way to signal back in time, their signals would already have reached us. Premise: No such signals have ever reached us. Conclusion: Future scientists never will find a way to signal back in time.

Paraphrasing Exercises #6 Premise: Japanese and European whale-hunting countries have no need to eat whales; they can choose their diets. Premise: Eskimos live in an environment so harsh that their survival obliges them to eat whales; they have no choice in dietary matters. Conclusion: Permitting primitive Eskimos to kill some whales for survival, while at the same time demanding that modern societies cease to hunt whales, is fair and reasonable, not hypocritical.

Paraphrasing Exercises #7 Premise: The number of atoms in all of space is so huge that we can never count them or count the forces that drive them in all places. Conclusion: There must be other worlds, in other places, with different kinds of men and animals.

Paraphrasing Exercises #8 Premise: Where marriages are prearranged, divorce rates are very low. Often one later comes to love the person to whom one is married. Premise: Where marriages are formed on the basis of romantic love, divorce rates are very high; often one later comes not to love the person chosen on that basis. Conclusion: We ought not suppose that romantic love is a necessary precondition of successful marriage.

Paraphrasing Exercises #9 Premise: Our tax system depends upon the willingness of persons to pay the taxes they owe. Premise: That willingness depends, in turn, upon the widespread belief that almost everyone, including competitor and neighbors, are also paying the taxes they owe. Conclusion: If the Internal Revenue Service (the IRS) cannot assure us that this fairness is reasonable for us to suppose, the entire system of voluntary tax payments is seriously(and perhaps irremediably) threatened.

Paraphrasing Exercises #10 Premise: People and government are obsesses with racism and talk about it endlessly. Premise: But we don’t listen and we don’t see, and therefore we remain in a state of dental, thinking ourselves absolved of all complicity in racism. Conclusion: invariably we conclude that it is the other guy who is in the wrong.

Diagramming Arguments Diagramming involves the laying out the structure of the argument in two-dimensional spatial relations. Premise and conclusion are numbered and arranged to identify the relations of support between propositions.

19 Diagramming (1) Contrary to what many people think, a positive test for HIV is not necessarily a death sentence. For one thing, (2) the time from the development of antibodies to clinical symptoms averages nearly ten years. For another, (3) many reports are now suggesting that a significant number of people who test positive may never develop clinical AIDS. 2 3 1

20 Diagramming, continued (1) If an action promotes the best interests of everyone concerned and violates no one’s rights, then that action is morally acceptable. (2) In at least some cases, active euthanasia promotes the best interests of everyone concerned, and violates no one’s rights. Therefore (3) in at least some cases active euthanasia is morally acceptable. 1 2 3

21 Interwoven Arguments (1) To hasten the social revolution in England is the most important object of the International Workingman’s Association. (2) The sole means of hastening it is to make Ireland independent. Hence (3) the task of the “International” is everywhere to put conflict between England and Ireland in the foreground, and (4) everywhere to side openly with Ireland. 1 2 3 4

22 Compressed argument Because (1) the greatest mitochondrial variations occurred in African people, scientists concluded that (2) they had the longest evolutionary history, indicating (3) a probable African origin for modern humans. 1 2 3 Interwoven Arguments, continued

23 1 2 3 Interwoven Arguments, continued The more mitochondrial variation in a people the longer its evolutionary history; The greatest mitochondrial variations occurred in Africa; Therefore African people have had the longest evolutionary history. African people have had the longest evolutionary history; Modern humans probably originated where people have had the longest evolutionary history; Therefore modern humans probably originated in Africa.

24 Multiple arguments (1) It is not necessary – no, nor so much as convenient – that the legislative should be always in being; but (2) absolutely necessary that the executive power should, because (3) there is not always need of new laws to be made, but (4) always need of execution of the laws that are made. 3 1 4 2 Interwoven Arguments, continued

Diagramming Exercises #1 In a recent attack upon the evils of suburban sprawl, the authors argue as follows: The dominant characteristic of sprawl is that each component of a community—housing, shopping centers, office parks, and civic institutions—is segregated, physically separated from the others, causing the residents of suburbia to spend an inordinate amount of time and money moving from one place to the next. And since nearly everyone drives alone, even a sparsely populated area can generate the traffic of a much larger traditional town.34

Diagramming Exercises #1 1 The dominant characteristics of sprawl is that each component of a community – housing, shopping centers, office parks, and civic institutions – is segregated physically separated from the others, causing 2 the residents of suburbia to spend an ordinate amount of time and money moving from one place to the next. And since 3 nearly everyone drives alone, 4 even a sparsely populated area can generate the traffic of a much larger traditional town.

Diagramming Exercises #2 1 At any cost we must have filters on our Ypsilanti Township library computers. 2 Pornography is a scourge on society at every level. 3 Our public library must not be used to channel this filth to the people of the area.

Diagramming Exercises #3 1 At this best, Lyndon Johnson was one of the greatest of all American Presidents. 2 He did more for racial justice than any president since Abraham Lincoln. 3 He built more social protections than anyone since Franklin Roosevelt. 4 He was probably the greatest legislative politician in American history. 5 He was also one of the most ambitious idealists. 6 Johnson sought power to use it to accomplish great things.

Diagramming Exercises #4 1Married people are healthier and more economically stable than single people, and 2 children of married people do better on a variety of indicators. 3 Marriage is thus a socially responsible act. 4There ought to be some way of spreading the principle of support for marriage throughout the tax code.

Diagramming Exercises #5 1 Vacuum cleaners to insure clean houses are praiseworthy and essential to our standard of living. 2 Street cleaners to insure clean streets are an unfortunate expense. Partly as a result 3 our houses are generally clean and 4 our streets generally filthy.

Diagramming Exercises #6 1 We are part of Europe. 2 It affects us directly and deeply. Therefore 3 we should exercise leadership in order to change Europe in the direction we want.

Complex Arguements Some arguments are exceedingly complex, involving several arguments interwoven together. One must understand the author’s intent and capture the flow of reasoning. Often, an argument can be analyzed in more than one way and more than one plausible interpretation may be offered. Once the structure of the argument is revealed through careful analysis, one can consider whether the premises really do support the conclusion.

35 Complex Argumentative Passages (1) The Big Bang Theory is crumbling… (2) According to orthodox wisdom, the cosmos began with the Big Bang – an immense, perfectly symmetrical explosion 20 billion years ago. The problem is that (3) astronomers have confirmed by observation the existence of huge conglomerations of galaxies that are simply too big to have been formed in a mere 20 billion years... Studies based on new data collected by satellite, and backed up by earlier ground surveys, show that (4) galaxies are clustered into vast ribbons that stretch billions of light years, and (5) are separated by voids hundreds of millions of light years across. Because (6) galaxies are observed to travel at only a small fraction of the speed of light, mathematics shows that (7) such large clumps of matter must have taken at least one hundred billion years to come together – five times as long as the time since the hypothetical Big Bang. (3) Structures as big as those now seen can’t be made in 20 billion years… (2) The Big Bang theorizes that matter was spread evenly through the universe. From this perfection, (3) there is no way for such vast clumps to have formed so quickly.

36 Diagram 4 5 6 7 3 2 1 Complex Argumentative Passages,

37 Problems in Reasoning Alonzo, Kurt, Rudolph, and Willard are four creative artists of great talent. One is a dancer, one is a painter, one is a singer, and one is a writer, although not necessarily in that order. Can you discern each man’s artistic field? Alonzo and Rudolph were in the audience the night the singer made his debut on the concert stage. Both Kurt and the writer have had their portraits painted from life by the painter. The writer, whose biography of Willard was a best-seller, is planning to write a biography of Alonzo. Alonzo has never heard of Rudolph.

38 Problems in Reasoning, continued Matrix Alonzo and Rudolph were in the audience the night the singer made his debut on the concert stage.

39 Problems in Reasoning, continued Both Kurt and the writer have had their portraits painted from life by the painter.

40 Problems in Reasoning, continued The writer, whose biography of Willard was a best-seller, is planning to write a biography of Alonzo.

41 Problems in Reasoning, continued Writer is not Alonzo, Kurt or Willard, so it must be Rudolph

42 Problems in Reasoning, continued Both Kurt and the writer have had their portraits painted from life by the painter. Alonzo has never heard of Rudolph

43 Problems in Reasoning, continued Since Willard is the painter, Kurt is the singer

44 Problems in Reasoning, continued Since Kurt is the singer, Alonzo is the dancer

45 Disputes and Definitions Obviously genuine dispute Disputants unambiguously disagree, either in belief or in attitude Merely verbal dispute Apparent differences are not genuine Resolved by coming to an agreement on how some word or phrase is used Apparently verbal but really genuine disputes When the misunderstanding involving the terms is resolved, there remains a disagreement that goes beyond the words used

46 Disputes and Definitions, continued Is there some ambiguity that can be eliminated? Does clearing up the ambiguity provide resolution? If yes, then merely verbal If no, then apparently verbal although really genuine

47 Definitions and Their Uses Definitions of symbols Word is being defined or the thing itself is being defined The word triangle means a plane figure enclosed by three straight lines A triangle is (by definition) a plane figure enclosed by three straight lines.

48 Definitions and Their Uses, continued Definiendum The symbol being defined Definiens The symbol, or group of symbols, that has the same meaning as the definiendum

49 Definitions and Their Uses, continued Stipulative definition Proposal to arbitrarily assign meaning to a newly introduced symbol Neither true nor false Neither accurate nor inaccurate

50 Definitions and Their Uses, continued Lexical definition Reports a meaning the definiendum already has May be either true or false

51 Definitions and Their Uses, continued Precising definitions Used to eliminate ambiguity or vagueness Its difiniendum is not a new term Established usage must be respected, while making the known term more precise

52 Definitions and Their Uses, continued Theoretical definition Attempts to formulate a theoretically adequate or scientifically useful description of the objects to which the term applies As knowledge about some subject matter increases, one theoretical definition may be replaced by another Different theories are accepted at different times

53 Definitions and Their Uses, continued Persuasive definition Intended to influence attitudes or stir emotions Need to be guarded against when distinguishing good reasoning from bad

54 Extension, Intension, and the Structure of Definitions Extension The collection of objects to which a general term is correctly applied Intension The attributes shared by all objects, and only those objects, to which a general term applies

55 Extension and Denotative Definitions Denotative definition Based on the term’s extension Often impossible to enumerate all the objects in a general class Ostensive definition Demonstrative definition Term is defined by pointing at an object Quasi-ostensive definition Uses gesture and a descriptive phrase

56 Intension and the Intensional Definitions Subjective intension Set of all attributes the speaker believes to be possessed by objects denoted by that word Objective intension Total set of characteristics shared by all the objects in the word’s extension Conventional intension Public meaning that permits and facilitates communication

57 Intension and the Intensional Definitions, continued Synonymous definition Another word is provided, whose meaning is understood, as the meaning of the word being defined Operational definition Limits a term’s use to situations where certain actions or operations lead to specified results Definition by genus and difference Identify the larger class of which it is a member and the distinguishing attributes that characterize it specifically

58 Rules for Definition by Genus and Difference A definition should state the essential attributes of the species A definition must not be circular A definition must be neither too broad nor too narrow Ambiguous, obscure, or figurative language must not be used in a definition A definition should not be negative where it can be affirmative

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