REVIEW: The Structure of Argument: Conclusions and Premises

REVIEW: The Structure of Argument: Conclusions and Premises An argument consists of a conclusion (the claim that the speaker or writer is arguing for) and premises (the claims that he or she offers in support of the conclusion). Here is an example of an argument: [Premise] Every officer on the force has been certified, and [premise] nobody can be certified without scoring above 70 percent on the firing range. Therefore [conclusion] every officer on the force must have scored above 70 percent on the firing range.

The Structure of Argument: Conclusions and Premises • When we analyze an argument, we need to first separate the conclusion from the grounds for the conclusion which are called premises. Stating it another way, in arguments we need to distinguish the claim that is being made from the warrants that are offered for it. The claim is the position that is maintained, while the warrants are the reasons given to justify the claim. • It is sometimes difficult to make this distinction, but it is important to see the difference between a conclusion and a premise, a claim and its warrant, differentiating between what is claimed and the basis for claiming it.

The Structure of Argument: Conclusions and Premises • We might make a claim in a formal argument. For example, we might claim that teenage pregnancy can be reduced through sex education in the schools. • To justify our claim we might try to show the number of pregnancies in a school before and after sex education classes. • In writing an argumentative essay we must decide on the point we want to make and the reasons we will offer to prove it, the conclusion and the premises.

The Structure of Argument: Conclusions and Premises • The same distinction must be made in reading argumentative essays, namely, what is the writer claiming and the warrant is offered for the claim, what is being asserted and why. Take the following complete argument: • Television presents a continuous display of violence in graphically explicit and extreme forms. It also depicts sexuality not as a physical expression of internal love but in its most lewd and obscene manifestations. We must conclude, therefore, that television contributes to the moral corruption of individuals exposed to it.

The Structure of Argument: Conclusions and Premises • Whether we agree with this position or not, we must first identify the logic of the argument to test its soundness. In this example the conclusion is “television contributes to the moral corruption of individuals exposed to it.” The premises appear in the beginning sentences: “Television presents a continuous display of violence in graphic and extreme forms,” and “(television) depicts sexuality…in its most lewd and obscene manifestations.” Once we have separated the premises and the claim then we need to evaluate whether the case has been made for the conclusion.

The Structure of Argument: Conclusions and Premises • Has the writer shown that television does corrupt society? Has a causal link been shown between the depiction of lewd and obscene sex and the moral corruption of society? Does TV reflect violence in our society or does it promote it?

Conclusion Indicators • Since dissection is sometimes difficult because we cannot always see the skeleton of the argument. In such cases we can find help by looking for “indicator” words. When the words in the following list are used in arguments, they usually indicate a premise has just been offered and that a conclusion is about to be presented. • Consequently • Therefore • Thus • So • Hence • accordingly • We can conclude that • It follows that • We may infer that • This means that • It leads us to believe that • This bears out the point that

Conclusion Indicators II • Example: • Sarah drives a Dodge Viper. This means that either she is rich or her parents are. • The conclusion is: • Either she is rich or her parents are. • The premise is: • Sarah drives a Dodge Viper.

Premise Indicators When the words in the following list are used in arguments, they generally introduce premises. They often occur just after a conclusion has been given. • Since • Because • For • whereas • In as much as • For the reasons that • In view of the fact • As evidenced by

Premise Indicators II • Example: • Either Sarah is rich or her parents are, since she drives a Dodge Viper. • The premise is the claim that Sarah drives a Dodge Viper; the conclusion is the claim that either Sarah is rich or her parents are.

Indicator words can tell us when the theses and the supports appear, even in complex arguments that are embedded in paragraphs. We can see whether the person has good reasons for making the claim, or whether the argument is weak. We should keep this in mind when presenting our own case. • An argument that presents a clear structure of premises and conclusions, without narrative digressions, metaphorical flights, or other embellishments, is much easier for people to follow.

Categorical Propositions • To help us make sense of our experience, we humans constantly group things into classes or categories. These classifications are reflected in our everyday language. In formal reasoning the statements that contain our premises and conclusions have to be rendered in a strict form so that we know exactly what is being claimed. These logical forms were first formulated by Aristotle (384-322 B.C.). They are four in number, carrying the designations A, E, I, O, as follows: • All S is P (A). • No S is P (E). • Some S is P (I). • Some S is not P (O).

Categorical Propositions II • Aside from these four logical types, there is no other way of stating the relationship between the subject and the predicate of statements. They can be illustrated by the four following propositions: • All politicians are liars. • No politicians are liars. • Some politicians are liars. • Some politicians are not liars.

Universal Affirmative Propositions • The first is a universal affirmative proposition. It is about two classes, the class of all politicians and the class of all liars, saying that the first class is included or contained in the second class. A universal affirmative proposition says that every member of the first class is also a member of the second class. In the present example, the subject term “politicians” designates the class of all politicians, and the predicate term “liars” designates the class of all liars. Any universal affirmative proposition may be written schematically as All S is P. where the terms S and P represent the subject and predicate terms, respectively.

Universal Affirmative Propositions II • The name “universal affirmative” is appropriate because the position affirms that the relationship of class inclusion holds between the two classes and says that the inclusion is complete or universal: All members of S are said to be members of P also.

Universal negative propositions • The second example • No politicians are liars. Is a universal negative proposition. It denies of politicians universally that they are liars. Concerned with two classes, a universal negative proposition says that the first class is wholly excluded from the second, which is to say that there is no member of the first class that is also a member of the second. Any universal proposition may be written schematically as No S is P Where, again, the letters S and P represent the subject and predicate terms.

Universal negative propositions II • The name “universal negative” is appropriate because the proposition denies that the relation of class inclusion holds between the two classes – and denies it universally: No members at all of S are members of P.

Particular affirmative propositions II • The word “some” is indefinite. Does it mean “at least one,” or “at least two,” or “at least one hundred?” In this type of proposition, it is customary to regard the word “some” as meaning “at least one.” Thus a particular affirmative proposition, written schematically as • Some S is P. says that at least one member of the class designated by the subject term S is also a member of the class designated by the predicate term P. The name “particular affirmative” is appropriate because the proposition affirms that the relationship of class inclusion holds, but does not affirm it of the first class universally, but only partially, of some particular member or members of the first class.

Particular affirmative propositions • The third example • Some Politicians are liars. is a particular affirmative proposition. Clearly, what the present example affirms is that some members of the class of all politicians are (also) members of the class of all liars. But it does not affirm this of politicians universally: Not all politicians universally, but, rather, some particular politician or politicians, are said to be liars. This proposition neither affirms nor denies that all politicians are liars; it makes no pronouncement on the matter.

Particular negative propositions • The fourth example • Some politicians are not liars is a particular negative proposition. This example, like the one preceding it, does not refer to politicians universally but only to some member or members of that class; it is particular. But unlike the third example, it does not affirm that the particular members of the first class referred to are included in the second class; this is precisely what is denied. A particular negative proposition, schematically written as Some S is not P. says that at least one member of the class designated by the subject term S is excluded from the whole of the class designated by the predicate term P.

Exercises • Translate the following sentences into standard form categorical statements: • Each insect is an animal. • Not every sheep is white. • A few holidays fall on Saturday. • There are a few right – handed first basemen.

Venn Diagrams Liars Politicians Anything in area 1 is a politician, but not a liar. Anything in area 2 is both a politician and a liar. Anything in area 3 is a liar but not a politician. And anything in area 4, the area outside the two circles is neither a politician or a liar.

Venn Diagrams II Liars Politicians The shading means that the part of the politicians circle that does not overlap with the liars circle is empty; that is, it contains no members. The diagram thus asserts that there are no politicians who are are not liars. All politicians are liars.

Politicians Liars Venn Diagrams III To say that no politicians are liars is to say that no members of the class of politicians are members of the class of liars – that is, that there is no overlap between the two classes. To represent this claim, we shade the portion of the two circles that overlaps as shown above. No politicians are liars.

Politicians Liars Venn Diagrams IV In logic, the statement “Some politicians are lairs” means “There exists at least one politician and that politician is a liar.” To diagram this statement, we place an X in that part of the politicians circle that overlaps with the liars circle.

Politicians Liars Venn Diagrams IV A similar strategy is used with statements of the form “Some S are not P.” In logic, the statement “Some politicians are not liars” means “At least one politician is not a liar.” To diagram this statement we place an X in that part of the politicians circle that lies outside the liars circle.

Claims about single individuals • Claims about single individuals, such as “Aristotle is a logician,” can be tricky to translate into standard form. It’s clear that this claim specifies a class, “logicians,” and places Aristotle as a member of that class. The problem is that categorical claims are always about two classes, and Aristotle isn’t a class. (We couldn’t talk about some of Aristotle being a logician.) What we want to do is treat such claims as if they were about classes with exactly one member.

Claims about single individuals II • One way to do this is to use the term “people who are identical with Aristotle,” which of course has only Aristotle as a member. • Claims about single individuals should be treated as A-claims or E-claims. • “Aristotle is a logician” can be translated into “All people identical with Aristotle are logicians.” • Individual claims do not only involve people. For example, “Fort Wayne is in Indiana” is “All cities identical with Fort Wayne are cities in Indiana.”

Two important things to remember about “Some” Statements • In categorical logic, “some” always means “at least one.” • “Some” statements are understood to assert that something actually exists. Thus, “some mammals are cats” is understood to assert that at least one mammal exists and that that mammal is a cat. By contrast, “all” or “no” statements are not interpreted as asserting the existence of anything. Instead, they are treated as purely conditional statements. Thus, “All snakes are reptiles” asserts that if anything is a snake, then it is a reptile, not that there are snakes and that all of them are reptiles.

Exercises • Draw Venn diagrams of the following statements. In some cases, you may need to rephrase the statements slightly to put them in one of the four standard forms. • No apples are fruits. • Some apples are not fruits. • All fruits are apples. • Some apples are fruits.

Translating into standard categorical form • Do people really go around saying things like “some fruits are not apples”? Not very often. But although relatively few of our everyday statements are explicitly in standard categorical form, a surprisingly large number of those statements can be translated into standard categorical form.

Common Stylistic Variants of “All S are P” Example: • Every S is P. Every dog is an animal. • Whoever is an S is a P. Whoever is a bachelor is a male. • Any S is a P. Any triangle is a geometrical figure. • Each S is a P. Each eagle is a bird. • Only P are S. Only Catholics are popes. • Only if something is a Only if something is a dog is it a cocker spaniel. P is it an S. • The only S are P. The only tickets available are tickets for cheap seats.

ONLY • Pay special attention to the phrases containing the word “only” in that list. (“Only” is one of the trickiest words in the English language.) Note, in particular, that as a rule the subject and the predicate terms must be reversed if the statement begins with the words “only” or “only if.” Thus, “Only citizens are voters” must be rewritten as “All voters are citizens,” not “All citizens are voters.” And, “Only if a thing is an insect is it a bee” must be rewritten as “All bees are insects,” not “All insects are bees.”

Common Stylistic Variants of “No S are P” Example: • No S are P. No cows are reptiles. • S are not P. Cows are not reptiles. • Nothing that is an S Nothing that is a known is a P. fact is a mere opinion. • No one who is an S No one who is a Republican is a P. is a Democrat. • All S are non-P. If anything is a plant, then it is not a mineral.

Common Stylistic Variants of “Some S are P” Example: • Some P are S. Some students are men. • A few S are P. A few mathematicians are poets. • There are S that are P. There are monkeys that are carnivores. • Several S are P. Several planets in the solar system are gas giants. • Many S are P. Many students are hard workers. • Most S are P. Most Americans are carnivores.

Common Stylistic Variants of “Some S are not P” Example: • Not all S are P. Not all politicians are liars. • Not everyone who is an S is a P. Not everyone who is a politician is a liar • Some S are non-P. Some philosophers are non Aristotelians. • Most S are not P. Most students are not binge drinkers.

Paraphrasing • The process of casting sentences that we find in at ext into one of these four forms is technically called paraphrasing, and the ability to paraphrase must be acquired in order to deal with statements logically. • In the processing of paraphrasing we designate the affirmative or negative quality of a statement principally by using the words “no” or “not.” We indicate quantity, meaning whether we are referring to the entire class or only a portion of it, by using words “all” or “some.” In addition, we must render the subject and the predicate as classes of objects with the verb “is” or “are” as the copula joining the halves.

Paraphrasing II • We must pay attention to the grammar, diagramming the sentences if need be, to determine the parts of the sentence, the group that is meant, and even what noun is being modified. • The kind of thing a claim directly concerns is not always obvious. For example, if you think for a moment about the claim “I always get nervous when I take logic exams,” you’ll see it’s a claim about times. It’s about getting nervous and about logic exams indirectly, of course, but it pertains directly to times or occasions. The proper translation of the example is “All times I take logic exams are times that I get nervous.”

Once our statement is translated into proper form, we can see it implications to other forms of the statement. For example, if we claim “All scientists are gifted writers,” that certainly implies that “Some scientists are gifted writers,” but we cannot logically transpose the proposition to “All gifted writers are scientists.” In other words, some statements would follow, others would not. • To help determine when we can infer one statement from another and when there is disagreement, logicians have devised tables that we can refer to if we get confused.

Conversion Table

Syllogisms • Syllogism – a deductive argument in which a conclusion is inferred from two premises. • In a syllogism we lay out our train of reasoning in an explicit way, identifying the major premise of the argument, the minor premise, and the conclusion. • The major premise consists of the chief reason for the conclusion, or more technically, it is the premise that contains the term in the predicate of the conclusion. • The minor premise supports the conclusion in an auxiliary way, or more precisely, it contains the term that appears in the subject of the conclusion. • The conclusion is the point of the argument, the outcome, or necessary consequence of the premise.

Syllogisms II • Example in an argumentative essay • In determining who has committed war crimes we must ask ourselves who has slaughtered unarmed civilians, whether as reprisal, “ethnic cleansing,” terrorism”, or outright genocide. For along with pillaging, rape, and other atrocities, this is what war crimes consist of . In the civil war in the former Yugoslavia, soldiers in the Bosnian Serb army committed hundreds of murders of this kind. They must therefore be judged guilty of war crimes along with the other awful groups in our century, most notably the Nazis.

Syllogisms III • The conclusion to this argument is that soldiers in the Bosnian Serb army are guilty of war crimes. The premises supporting the conclusion are that slaughtering unarmed civilians is a war crime, and soldiers in the Bosnian Serb army have slaughtered unarmed civilians. The following syllogism will diagram this argument. All soldiers who slaughter unarmed civilians are guilty of war crimes. Some Bosnian Serb soldiers are soldiers who slaughter unarmed civilians Some Bosnian Serb soldiers are guilty of war crimes.

Enthymeme • Enthymeme - An argument that is stated incompletely, the unstated part of it being taken for granted. An enthymeme may be the first, second, or third order, depending on whether the unstated proposition is the major premise, the minor premise, or the conclusion of the argument. • Enthymemes traditionally have been divided into different orders, according to which part of the syllogism is left unexpressed.

Enthymeme II • A first order enthymeme is one in which the syllogism’s major premise is not stated. • For example, suppose someone said, “We must expect to find needles on all pine trees; they are conifers after all.” Once we recognize this as an enthymeme we must provide the unstated (major) premise, namely, “All conifers have needles.” Then we need to paraphrase the statements and arrange them in a syllogism, indicating by parentheses which one we added was not in the text: (All conifers are trees that have needles.) All pine trees are conifers. All pine trees are trees that have needles.

Enthymeme III • A second - order enthymeme is one in which only the major premise and the conclusion are stated, the minor premise being suppressed. • For example, “Of course tennis players aren’t weak, in fact, no athletes are weak.” Obviously, the missing premise is “Tennis players are athletes,” so the syllogism would appear this way. No athletes are weak. (All tennis players are athletes.) No tennis players are weak.

Enthymeme IV • A third – order enthymeme is one in which both premises are sated, but the conclusion is left unexpressed. • For example, “All true democrats believe in freedom of speech, but there are some Americans who would impose censorship on free expression.” The reader is left to draw the conclusion that some Americans are not true democrats. The syllogism: All true democrats are people who believe in freedom of speech. Some Americans are not people who believe in freedom of speech. (Some Americans are not true democrats.)

Exercises • No certainty should be rejected. So, no self-evident propositions should be rejected. • Some beliefs about aliens are not rational, for all rational beliefs are proportional to the available evidence. • John is a member of the police force and all policemen carry guns.

Validity and Truth • No matter how diligent we are in constructing our argument in proper form, our conclusion can still be mistaken if the conclusion does not strictly follow from the premises, that is, if the logic is not sound. • For example, All fish are gilled creatures. All tuna are fish. All tuna are gilled creatures. • This seems correct.

Validity and Truth II • But suppose we want to claim that all tuna are fish for the simple reason that they have gills and all fish have gills. Our syllogism would then appear in the following form: All fish are gilled creatures. All tuna are gilled creatures. All tuna are fish. • Of course, this syllogism is problematic. The mistake seems to lie in the structure itself. From the fact that tuna have gills we cannot conclude that tuna must be fish, because we do not know that only fish have gills.

REVIEW: The Structure of Argument: Conclusions and Premises