PHIL 211 Cosmos to Citizen Dr. Mike Miller Mount St. Mary’s College Logic Slides 2Kinds of Arguments
There are really only two types of arguments: Good and Bad But before you can assess if an argument is good or bad, you must first understand the two different kinds of good arguments: Deductive and Non-Deductive
A Deductive argument is one whose premise, if true, provides conclusive evidence for the truth of the conclusion. This means that if we accept the truth of the premises of a properly formed deductive argument (sometimes this requires a little imagination), it is impossible for us to say the conclusion is false without admitting we are acting illogically. • Consider the following deductive argument: • All cats are mammals. • All mammals are animals. • Therefore, all cats are animals. • The argument is set-up in such a way that if we believe the premises (and that shouldn’t be too hard because they are certainly true), then the conclusion must also be true. This argument is classified as a ‘good’ deductive argument.
Aristotle said that a person who refuses to accept the conclusion of a good deductive argument as true (the type of argument where the premises really do support the conclusion and the premises are true), then that person is no better than a vegetable (that is, alive - but not thinking)! Aristotle went on to say that it is impossible to have a rational conversation with this kind of person. • Don’t be fooled, however, into thinking that every deductive argument is ‘good.’ There are plenty of ‘bad’ deductive arguments out there. Consider the following: • All animals are fish • All fish are mammals • Therefore, all animals are mammals. Although this argument is ‘bad’ (because the premises are false) the premises actually would support the conclusion if they were true. They are not true, but if they were true they would provide conclusive evidence for the truth of the conclusion. Therefore, this argument is deductive even though it is also a ‘bad’ argument.
We will study 7 different ‘forms’ of deductive arguments later in this presentation (6 of which are discussed in detail in Weston, Chapter 6): • Categorical Syllogism (CS) • Modus Ponens (MP) • Modus Tollens (MT) • Hypothetical Syllogism (HS) • Disjunctive Syllogism (DS) • Dilemma • Reduction ad Absurdum • These different kinds of deductive arguments are called ‘forms’ because it is the structure of the argument (how the premises and conclusion are written) and not the content of the premises or conclusion that make the argument deductive.
Now, let’s turn our attention to non-deductive arguments. A Non-Deductive argument is one whose premises, if true, provide reliable, although not conclusive, evidence for the truth of the conclusion. This means that in every non-deductive argument if we admit that the premises are true (again this often takes an act of imagination) then the most we can say about the conclusion is that is likely to be true. Conclusions of non-deductive arguments are never absolutely certain, even if they may be almost certain. Non-deductive arguments usually appeal to some notion of similarity between what has happened or been observed in the past and what will happen in the future.
Consider the following non-deductive argument: Since the Mount softball team has won their last 19 games this season (all against highly ranked opponents) and State U has lost 14 straight, it is likely that the Mount will win their game against State U tomorrow. If the premises are true, the conclusion is very likely true. (If I were a betting man I would certainly place a bet.) However, since it is always possible that a highly favored team may lose a game they are expected to win the conclusion of this argument does not follow with absolute certainty (even if the premises are true). Therefore, the argument is non-deductive. Please note that non-deductive arguments are not necessarily worse than deductive arguments because their conclusions are never certain. They are just different. Both deductive and non-deductive arguments are useful and have their advantages.
Is the following argument deductive or non-deductive?: If you don’t eat lunch you will collapse like a car without fuel. This argument is non-deductive because the conclusion does not necessarily follow even if the premise was true. Many people skip lunch and they don’t collapse. The following is also a non-deductive argument: Since no rational person believes in Santa Claus, no rational person should believe in Jesus either. The argument is non-deductive because even if the premise was true the conclusion does not necessarily follow. That is, the premise does not exclude the possibility of a rational person believing in Jesus because no rational adult believes in Santa. (If you are interested, the argument is ‘bad’ because the difference between believing in Jesus and believing in Santa is greater than any possible similarity.)
There are two different types of non-deductive arguments: • Inductive: • Generalizations • Analogies • Arguments from Authorities • Arguments about causes: • Agency (who did it?) • Motivation (why it was done?) • The Cause of action or event The next 17 slides will focus upon these non-deductive arguments (all of which are discussed in detail in Weston, Chapters 2–5). We will first discuss 3 different types of inductive arguments (generalizations, analogies, and arguments from authority), and then make some general comments concerning arguments about causes.
The last two pies I bought from David’s Bakery were fantastic. I bet the next one will be fantastic too. Generalization We generalize every day, arguing that what has happened before is likely to happen again. For example, You are generalizingif you make a conclusion about a group (the population) from a claim about some part of it (the sample). As we increase our experience our generalizations typically get better because we have more examples from which to generalize (that is, we have a bigger sample). Generalizations can be very good arguments. Surveys are common examples of generalizations. Some surveys are outstanding. Others are very bad. The difference often depends upon the similarity between the sample and the population. If generalizations are made with faulty logic, they commit the fallacy of hasty generalization.
Imagine that you wanted to conduct a survey about what people in Emmitsburg like to eat for dinner. To be a good generalization the survey must abide by the following rules: • Rule 8: Give more than one example • Generally, the larger the population, the more samples are needed. If your survey makes a conclusion about what 2,000 people like to eat for dinner, you cannot simply ask 6 people and draw a conclusion. • Rule 9: Use Representative examples • Make sure that your samples actually represent the population. Even if you ask 200 women (which could certainly be a large enough sample), they are not representative of all the people in Emmitsburg. • Rule 10: Background information is crucial • The generalization made must not be misleading or bias. Unfortunately many surveys are. It takes a lot of work to make a good survey. Be careful that a generalization doesn’t mislead you. • Rule 11: Consider Counterexamples • Ask questions to help you determine if the conclusion needs to be revised, limited, or given up entirely.
Are These Good Generalizations? Your sociology professor asks you to conduct a survey about attitudes of students on campus about sex before marriage. So, you ask 28 of your friends if they think sex before marriage is a great idea or not. 20 say “No” and 8 say “Yes.” Is this a good survey? Should the auto plant accept the batch of nuts and bolts from its supplier? The inspector chooses 10 pairs from the 20,000 items, inspects them under a micro-scope, finds that all are acceptable, and passes the lot. Was that a right thing to do?
Be careful not to believe something just because you hear it many times from many different sources. That is, be wary when somebody says, “I know a person who . . .” Urban legends (sometimes known as the ‘person who’ fallacy) are everywhere, and almost always false. For example, have you heard the following . . . Dear Friend. Please forward this message because Bill Gates is testing a new email tracking system and will send anyone who forwards this message to 10 other friends to Disney World for free. This is not a hoax. It happened to a friend of mine. A warning to all parents: Don’t let your children eat the candy know as “Pop-Rocks.” Years ago Mikey (from those old Life cereal commercials) died because he ate Pop-Rocks and then drank a Coke. Kentucky Fried Chicken changed its name to KFC because they were being sued for liable because their ‘chicken’ is actually horsemeat. Not sure if what you heard is an urban legend? Check out: http://urbanlegends.about.com
Reasoning by Analogy When you Reason by Analogy you argue from a similarity between two cases. Generally, an argument by analogy tries to argue that since two things (an item or an event) are similar in many ways, the second thing discussed must also have a certain characteristic that the first one has. • A argument involving an analogy typically sound like this: • Since objects A and B have properties a, b, c, . . . n and object A has property x, we can infer that object B also has property x. The Mayor did not give the city’s firefighters a raise last year when they asked for one. Therefore, the Mayor should not give the city’s sanitation workers a raise this year.
Note that analogies are not always expressed as formal arguments, but simply sketches of arguments. Since many things in analogies are left unstated, you must often: • Infer the conclusion. • Come up with the similarities and/or the differences between the things being compared. • Determine what general principle is being applied to both sides of the analogy. This principle is the ‘glue’ which the person giving the analogy uses to unite both sides. • For an analogy to be ‘good’: • All the premises must be true. • Rule 12: The Analogy requires a relevantly similar example. If there are more significant differences than similarities between the two sides, the analogy is a bad one.
Is the following a ‘good’ analogy? Blaming soldiers for war is like blaming firemen for fires. What is the unstated Conclusion?: What are the similarities?: What are the differences?: What’s the general principle at work here? (That is, what is the ‘glue’ that unites the two examples in the analogy?): Is it a good analogy?
You wouldn’t buy a kitten at a pet store to give to your dog. Why, then, do you consider it acceptable to buy white rats for your boa constrictor? What is the unstated Conclusion?: What are the similarities?: What are the differences?: What’s the general principle at work here? (That is, what is the ‘glue’ that unites the two examples in the analogy?): Is it a good analogy?
Arguments from Authority No one is an expert on everything. Sometimes we must rely on the expertise of other people, organizations or referenced works to tell us what we need to know. Here’s a typical argument from Authority: Dr. Renpher, a two time winner of the Noble Prize for biology, says that the corpus luteum secretes progesterone. Therefore, the corpus luteum does secrete progesterone. However, as you know, you should not trust everything that everyone says. Little Johnny, the six-year-old kid down the street, says the Japanese economy will recover in three months only if their banking system no longer leverages pre-tax buyouts on foreign debt. Maybe he is right, but do you think it reasonable for a six-year-old be an expert of foreign monetary policy? I would trust what a six-year-old has to say about dinosaurs or Dr. Seuss books, but not technical and abstract material – unless (by some unusual circumstance) there was some reason to think he actually is an expert.
A ‘good’ argument from authority must follow these rules: • Rule 13: Sources should be cited • A detailed claim is more likely to be believed if a reference is given. If you are unsure if the fact is true, you can look it up yourself. Unnamed sources are generally not to be trusted. • Rule 14: Seek informed sources • Sources must be qualified about the fact being discussed. You should question the veracity of claims made by someone if you have no evidence to think that they are experts in that field. Also, beware of anyone making claims to know what cannot be known (such as what Princess Diana was thinking just before her car crashed in Paris). • Rule 15: Seek impartial sources • Those that have something to gain or lose in a dispute are generally not the best sources of information. Impartial sources of information are usually the best. • Rule 16: Cross check sources • When experts disagree, look for other authorities to back-up the claim.
Would you accept the following arguments? Why or why not? • Your mother: You can get AIDS by touching someone with AIDS. • Friend: My uncle in San Francisco says that President Carter failed second grade. • 55 year-old salesman: I think this car is the coolest car on the planet! Everyone in the dorm is going to love it. • The Lancet Journal (April 4, 2003): Women who use oral contraceptives have a 60% greater chance for cervical cancer than those who do not. Is your Mom an authority about medicine? What have you learned about AIDS? Is she right? I wouldn’t accept this claim, unless I knew your uncle was a presidential historian. The salesman is probably biased because he wants to make a sale. And is it likely that he knows what a college student would love? The Lancet is a respectable journal with peer reviewed articles. I would believe it. Don’t forget your own authority. Your experience counts too.
There is a difference between attacking what a person says and the character of the person speaking. The two are not the same. Since you can’t assume that bad people always give bad arguments, the following rule applies: Rule 17: Personal attacks do not disqualify a source That is, when considering the quality of an argument or a claim, the personal quality of the person speaking makes no difference! Consider the following: John’s argument to put a stop light at 5th and Main Street can’t be right because John is a real jerk! Just yesterday he hit an old lady! • Don’t make this mistake (called an ad hominem fallacy). John’s argument might be a good one, even if John really is a jerk. You must consider John’s argument and John’s character separately. Note: Good people do not necessarily make good arguments either. However, character does matter in a court of law, as when a witness has been convicted of a felony. Why is this an exception to the general rule?
Arguments about Causes Arguments about cause and effect are very common. In these arguments you are looking for the correlation between two events or kinds of events. For example . . . The facts: Spot barked. Sean woke up. Is it fair to say that Spot’s barking woke Sean up? • Effective arguments about causes: • Rule 18: Explain how cause leads to effect • Good arguments not only show the correlation between events A and B, they explain why A caused B. Obviously, the cause must precede the effect and take place close to the effect in space and time. • Rule 19: Propose the most likely cause • The most likely causes are ones that fit with well-established beliefs. The best arguments are those where it is impossible for the cause to happen and the effect not happen, given normal conditions.
Be certain not to forget the following rules when making arguments about causes. If someone breaks any one of the following rules they are making a mistake in reasoning called a false cause fallacy: Rule 20: Correlated events are not necessarily related I won the lottery because I wore my lucky socks. Really? Putting on the socks may have happened before you won the lottery, but how did the socks cause you to win? Rule 21: Correlated events may have a common cause Cleo is irritable because she can’t sleep properly. Well, maybe Cleo is irritable and unable to sleep because she drinks 6 cups of espresso every day.
Rule 22: Either of two correlated events may cause the other Sitting close to the TV will give you bad eyesight. Whoever made this brief argument has reversed the cause and the effect. I think it more likely that having bad eyesight leads one to sit too close to the TV. Rule 23: Causes may be complex If people really want the help those who are starving in the world today, they should try to eat less themselves. Then there would be more left over for everyone else. Well, less consumption of food would help alleviate world hunger, but it certainly couldn’t end it alone. The problem with global poverty is simply too complex to be solved by one solution.
We are now near the end of our discussion about non-deductive arguments (arguments by example, arguments by analogy, arguments from authority, and arguments about causes). In each of the argument types the premises, if true, provided reliable, although not conclusive, evidence for the truth of the conclusion. No one can be absolutely sure that non-deductive arguments provide a certain truth because the content of the arguments does not allow such confidence. (The content of an argument is what the argument is about, whether it be a neighbor’s barking dog, the outlook for the Japanese economy, or the safety of 20,000 bolts.) Think about it, how can anyone be certain that things that have not yet happened will happen, or that things that are related in some ways are actually related in additional ways? And, how can we be sure that even an unbiased expert might not make a mistake? Or for that matter, can we be confident that what appears to cause something to happen actually did so – if we didn’t clearly see it with our own eyes?
The content of non-deductive arguments simply can’t give us absolutely certain truth. But this does not mean that non-deductive arguments are not any good. In fact, we use non-deductive arguments all the time (we would be hard pressed to make it through the day without doing so). And even though the conclusions of non-deductive arguments are never certain, some non-deductive arguments provide conclusions that are very, very, very likely to be true. For instance, would anyone doubt this inductive argument?: The sun has risen for over 15 billions years. Therefore, the sun will rise tomorrow. I trust you remember that deductive arguments are different. For in their case the premises, if true, provide conclusive evidence for the truth of the conclusion. This means that if the content of non-deductive arguments makes them what they are, then deductive arguments are made by their ‘form.’
Deductive Arguments The form of a deductive argument is its structure, without regard to its content. As a matter of fact, you can recognize deductive arguments by ‘stripping’ them of all their content. To do this, you ignore what the argument is about, and look how it is structured. For example, take a look at the following three arguments. All Zobots are Quizars All Quizars are Venmores Therefore, all Zobots are Venmores All Pick-ups are trucks All trucks are motor vehicles Therefore, all pick-ups are motor vehicles All Dogs are Mammals All Mammals are Animals Therefore, all Dogs are Animals • All three arguments have the same form, even though they are about different things. Do you recognize this form? • All A are B • All B are C • Therefore, all A are C
The type of deductive argument we just looked at is called a Categorical Syllogism (CS). The CS form has two premises and one conclusion, each of which include the qualifiers ‘some,’ ‘no’ and/or ‘all.’ For instance, the following are all examples of Categorical Syllogisms: All cars are blue. Some things in the Smithsonian Museum are blue. Therefore, some cars are in the Smithsonian Museum. Some dogs are mean. No mean things are loved. Therefore, all dogs are not loved. No Gigowitz is Reggotin. All Reggotin things are Peffin. Therefore, some Gigowitz are Peffin. Some US presidents have been born in Nevada. Some US presidents have the middle name of ‘Herbert’ Therefore, some Presidents born in Nevada have the middle name of Herbert. Some of the arguments above are ‘bad’ (maybe the premises do not actually support the conclusion, or maybe a premise is false), but even then each of the arguments above is a categorical syllogism.
We will next discuss 6 different forms of deductive arguments in the following slides. Please note that the following 6 forms discussed in this set of slides (unlike the categorical syllogism just discussed) are always valid – meaning that if the premises are true the conclusion must be true too! Please understand that valid does not mean true. That is, an argument may be valid but its conclusion false. For example, the following categorical syllogism is valid – that is, if the premises were true then the conclusion must be true as well – but its conclusion is obviously false. • Now, once again, the following 6 deductive forms are always valid. That does not mean, however, that you should always consider their conclusions true. It just means that if the premises are true, then the conclusion also has to be true. • This is an important point. For if you give a valid deductive argument and can prove your premises to be true, then the person to whom you are giving your argument must accept your conclusion as true! Now that is power! All cats are brown. All brown things are amphibian. Therefore, all cats are amphibian.
OK. Since the form and not the content of deductive arguments makes the arguments deductive, logicians often use symbols to make the form of deductive arguments more clear. That is, using symbols help focus on the form and not the content. For categorical syllogisms letters often take the place of words (any letter will do, as long as a unique letter takes the place of one term every time it is used in the argument). For example: All Apples are Fruit All Alaskans are named Fred All A are F All Fruits are Delicious All Fred’s are Dead All F are D Therefore, all Apples are Delicious So, all Alaskans are Dead Thus, all A are D When you are trying to recognize the type of deductive argument pay attention to the form, and not the content. So, ach of the three arguments above has the CS form. In other deductive arguments letters can also take the place of sentences. For example, ‘If you hit a grand slam, then we will win the game’ becomes ‘if H, then W’ (or ‘if S, then G’ or ‘if P, then Q’ – the letters don’t matter if you are consistent).
A deductive argument that is easy to recognize is called Modus Ponens (Latin for ‘method of putting’). It has the following form: • If P then Q. P. Therefore, Q (where P and Q stand for any proposition). • Here are two modus ponens (MP): The mayor said that if it rains the town picnic will be cancelled. It is raining. Therefore, the picnic is cancelled. If Ohio State football is on television, then Grandpa is watching the game at home. Ohio State is on television, so we can find Grandpa at home. Can you write each in its symbolic form?
Modus Tollens (meaning ‘the method of taking’) is somewhat similar to MP. However, MT has the following form: • If P, then Q. Not-Q. Then not-P • Don’t be confused by ‘not-Q’ or ‘not-P.’ It just means the logical opposite of whatever Q and P stand for. For example: • Q: I can ride a bike not-Q: I cannot ride a bike • I like Brad Pitt I hate Brad Pitt • I don’t enjoy rollercoasters. I love rollercoasters (Do you understand why not-Q has a ‘positive sound’ to it here?) • Here are two examples of MT: • If Biff wins the election, then he will throw a party at his house tonight. There is no party at Biff’s house tonight. He must not have won the election. • If it rains, then the street will get wet. The street is dry. So, it must not have rained.
A Hypothetical Syllogism (HS) has the following form: • If P, then Q • If Q, then R • Therefore, if P, then R • For instance, • Hypothetical syllogisms can have any number of premises, as long as each has the form ‘if P, then Q.’ If Gabby wins the lottery, she will want to pay back her debts. If she wants to pay back her debts, she will give me the $1,000 she owes me. So, if Gabby wins the lottery, I’ll get my $1,000 back.
The Disjunctive Syllogism (DS) has the following form: • P or Q • Not-P • Therefore, Q Here are a couple of examples: Either he is alive or dead. He’s not alive. Therefore, he’s dead. Either Jesus is a madman, or he is God. Jesus is not a madman. Therefore, Jesus is God Either the British must come by land or by sea. They did not come by sea. Therefore, they must come by land.
Dilemma are also deductive arguments. Traditionally, dilemmas involve choices between two bad consequences. In logic, the consequences can both be bad, good or indifferent. Dilemma have the following form: • P or Q • If P, then R. • If Q, then S. • Therefore, R or S. Either I stay up and read philosophy, or I go to sleep. If I read philosophy, I’ll learn something useful. If I go to sleep, I’ll feel better in the morning. Therefore, either I’ll learn something useful or I’ll feel better in the morning. This argument doesn’t tell you what to do (other arguments are needed to help you there), but it does make clear the consequences of your choices.
The last deductive argument we will examine is called Reductio ad Absurdum (or, a reduction to the absurd). Those that use this argument form well prove their point by showing that the exact opposite of what they want to prove leads to a contradiction (or an absurd conclusion). Imagine my brother thinks that I’m harming my 4 year-old daughter by not letting her watch movies like Star Wars and Harry Potter. He thinks kids should be aware that life is often dangerous and hard, and if you keep them too protected they will grow up unprepared for the reality of life. I want to prove him wrong. I would start my argument by assuming that I should let my daughter watch Star Wars because it will ‘toughen her up.’ If true, I probably should let her watch Rocky and Jaws as well. Maybe I should sit her down to watch The Godfather while I’m at it. And if I really wanted to prepare my daughter for life, I should not feed her for a day, or make her walk home from preschool once in a while. But these things would be absurd. So, I won’t let her watch movies like Star Wars.
Be assured, deductive and non-deductive arguments are often more complex than the ones we have looked at. However, once you recognize how the arguments work, you should be able to recognize them no matter how complex they might be. Keep your eyes and ears open and you will find examples of the arguments we just examined all over the place. Keep a special lookout for examples of these arguments in our class readings. In the 3rd set of slides we will discuss common mistakes made in reasoning – called fallacies.
Please contact me with any questions about the information in these slides or the related assigned reading: • Weston, Chapters II – VI • Logic Handout, p. 4-5