4.0 Deduction and Induction

4.1 General Comments

We have already reviewed the most general characteristics of deduction and induction. You should therefore remember that, simply put, deduction begins with a general principle upon which we all agree and applies that to a specific case; induction, by contrast, starts with a collection of observations, measurements, research results (in short, collections of facts) and moves to a general conclusion from that collection of data.

4.2 Deduction: Some Points to Observe

The strength and validity of a deductive argument depend upon three things: first, there must be agreement about the general principle with which the argument begins; second, the special application must be correct and clear, with no disputes about its validity; and, third, the conclusion must be derived properly from putting these two together. Here is a simple example:

All human beings must eventually die.
Mr. Jones is a human being.
Therefore, Mr. Jones will eventually die.

We all accept the truth of the opening statement, based on our education and experience. We accept the truth of the second statement through our perception of Mr. Jones. And the conclusion (the third statement) seems to follow logically from the first two (i.e., the principle has been applied to the specific case correctly).

Now, what is important to notice about such a deductive argument is that the truth of the conclusion is compelling. If we are rational, then we have to agree. To accept the truth of the first and second statements and to agree that they have been combined reasonably, and then to decline to accept the truth of the third would be to violate a basic principle of reason. I am free in a modern liberal society to reject that conclusion, but I cannot do so and claim that I am acting rationally, unless I can prove that there is something wrong with either of the first two statements or with the way they have been put together.

If I find, for some reason, that the conclusion is not true (i.e., Mr. Jones continues to live apparently for ever), then something must be wrong with my opening statements (see Section 5.5 below on falsification for a brief discussion of this point).

The power of deductive arguments comes from this compelling rationality. That is, as you may know, one of the great attractions of mathematics, especially geometry, which is entirely deductive in nature. Hence, someone who can frame an argument in a deductive structure has the most powerful rational means of persuasion available.

That is one reason why we are always searching for mathematical ways to quantify and resolve really difficult arguments, the ones we have trouble agreeing about, like those involving moral issues or the guilt or innocence of an accused person, something we have so far been unable to do after almost three hundred years of trying. If we could find a convincing way to frame these problems in mathematical terms, then the decisions we have to make (e.g., the question whether this person is guilty or not) would be rationally compelling for everybody (as compelling as, say, a geometric proof). The subject known as Risk Analysis seeks to do this, so that we can evaluate what we ought to do in a particular situation in a quasi-mathematical (and thus, people believe, more certain) manner.

4.3 The Opening General Principle

Where do we find the general principles upon which we base a deductive argument? Well, these can come from a number of places. The important thing is that we all acknowledge them as true or as things which we ought to do or to think or things which hold true in nature.

1. Some truths are self-evident and require no proof. Mathematics, for example, starts with some general principles which are self-evidently true, that is, everyone agrees that they must be true (e.g., The whole of a figure is made up of the sum of its parts and is greater than any single one of its parts; things equal to the same thing are equal to each other; if I subtract the same amount from two things which are perfectly equal, the remainders will be equal; and so on). We cannot prove these, but we agree that they are true, and we would tend to believe that anyone who denied their truth was irrational.

2. We share certain basic moral principles (through our culture or our training or as human beings); for example, torturing innocent victims for pleasure is wrong; society has a duty to help the mentally ill, criminal acts against society ought to be punished, and so on. Again, these are not capable of iron-clad proof, but we (or most of us) agree with most of them without further discussion. Members of a particular social or religious group will often share a very clear set of principles which enables them to construct and conclude arguments among themselves on these principles (although often in the multicultural world beyond the meeting house the public will not accept the principles that work inside it). That, indeed, is one of the attractions of a small group: decision making is much easier among people who share a common set of principles (it is, of course, also a potential danger to clear thinking, since members might not be tempted to examine the truth of those shared principles).

3. Certain documents enshrine principles upon which we, as citizens of Canada or of the world, are expected to share. These are the documents which form declarations of various human rights (constitutions of various countries, the United Nations charter, Magna Carta, and so on). The decisions of the Supreme Court are constantly informing us about what these principles amount to in particular cases.

4. Even where we do not agree on certain moral principles, we (or most of us) agree on the general principles that in a liberal democracy the elected government has the right to make the laws and that the citizens under normal circumstances have an obligation to follow the laws. Thus, the statement of a legal requirement (i.e., a law as defined by present legislation) can be the opening to a deductive argument. If we all agree that we ought to obey the law, and if we agree that a certain law prohibits certain things, then we should all agree that we ought not to do that thing.

5. An opening general principle may be a hypothesis which we wish to test by constructing an argument upon it and then testing the conclusion. This procedure is central to the process of thinking we call scientific reasoning. We may not know that this general principle is true, but we agree to it provisionally in order to produce a conclusion which we can test.

6. Many (perhaps most) starting general principles in a deductive argument will be well-known truths or probabilities whose reliability has been established through experiment and observation (i.e., inductively). The proofs have been so reliable that we now take the general principle as universally agreed upon and can construct a deductive argument upon it (e.g., People who drive while intoxicated pose a great danger to other drivers; many people who practice unprotected sexual activity contract serious venereal diseases; at higher altitudes there is less oxygen in the atmosphere than lower down; and so on). Many scientific arguments rest on a deductive structure which starts with a principle of this sort, a shared truth which has been established beyond all reasonable doubt.

4.4 The Importance of Step 2 in a Deductive Argument

Even when we agree about the opening general principle, a deductive argument may run into difficulty in the specific application, because we may have trouble agreeing on the definition of the specific application.

Here is an example containing two very powerful and persuasive deductive arguments which reach opposite conclusions about a common modern experience, even though few people would have trouble agreeing with the opening principles of each one.

Argument 1

General Principle: Killing an innocent person is always wrong.
Specific Application: A foetus is an innocent person.
Conclusion: Therefore, killing a foetus is always wrong.

Argument 2

General Principle: Every woman must have the right to full control over her own body at all times.

Specific Application: The foetus is a part of a woman's body.

Conclusion: Therefore every woman has the right to full control over her own foetus at all times.

Most people have no trouble accepting the opening general statements of both of these arguments. And it is clear that they are both put together properly (that is, the application of the particular case to the general principle is valid). The difference of opinion concerns the claims made in the two Specific Application statements, which concern the definition of the foetus. If one accepts the definition given in Argument 1, then one must accept the conclusion; if one accepts the definition given in Argument 2, then one must accept the conclusion of the second argument.

How is one to adjudicate between these two definitions of a foetus? That is the heart of the abortion argument. Attempts to resolve it involve a number of different strategies including appeals to religious authorities (like the Pope or fundamentalist doctrines), appeals to scientific studies of conception and embryonic development, or appeals to the law or human rights. Because there is no agreement about who has final authority in defining the foetus, the deductive structures, while very persuasive to some people, fail to resolve the issue.

Many of our most interesting arguments are of this sort, where we are trying to insist that a particular example fits under a specific application of a general principle. That is the basis for most murder trials, for example, whose overall logic goes something like this:

General Principle: A person who has a strong motive, a convenient opportunity, and a direct link to the murder weapon is a very strong suspect in a murder trial.

Specific Application: Mr. X had a strong motive, many convenient opportunities, and a direct link to the murder weapon.

Conclusion: Therefore Mr. X is a strong suspect.

The general principle is given to us by experience. Most of the trial focuses on the second step, one side arguing that it is a true statement, the other arguing that it is not (or that there is some doubt about it). That argument always involves induction (facts like DNA samples, fingerprints, shoe patterns, telephone records, and so on).

4.5 The Importance of Deduction in Falsification Theories of Science

Many scientists claim that the essence of science is the construction of deductive arguments whose conclusions are then tested to see if they fail to meet a test of truth. If they do fail, then the argument is wrong and thus the initial starting principle must be false.

Here is an example from the history of science of how this might work in scientific practice.

General Principle: All planets in our solar system move in circular orbits around the sun.

Specific Application: Mars is a planet in our solar system.

Conclusion: Therefore, Mars moves in a circular orbit around the sun.

The logic of this argument is compelling if we accept the General Principle and the Specific Application. For many years, the General Principle was accepted without question, since circularity was seen to be a divine property appropriate to heavenly creation. However, once people started rigorous and repeatedly testing the conclusion to this argument by observing Mars (i.e., by induction) with improved instruments, they quickly learned that the conclusion is false. Mars's orbit is not circular. Therefore there is something wrong with this argument: either Mars is not a planet (and thus the definition in the Specific Application is incorrect) or the General Principle must be wrong.

Astronomers had to go back and come up with another argument, and Kepler posited the hypothesis that planets in our solar system move in ellipses, with the sun at one focal point. The conclusion to the new argument (i.e., that therefore Mars moves in an elliptical orbit around the sun) then became subject to rigorous testing.

According to this view of science (which has its critics) science never asserts what is true; rather, it is constantly testing claims by drawing deductive conclusions from those claims and subjecting the conclusions to inductive testing. What remains is not necessarily something true, but something which has not yet been proved false. This, such falsificationists say, accounts for the fact that science is progressive, that is, its knowledge gets increasingly more secure (i.e., less false).

We should stress here the importance of this method of arguing in science (and science students especially should take note). Science is not simply the collection of evidence in order to construct a theory. It is better characterized as the construction of a theoretical general principle (a hypothesis) on the basis of which certain conclusions are derived in the form of predictions. The predictions are then independently tested by experiment and observation (Does what is predicted occur as the hypothesis indicates?). In this process, the number of experiments may be quite small, but they will be crucial tests of a theory.

4.6 The Deductive Structure of Listing the Alternatives

A very powerful and common deductive structure for an argument involves listing all the alternatives and then by negative proofs showing that all but one of the alternatives are impossible or entirely impractical. This then leads naturally to the conclusion that the one remaining option must be advisable or true or highly probable. In other words, you establish the truth of the conclusion, not so much by focusing on it directly, but by eliminating all other possibilities. Notice the following typical examples:

Argument 1

Only two people's fingerprints were found on the murder weapon, those of Ms Smith and of Mr. Wesson. Thus, one of the two must have fired the fatal bullet.

At the time of the murder, Ms Smith was on an extended holiday in Europe; she did not return until three days after the killing.

Therefore, Ms Smith could not have fired the fatal shot, and Mr Wesson must have.

Argument 2

We have three options for dealing with this crisis: we can ignore it and hope it will solve itself, deal with it immediately ourselves, or work co-operatively with the provincial government to resolve it.

The issue is too serious to ignore, and we simply do not have the money necessary to deal with it immediately ourselves.

Therefore we must work co-operatively with the provincial government to resolve it.

Argument 3

Hamlet delays killing Claudius either because he is a coward, because he never has a suitable opportunity, because he is suffering from some inner problem, or because he does not believe the ghost.

We know that Hamlet is not a coward, and he repeatedly states that he believes the ghost. Moreover, he has frequent and easy access to Claudius, so there is no lack of opportunity.

Thus, he must be suffering from some inner problem.

Notice that the overall structure of each of these arguments is deductive. That is, if the first and second statements are true then the conclusion is rationally compelling (i.e., we must agree). However, the truth of the second stage of each argument will usually require an inductive argument (facts, experiments, specific details of the text, and so on). Most of the argument will be taken up with this task.

This form of argument is extremely important and common in business, political and social policy, literary interpretation, and science, anywhere where one has to adjudicate between competing options and does so by showing that all of them except one are impossible or very inadvisable or that all of them are less persuasive than a particular one. It is also common in many people's methods for resolving their own personal decisions.

The structure discussed here (listing alternatives and resolving the argument by dismissing all options but one) is a common one in risk analysis, where we list all the different possible outcomes of a decision or event and then, if we can, eliminate all but one by analyzing what each option involves. This is an important principle in business decisions, for example, about the level of environmental protection and control a company will undertake.

This form of deductive reasoning is the basis for one of the most famous arguments for why we should believe in God (the argument is known as Pascal's Wager). It goes something like this:

1. Either there is a God who eternally rewards those who believe in Him and eternally punishes those who do not, or there is no such God.

2. If I do not believe in God and He does exist, then I shall be eternally punished.

3. If I do not believe in God and He does not exist, then nothing bad or good will happen to me.

4. If I do believe in God and He does exist, then I shall be eternally rewarded.

5. If I do believe in God and He does not exist, nothing good or bad will happen to me.

6. Conclusion: I have a great deal more to lose and to fear from not believing and being wrong than I do from believing and being wrong. Therefore, it is prudent to believe.

Notice how this argument depends upon listing alternatives, evaluating the consequences of each one, and deciding on the basis of the possible outcomes.

A similar form of reasoning used to be called in the press the Maximin Strategy. It involves, as a start to resolving a difficult personal decision, listing all the worst possible consequences of all the various options you face. You select that option, the worst possible outcome of which is preferable to the worst possible outcome of any of the others. This form of thinking is highly recommended for conservative pessimists.

4.7 The Problem of Hidden or Misleading Assumptions

The full study of the ways in which deductive arguments can go astray is complex and difficult. However, here it is important to note a few basic ways in which the logic of a deductive argument can create problems.

The first thing to be careful of in analyzing a deductive argument or in constructing one of your own is any assumption hidden in the argument, that is, a general principle which is necessary to the argument but which is implied rather than stated openly.

For example, here is a deductive argument:

Canadian fishermen have the exclusive right to harvest those fish, because the fish are coming to Canadian rivers to spawn.

There's a hidden assumption here on which the conclusion depends. The assumption is a general principle something like the following: "The fishermen of the country where fish come to spawn have the exclusive right to harvest those fish." The assumption, which may or may not be true or agreed upon, is not stated.

Hidden assumptions can be very misleading because, since they are not clearly stated, the reader may not focus upon them the critical attention they merit. Notice that a hidden assumption is not necessarily wrong; it might be quite acceptable. But unless you as reader are aware that it is there, you cannot evaluate it.

4.8 Exercise in Hidden Assumptions

Notice the following examples of short arguments in which deriving the conclusion has required a general principle which is not stated. Identify the hidden assumption and state whether, in your view, the assumption is a general principle about which we agree or not.

1. You should not vote for that candidate for the federal parliament. He has been married twice.

2. We must provide more money and time for the faculty to conduct scholarly research. We all want to improve the quality of the student's learning at this institution.

3. Hamlet is much given to moody speculation. Clearly he is not fit to be the king of Denmark.

4. Which would you rather have, a healthy environment or unemployment? Without the clear-cutting of old growth forests, we will have unacceptably high unemployment levels.

5. The person should not be admitted to the course on combat flight training. After all, she is a woman.

6. The government should not permit the people of Quebec to separate because the break-up of the country will hurt the Canadian economy.

7. Elisa and Henry do not talk to each other very much. Clearly, their marriage is not going very well.

8. People who smoke inflict damage on themselves. Therefore, Medicare should not pay their medical expenses for treating conditions related to their smoking.

9. Podunk College is a much better university than Folsom University. At Podunk College 89 percent of the faculty have PhD degrees; whereas, at Folsom University only 75 percent of the faculty have PhD degrees.

10. The Canadian military must pay for that soldier's sex change operation, because outside the military Medicare covers such medical procedures.

4.9 False Dilemma

A particularly common and often persuasive mistake in deductive arguments is the one called the False Dilemma. This occurs when the arguer gives the argument a deductive structure by listing the options or alternatives at the start and then goes on to disprove all the possibilities but one (see Section 5.6 above). However, the list of alternatives is not complete but is, deliberately or not, misleading because it does not include all the options.

Here are some simple examples of the False Dilemma mistake in deductive structure:

Argument 1

We have only two choices in dealing with a worker who is drinking on the job: we can ignore the problem or we can fire the worker for cause.

We cannot afford to ignore the problem, because the drinking creates dangers for the other workers and hurts productivity.

Therefore we have to fire any worker who is drinking on the job.

Argument 2

Everyone agrees that there are only two probable accounts for the creation of animal and plant species, the one in Genesis and the one provided by Darwin.

Clearly, there are inconsistencies, inaccuracies, and errors in Darwin's account.

Therefore, the only probable account for the creation of animal and plant species is the one in Genesis.

Argument 3

Either we give back all our land to the Native communities, as they are demanding, or we require them to become fully fledged and equal citizens, just like everyone else.

We cannot afford to give back all the land.

Therefore, we have to require them to become fully fledged and equal citizens just like everyone else.

Each of these arguments begins with a list of options or alternatives, and each list is incomplete and misleading. If you accept the list, however, as a genuine and complete statement of all the options, then you may be easily misled by the rest of the argument.

In any argument, therefore, where you are considering a range of options, make sure the list is complete. If you are excluding something, make sure you explain why that is not an option. This is also a very important analytical tool in evaluating arguments, especially from politicians and policy makers.

4.10 Overstating or Understating the Conclusion

One common problem in deductive arguments is a tendency to overstate or understate the conclusion. You need to be careful that the degree of certainty in your conclusion matches the degree of certainty in your general principle and specific application. Here is an example of this point:

General Principle: Teenage drivers are often more reckless than mature drivers.

Specific Application: Jack is a teenage driver.

Conclusion: Therefore, Jack must be more reckless reckless than mature drivers.

The conclusion here is overstated, because the general principle does not include all teenage drivers. You are not entitled to make such a quick conclusion about Jack's driving. A better conclusion would be something like "Therefore Jack may be a reckless driver."

Here is another example:

General Principle: Many native land claims are perfectly justified by Canadian law.

Specific Application: This petition represents a native land claim.

Conclusion: Therefore, this petition is perfectly justified by Canadian law.

The conclusion here is very firm (is perfectly justified), but the initial principle doesn't entitle you to such a firm conclusion, since the opening claim does not say all.

A common source of trouble here are words like never, always, none, all, and so on, words which are all inclusive of a group. Do not use these words when your opening assumptions entitle you only to say some, a few, many, and so on. For example:

General Principle: Many college students in Canada require financial aid in order to continue their schooling.

Specific Application: This group of students at Malaspina are Canadian college students.

Conclusion: Therefore, they all need financial aid in order to continue their schooling.

Again the conclusion here is overstated, showing a degree of certainty not warranted in the General Principle. Your conclusion should thus be more tentative: "Therefore some them may well need financial aid. . . . "

4.11 Analogies

Deductive arguments often make use of an analogy, that is, a comparison with some other example of a similar case. Here is an example:

General Principle: The attempts to prohibit the manufacture and sale of alcohol in the US during Prohibition were a massive failure.

Specific Application: The present attempts to deal with illegal narcotics are just like that earlier situation with alcohol.

Conclusion: Therefore, the present attempts to deal with illegal narcotics are a massive failure.

Notice very carefully this form of argument (which is common). To persuade the reader or listener of the conclusion, the arguer has introduced an analogy (or comparison) between attempts to eliminate alcohol and attempts to eliminate narcotics. The strength of the argument here is going to depend on the extent to which the arguer can persuade the reader that the analogy is a good one.

Now, analogies are dangerous things, simply because no two situations are exactly the same, and one can always find some differences which work against the arguer's purpose in introducing it. So they need to be used with extreme care, with full attention to the following points:

1. Never introduce an analogy unless you are well informed about the details of the example you are calling attention to and are prepared to defend the similarity between the two things being compared. The argument will suffer from a False Analogy if the reader fails to see the similarity or sees only differences. This is particularly true if you are going to use historical analogies (e.g., What is going on in Quebec today is just like the student unrest of the mid-1960's).

2. Be very careful of extreme analogies, that is, bringing into the argument an example of something so extraordinary that the comparison is suspect. For example, be very cautious about comparing anything with Nazi Germany's treatment of the Jews. That may be rhetorically effective, but unless the situation you are describing is as horrific as the original event, the analogy simply indicates to the reader that you do not understand what you are talking about or are exaggerating wildly for the sake of it.

3. In general, stick to analogies which bring together things which are, indeed, very similar. For example, if you are arguing that the high salaries of NBA players are spoiling the game, you might want to make an analogy with what is happening with high salaries in the NFL. Those situations are close enough to make the comparison carry some persuasive weight. Similarly, if you are arguing about an educational issue in BC, you might want to draw an analogy with what is happening in the same area in, say, Alberta or Washington State.

4. If you are not sure whether to introduce an analogy or not, you probably should leave it out. Analogies are not all that persuasive most of the time, and if they are stretched or inappropriate they weaken the argument. If there's any doubt that the reader might not see the similarity between the two cases, then you might have to argue it. For example, if you wanted to make the argument that the prohibition of alcohol was very like the prohibition of narcotics, then you might have to make that point in detail, rather than just assuming that the reader sees it clearly.

5. Analogies, in general, should not carry the weight of the argument. They are often very useful for illustrating and emphasizing points you have already made in other ways, but in themselves, unsupported by other arguments, they are quite weak (although frequently popular, especially among politicians).

4.12 Induction

As mentioned previously, a second manner of conducting arguments is called induction or inductive reasoning. Induction or inductive reasoning involves, as we have remarked already, facts, observations, experimental data, perceptions, and so on, in other words, individual acts of sense experience. The inductive process starts with a single perception: e.g., "That pine tree has cones," "When it first appears, the Ghost in Hamlet is dressed in armour," "The patient has red spots on her arms," and so on.

The basis of all induction is repeated observation, so that the facts about similar experiences accumulate to the point where one sees a repetitive pattern and can draw a conclusion about it. Having repeatedly observed in similar circumstances the same event or one very similar, you draw a conclusion about the pattern you have seen.

Suppose, for example, you observe a crow and notice that it is black. You continue to observe crows repeatedly, and every time you notice that the colour is black. After a certain number of similar experiences, you will draw a conclusion: "All crows are black." And, on the basis of this generalization, you can now make a prediction: "My cousin Jane has written to tell me she has a pet crow. It must be black, because all crows are black."

Notice the nature of this conclusion. You have not observed all crows in the world (that would be impossible). You have seen only a sample, but you feel confident that the conclusion is a good one. You would, of course, be forced to change it, should you ever perceive a purple, white, yellow, or polka-dotted crow (in scientific terms, you would have falsified the hypothesis that all crows are black).

This final point introduces a vitally important point about induction: it is never finally certain. Since the process involves making a large generalization on the basis of a limited number of observations, the conclusion is only more or less probable, rather than iron clad. Induction can, however, provide important and conclusive negative results; that is, a particular observation or set of experimental results can serve to prove a general claim wrong (e.g., seeing a yellow crow would prove the assertion "All crows are black" false).

4.13 Making Inductive Generalizations

The single most challenging part of inductive reasoning is dealing with these questions: How many repetitive observations do I have to make before I draw a conclusion? What sort of conclusion am I entitled to draw? How confident can I be that this conclusion is valid? Much of your study at college will be dealing with these questions, particularly if you are a student of social science, where the statistical analysis of inductive evidence is a crucial (and for some students a very difficult) part of the curriculum.

There is not time here to go into the details of what can be a very complex subject, but at a very basic level we can suggest the following points to watch in inductive arguments:

1. The strength of the conclusion is going to depend upon the quality and the quantity of the observations (evidence) you introduce. No inductive argument based on a single piece of unreliable evidence is very persuasive.

2. The evidence you put into an inductive argument must be good evidence. Again, you will be learning what that phrase means in different subjects, but, in general, the evidence should meet the following criteria: it should be accurate, up-to-date, based on a reliable source, and easy to verify or replicate. It should not be subjective, fabricated, or based on a clearly biased or suspicious source. In literary arguments, the evidence normally will come directly from the text under discussion or from secondary sources (i.e., books or articles written about that text). It will not come from something not directly provided by the text (e.g., what you think the childhood experiences of the heroine might have been like). And it is important to note that the quality of the evidence is always more important than the quantity: a few excellent examples are much more persuasive than a much larger quantity of inferior material.

3. Part of the previous point requires you to identify clearly any special authorities to which you appeal for evidence. You should never just refer vaguely to experts (in phrases like "Scientific studies have shown . . . ," "Many critics maintain that . . . ," "It has been verified that. . . ." and so on). If you want to use phrases like that, then you are going to have to provide specific references.

4. Most importantly, the language in the conclusion must match the degree of certainty in the evidence. An inductive argument, especially one about literature, will normally entitle you only to talk about what is probably the case rather than to use a vocabulary indicating certainty (so words like prove, demonstrate, and so on--which indicate a firm certainty--are generally less advisable than words like suggest, raise the possibility, perhaps indicate, and so on), unless the probability is so high as to be almost certain (e.g., I can be certain that if I throw some heavy object out of the window it will fall to earth).

Note very carefully that a tendency to overstate the conclusion, that is, to make the conclusion much more definite than the evidence suggests or to offer insufficient or poor evidence is a quick way to make inductive arguments look suspect.

4.14 Exercise in Simple Inductive Argument

Below are some simple inductive arguments, with some evidence presented and a conclusion (which is in bold). Score each argument out of 4, as follows: 0-very poor; 1-some probability perhaps, but not very convincing; 2-partially true perhaps, but the evidence is not as good as it could be to support the conclusion; 3-good; 4-excellent, with a conclusion arising naturally out of the evidence. If you think the conclusion might be improved, then provide an improved version.

1. The ghost in Hamlet spends more time complaining about his ex-wife's remarriage than the fact that his brother murdered him. Clearly this demonstrates he is obsessed with his inadequate sexuality.

2. The ghost in Hamlet comes into Gertrude's bedroom to confront Hamlet, but his ex-wife cannot see him. This suggests something interesting, that Hamlet Senior, renowned as a warrior king, may not feel quite so commanding and competent in the bed room.

3. The driver's blood alcohol level was three times the legal limit. Three separate witnesses indicate that he was driving on the wrong side of the road without lights on, and the preliminary analysis indicates that he was speeding well above the limit. And the brakes on the car are defective. He might be to blame in the accident.

4. We have conducted an experiment ten times under standard conditions in which we added a small piece of zinc to hydrochloric acid. Every time hydrogen gas was produced. Thus, the interaction of zinc and hydrochloric acid under similar conditions will always produce hydrogen gas.

5. The people of Quebec clearly do not want to separate from Canada. In the last referendum on separation, the people of Quebec rejected the referendum question by a margin of 51 to 49 percent.

6. In this poem, nature is always described as "green," "verdant," "ripe," "blooming," and "fertile." The writer is here suggesting that nature is a rich source of life.

7. Odysseus obviously has a very cruel streak. We see this when he grinds out the eye of Polyphemos, the Cyclops, with a sharpened and burning pole and at the end when he slaughters the suitors and punishes the servants, some of them very brutally.

8. The Liberal candidates promised that they would repeal the GST. Once in office, they refused to carry out that legislation. They are all liars.

9. Some released sex offenders have committed new offences. We should never release any sex offenders, since they will always reoffend.

10. Several scientists have said that greenhouse gases are increasing. We must urge governments to pass strict legislation controlling industrial and automobile emissions.

11. My astrologer and the Ouija board have told me repeatedly me that it will rain on Friday. I think we should call off the picnic.

4.15 Some Potential Problems in Inductive Arguments

We have already mentioned three very common ways in which inductive arguments can go astray: first, generalizing on the basis of insufficient evidence, second, stating the conclusion with an inappropriate level of confidence, and, third, using poor evidence (inaccurate, unreliable).

There are some other problem areas, as follows (this list is not intended to be exhaustive).

1. Don't end up begging the question, that is, assuming the truth of what you have set out to prove. For example, consider the argument: "The government must reduce spending because the government is spending too much money." This argument is using as evidence what it set out to prove or recommend. Here are other examples: "People should not break the law because breaking the law is bad," "Odysseus spends little time at home because he is always away," "I failed the course because my marks were too low."

2. Be careful not to bring in a non sequitur, that is, some evidence which is apparently irrelevant to the point you are trying to argue (e.g., "Hamlet is clearly insane because Polonius doesn't want his daughter associating with him"). Here the evidence doesn't seem, as stated, to have anything to do with the claim. Another example is as follows: "I failed the course because my teacher was overweight" or "I won't vote for Candidate Jones because her father is a communist." If there is a connection between the teacher's weight and your failure or the political beliefs of Candidate Jones's father and your voting decision, you will have to lay that out in detail. As it stands, the teacher's weight and the father's political beliefs here seem like a non sequitur, something irrelevant to your conclusions (the connection is not apparent to the reader).

3. Remember that coincidence is not cause. That is, just because B happens after A, that does not necessarily mean that A causes B. For example: "That girl is a bad influence; my Jimmy didn't drink until he met her." She might be the cause, but simply asserting the fact as stated is no proof. Of course, if there is repeated evidence (i.e., every lad she ever has gone out with has developed a drinking problem), then the argument would be more persuasive; it would not, however, be air tight. This error, as you may learn if you study correlation in statistics, is a major source of mistakes in certain areas of social science.

4. Do not simply appeal to the authority of someone well known, even if that person is an expert, unless you can point to a specific study or facts associated with the name: e.g., "Henry Kissinger says we are right to be fighting the communists. So we should be." Henry Kissinger might be right, but simply mentioning his name doesn't provide any meat to the argument. Appeals to authority may be useful in supplementing an argument, but in themselves they are not very useful.

5. Concentrate on the facts and principles of an argument. Don't try to make a case simply by attacking the motives, the appearance, or the other beliefs of those who do not support the position you are advancing.

4.16 Exercise in Evaluating Short Arguments

Comment on each of the following arguments. Note that some are deductive and others inductive. If you can perceive a specific problem, then identify it. If you think the argument is quite persuasive, then indicate that.

1. Of course, his argument is hopelessly wrong. After all, he's a Roman Catholic priest. What do you expect?

2. The survey questionnaire on plagiarism was completed by 85 percent of the faculty. Three-quarters of the respondents said they definitely felt that plagiarism in first-year papers was on the increase. I think we have a problem here which we should investigate further.

3. I've had ten cats at different times; they all ran away. Obviously, cats make bad house pets.

4. In the opening of the Odyssey the gods repeatedly state that anyone who violates someone else's home must be punished. This strongly suggests that there is some divine moral order in the world of this book.

5. The economy started to go downhill right after the NDP government was elected. Clearly, they don't know how to run a provincial economy.

6. The people who oppose my reforms all have vested interests in keeping things the way they are. As far as I am concerned, their snouts are so deeply immersed in the trough, they are incapable of any intelligent discussion more than grunts to each other while they chow down on the public purse.

7. This is a really good poem because it has a sonnet structure, with a basic blank verse rhythm, and a strong repetitive rhyme scheme.

8. Look, this player for the entire season led the team in scoring, in rebounding, in assists, and in blocked shots, and he played in every game during the season. He is clearly a strong candidate for the most valuable player on the team.

9. Students should all have to study first-year English at college because they all need at least two semesters of English. And my mother is all in favour of the regulation, too.

10. Women are obviously different from men in some important ways, but their similarities are much more significant than their differences. And thus they must receive equal treatment, if we believe in equality under the law.

11. That film is pornographic; two or three scenes feature full male and female nudity.

12. Macbeth gets very keen on becoming king after he meets the witches. This proves that they are the cause of his ambition.

4.17 Induction in Arguments on Literary Topics

Many essays on literary topics are principally inductive arguments. In them the arguer is examining the text of a work of literature, locating patterns (e.g., patterns of imagery, or behaviour, description, and so on), and drawing conclusions on the basis of those patterns.

The most clearly argumentative essay on a work of literature is a review in which the arguer evaluates the text or something in it by focusing on very particular features in the work itself and explaining how these facts affect the quality of the work for better or worse. For example, in a film review, the critic will usually refer to patterns in the characterization, the camera work, the special effects, and the dialogue (or in some of these) to argue for a certain judgement (two thumbs up or down or one up and one down).

When you write an argumentative essay on a work of fiction (poem, play, film) or on a painting or piece of music, the quality of the argument is going to depend upon the way in which you can point to direct evidence in the work and persuade the reader of your review that your assessment of those details is persuasive. Unless the argument is very firmly anchored on the specific details of the work (i.e., has a firm inductive basis), it will not be very persuasive.

We will be addressing this matter again, but for the moment it is important to remember that any evaluative argument about a literary work which does not deal with the facts of the text is not going to be effective. Thus, you should not turn an evaluative argument about a work into a digressive study of the biography of the author, a summary of her other works, a psychological self-assessment of your mood at the time, or a weighty discussion of matters outside the work you are considering.

4.18 Deduction and Induction in Combination

Most arguments combine both deduction and induction. Deduction supplies the shape of the argument and induction establishes agreement about one or more stages in the argument. Notice the following examples:

Argument 1

General Principle: Many forms of bacterial infections can be successfully treated with antibiotics.

Specific Application: Many cases of ulcers are bacterial infections.

Conclusion: Therefore, many cases of ulcers may be capable of being treated successfully with antibiotics.

Argument 2

General Principle: In a democracy, all candidates for public office who accept donations from foreign governments must be forced to resign.

Specific Application: Candidate Jones, who has just been elected in a democratic process, has accepted cash donations from the governments of several foreign countries.

Conclusion: Therefore, Candidate Jones must be forced to resign.

In these two arguments, it is easy enough to agree to the General Principle. But before accepting the conclusion, we will need to know if the statement in the Specific Application is true. To establish the truth of that in each case, the arguer will have to provide some inductive reasoning (e.g., facts, experimental results, investigative data, and so on). Here's another example of deduction and induction used in combination:

General Principle: All cholesterol is damaging to the human circulatory system.

Specific Application: Brand X contains a significant amount of cholesterol.

Conclusion: Therefore, Brand X is damaging to the human circulatory system.

In this deductive argument, the opening General Principle is not something we all agree on; most of us probably don't know one way or the other. So, before going any further, the arguer will have to establish the truth or high probability of that claim. This will require an inductive argument. Once, the arguer has persuaded the readers that the opening statement is correct, then the argument can proceed to the next step, which would be to establish the truth of the Specific Application (again by induction).

Here's another combination argument, one which begins with two General Principles:

General Principle 1: All animals must come from at least one living animal parent.

General Principle 2: Some animals species were on earth before others.

Specific Application: Invertebrate animals were alive on earth long before vertebrate animals appeared.

Conclusion: Therefore, vertebrate animals must have come originally from invertebrate animals.

Before accepting the conclusion, we will want to confirm the validity of the General Principle 2 and of the Specific Application. Establishing these will require inductive evidence. If these principles are correct (and they both have been established beyond reasonable doubt for many years), then the conclusion is rationally compelling. The above argument is the best single proof for the truth of evolution.

The point of these examples is to show that deduction and induction are commonly combined, with deduction providing the overall structure and the basic logic leading to a conclusion and induction confirming the truth of the statement in the general principle or the specific application. The inductive part of the argument will normally take up most of the space, since the presentation and interpretation of evidence is more time consuming than the deductive process.

This last point can be summed up in the famous example from Francis Bacon about the three sorts of scientists: ants, spiders, and bees. Ants spend all their time collecting facts (they are purely inductive); spiders spend all their time spinning amazing designs out of their own abdomens (they are purely deductive). But bees collect material from the natural world and transform it into complex organized structures (i.e., they combine induction and deduction). Bacon encouraged would-be scientists to become like bees.