Introduction

Human beings are called the rational animal. While rationality is not particular to human kind, it is arguably our most important characteristic. The ability to reason has given us science and technology, the ability to survive and flourish, and the ability to deal with the problems of daily life and to philosophize about the universe.

Reason is a powerful tool and with it comes the responsibility of its proper use. You already know how to reason and probably do it quite well. In fact, you already know how to do everything we will talk about in this course. The aim of this course, however, is to teach you to reason better. Part of this involves understanding how reason works and the rules the proper use of reason needs to follow. These are things you probably don't know or haven't thought about carefully.  By learning about these you can make your own arguments stronger, and can evaluate the arguments of others more effectively.

Take a look at the following six passages. Which of these do you think are good arguments?

1. The discussion of the status of same-sex partnerships ignores one thing. Since prehistoric times, the family has always meant a male-female partnership intended for raising children. Who are we to undermine countless years of family life and the unquestionable facts of biology?

2. I can't believe you're telling me I should drink less. You drink at least as much as I do. You practically live on a barstool. In fact I've never seen you without a beer in your hand.

3. I find it a little odd that you'd support euthanasia for the seriously ill.  That's one of the policies that  Hitler supported

4. Father O'Neill says that abortion is a mortal sin. He says that it is murder since the fetus has a soul from the moment of conception. But he is a Catholic priest, and priests are required to hold views like that, so I don't think we really have to take him seriously.

5. People who claim that hunting is wrong because it kills living things are just sentimental wimps who think that feelings are a subsitute for facts.

6. I went for a walk last night but when I got to Kensington it started to snow, so I turned around and went home.

If you said that none of them are good arguments, and that (6) isn't even an argument at all, then you are on the right track. If you thought otherwise, then this course can help you understand why you were mistaken

  Identifying Arguments

What Is an Argument?

When asked to think about an argument we often imagine a disagreement of some sort, where two or more people are involved in a fight about some point or issue. This is the colloquial or everyday understanding of the word “argument.” We will use the word to mean something considerably broader than this. Arguments do not always involve disagreements. Television ads are arguments, yet you are not involved in a disagreement with your television (I hope). The broader definition of argument we will work with is similar to the one offered in the following audio clip:

www.wilstar.com/midi/ram/argument_clinic.ram The character seeking an argument in the above sketch gives us a pretty good definition of an argument. He describes an argument as “a collective series of statements to establish a definite proposition.” Notice, however, that the man behind the desk assumes that in order to have an argument he must take up a “contrary position”. This involves a different understanding of the word “argument” that is more like the one mentioned above. In a disagreement there are (at least) two contrary positions, and each side attempts to convince the other of the merits of their views. For our purposes, we will understand the word “argument” in the first sense rather than the second. I would like to augment the above definition as follows:

Argument: an attempt to justify or prove a conclusion through rational means.

The reason this is a more suitable understanding of the an argument is that arguments do not only occur when there are disagreements. Whenever someone tries to convince someone else of the truth of a claim through rational persuasion, that person is making an argument. When we do this, it is not necessarily the case that the person to whom the argument is directed disagrees with us. The other person might have no opinions one way or the other.

The idea that an argument justifies a conclusion by means of rational persuasion is important. There are other ways to make people accept a conclusion, but the use (or threat) of force or intimidation to make people believe something is not an argument.

The Components of an Argument

Every argument has the following components:

1. A Conclusion What the argument is trying to get you to accept. In any argument there is a claim the truth or falsity of which the speaker wants you to accept.

2. Premises Reasons used to support the conclusion. These are the points used to convince you of the truth of the conclusion of the argument. Sometimes there can be as few as one premise in an argument, or as many as one can write out or state.

Indicator Words

As we will see, in order to evaluate an argument it is important to be able to identify which part of the argument is the conclusion, which parts are the premises, and to be able to distinguish one premise from another. Indicator words can assist you with this task. There are certain words and phrases that tend to introduce conclusions and premises in arguments. We will call these “indicator words.”

Indicator Words for Conclusions thus, therefore, hence, so, it follows that, shows that, indicates that, proves that, then

Indicator Words for Premises

for, since, because, for the reason that, on the grounds that, follows from

Example

Ted won the intercollegiate ten thousand meters last year and has been training hard ever since, so he should win easily this year. The word “so” indicates the presence of a conclusion. “He should win easily this year” is the conclusion of the argument. The rest of the passage is used to justify the conclusion and hence, make up the premises of the argument.

Example

Hockey is Canada's national sport. A country's national sport is likely to be very popular in that country. Therefore, hockey is likely to be very popular in Canada.

“Therefore” is another indicator word that tends to introduce a conclusion. “Hockey is likely to be very popular in Canada” is the conclusion of the argument, and the other claims are serving as premises to support this conclusion.

Example

Since you have proven untrustworthy in the past, I shouldn't give you my credit

card number.

“Since” is also an indicator word, but tends to indicate the presence of a premise. The claim that “you have proven untrustworthy in the past” is serving as a premise, or is being used to support the claim that “I shouldn't give you my credit card number”.

Be Careful When Relying on Indicator Words

Sometimes, claims or statements use indicator words, but aren't arguments.

Example

Since John's wife left him, he's been depressed.

Although the word “since” appears here, it is not being used to introduce a premise. The above passage is not an argument at all since it is not trying to convince us of anything.

Example

John's wife filed for divorce on the grounds that he had an affair with the dry cleaner.

“On the grounds that” tends to introduce a conclusion, but does not serve that function here.

Because indicator words are not a foolproof way of identifying premises and conclusions, you should not rely on them entirely. They will be most reliable as guides to identifying premises and conclusions when you are already sure that the passage you are dealing with is an argument. The above two passages are not arguments, which is why the indicator words they contain do not indicate the presence of conclusions or premises.

The best way to identify an argument is to learn how to distinguish one from other kinds of written or spoken passages that sometimes look like arguments. There are two kinds of passages that can frequently be confused with arguments. These are explanations and descriptions.

Explanations

Arguments try to convince you of a conclusion or give you reasons to believe something is true. Explanations tell you why something is true or is the way it is but give you no reasons to believe it is true.

If you read a passage and suspect that it might be an explanation rather than an argument, but are still unsure even after thinking about the general difference between arguments and explanations, then you can make use of the following methods for distinguishing between arguments and explanations.

There are several questions you can ask about a passage that will help you determine whether it is an argument or an explanation.

1. Does the passage in question give us evidence or causes?

Explanations usually answer why-questions. When someone offers an explanation it is in response to a question about why something is the way it is, why someone did such and such, or why something happened. Usually, when we answer such questions we do so by talking about what caused them to happen. Thus, if a passage identifies a cause for the main claim being discussed, then it is probably an explanation. On the other hand, if a passage gives us evidence, then we probably have an argument. Think of the purpose of evidence in a trial. Evidence is presented as part of an argument used to convince the jury of the guilt or innocence of the defendant. Although motive is important, the crucial thing in a trial is whether or not the person accused did in fact commit the crime, not why they did it. Evidence aims at establishing what is true. Arguments try to convince you that a particular claim is true, so arguments invoke evidence in the form of premises

Example John went to lunch because he was hungry. The main point of this passage is that John went to lunch. The rest of the passage identifies the cause of his going to lunch. Because it identifies the cause of John's going to lunch, this is an explanation. It answers a why-question: “Why did John go to lunch?” If this were intended to be an argument it would not explain John's going to lunch, but would instead try to convince us that it is true that John went to lunch. Saying that John was hungry does not give us any reason to believe that he in fact went to lunch. The following does give us reasons, or evidence, to believe that John went to lunch, and is therefore an argument:John went to lunch. It's twelve o'clock, and he always eats lunch at twelve o'clock.

Example The last person he asked out on a date laughed at him, hence John is afraid to ask anyone out. This explains John's fear of asking people out on dates. It is therefore an explanation and not an argument.

Example

Since John was in a terrible accident, he has no nose. This is an explanation because it identifies the cause of John's lack of a nose. Notice that all of these explanations contain indicator words. This shows why one cannot rely only on indicator words to identify conclusions and premises. Explanations do not contain premises or conclusions, even though they can contain indicator words.

Arguments About Explanations

You need to be careful not to jump to the conclusion that a passage is an explanation just because it mentions causes. One often sees arguments about which one out of a number of competing causes is the correct one for some event or phenomenon. Example Everyone thinks that Dewy broke the Ming Vase, but I know it was the dog. I saw the dog skulking away with his tail between his legs right after I heard the vase break. In this case we are presented with two explanations for the vase breaking: Dewy broke it or the dog broke it. The passage tries to convince us that one of these explanations is correct and that the other is mistaken. The claim about the dog's behaviour is used as evidence to support the veracity of the speaker's explanation. Although this passage mentions causes, its aim is not simply to explain why the vase broke, but to prove what the correct explanation is. Hence, this is an argument.

1. What am I most willing to believe?

Identify the main point of the passage. What is it about? If it assumes you already know or accept the main point and then offers reasons why it is true, it is an explanation. This is a reliable guide for the following reason. Think about the purpose of an argument. When you argue with someone you try to get him or her to accept something they didn't accept before. If the other person accepts everything you say, then no argument is needed, for you don't need to convince them of anything. A rule of argumentation is that premises must always be more certain than conclusions. If they weren't, then they couldn't be used to support or justify conclusions. In an argument, then, the main point (the conclusion) is usually something that is not obviously true, and the purpose of the argument is to provide evidence that it is true. In the case of an explanation, the main point is usually obviously true, and what isn't so clear is why it is true.

The following chart helps to illustrate the differences between arguments and explanations in terms of which claims are certain and which are uncertain.

More Certain

Less Certain

Arguments The Other Points

The Main Point

Explanations

The Main Point

The Other Points

Example There are several reasons why a child's school performance can

deteriorate suddenly. Often it is because of a problem at home, such as the parents going through a divorce. Such transitions can be extremely difficult for children. They become preoccupied, withdrawn, and easily distracted, all of which has an adverse effect on their ability to concentrate.

This is an explanation of why many children suddenly do worse at school. We are probably willing to accept the claim that problems at home are a major contribution to poor performance at school. Since that is the main point, and we are willing to accept it without any convincing, and since the rest of the passage explains why the main point is true, we have an explanation.

Example Although there are several reasons why a child's school performance can deteriorate suddenly, the most common of these is because of a problem at home, such as the parents going through a divorce. Statistics show that 76% of children who suddenly do poorly at school come from families with unstable relationships.

This is an argument. In this case, we are more willing to believe the statistic about children (that's the power of statistics) than we are to accept the more general claim about why children suddenly do poorly at school. The statistic serves as evidence for the main point, which we might be unsure of before we learn that statistic. Notice that that this argument also talks about causes, but the purpose of the passage is to convince us that a particular explanation is the correct one and not merely to provide an explanation.

2. What makes more sense?

This involves three things. o Use The Principle of Charity

We should interpret the speaker or author in as charitable a fashion as we can. That is, given the choice between a weak argument and a reasonable explanation, treat the speaker's words as an explanation if the circumstances support this interpretation. Being charitable to the speaker means attributing the more plausible claim to the speaker.

Example Mark is a miser. His family had very little money when he was growing up and his father made him work in the salt mines to supplement the family income. He was taught to save every penny and not to waste anything.

While the speaker might intend this to be an argument to prove that Mark is a miser, it would be a poor one. It is much more plausibly interpreted as an explanation for Mark's behaviour. To prove that Mark is a miser it would be much more effective to point

out that he's never paid for a round of drinks at the pub, that he only goes to the movies on Tuesdays, and so on.

Example Sparkly Toothpaste contains tiny gnomes who work for hours after you have stopped brushing to clean your teeth continuously.

While this could be an argument for you to buy Sparkly Toothpaste, it is more plausibly an explanation for why it gets your teeth so clean. It would be easier to argue that you should buy it if it were less expensive than other kinds toothpaste and if it gets your teeth cleaner than other brands of toothpaste.

o Focus on the context of the remark or passage.

“Context” here refers to the circumstances in which the passage appears. This can be a matter of who makes up the intended audience (i.e., what kind of people are they and what are they likely to know or believe?) and what else is happening when the claim is made. In general, determine what the audience is expected to know.

o Will they already be aware of or accept the main point? If so, then it is an explanation. If not, then it is an argument.

Example (Said as you approach the DVD player) Don't waste your time. It's broken. You can't play any movies on that player.

This is an argument intended to provide you with evidence that trying to use the DVD player will just waste your time. You don't accept the main point yet (that you can't play any DVDs on that player) because you intend to do just that since you don't know that it is broken.

Example (Said as you try to play a DVD) Don't worry. You didn't break it. It's unplugged.

This is an explanation. You already know the DVD player doesn't work and I'm explaining why.

Example (You meet someone who never practices safe sex and say) Sex without a condom is very dangerous. Sexual contact can transmit AIDS.

This is an argument. You are trying to convince the other person

that unprotected sex is dangerous.

Example (Said to a room full of professional philosophers) God plays a central role in Leibniz' metaphysical system to account for the apparent relations between human minds since, in his view, human beings are windowless monads.

This is more plausibly interpreted as an explanation of why Leibniz requires God in his metaphysics than an argument that he does require God. This is because a room full of professional philosophers will already know that God plays an important role in Leibniz' metaphysics. Since they are likely already to accept the main point, this is better regarded as an explanation.

o Are there better arguments? That is, is there another, more direct and obvious way to argue for what seems to be the main point?

Part of what it means to use the principle of charity is that you treat the speaker as though he or she is intelligent. Intelligent people use good arguments based on premises that are obviously related to the conclusion and are not contentious.

o Example Abortion is immoral because it is illegal.

This could be intended as an argument, but is more charitably interpreted as an explanation. The fact that something is illegal does not necessarily mean it is immoral. Law and morality do not always coincide. One could more effectively argue that abortion is immoral by talking about the immorality of killing, etc.

Example In France, the films of Pauley Shore are considered a superior art form. His work is similar to the early films of Jerry Lewis, which were extremely popular among the French.

Again, this could be intended as an argument that tries to show that Pauley Shore's films are worthy of artistic merit, but is more plausibly interpreted as an explanation for his popularity in France.

To argue that Pauley Shore's films are worthy of artistic merit, one would instead list off all of the awards his films have one at film festivals, cite positive reviews by reputable film critics, etc.

Descriptions  Descriptions are neither arguments nor explanations. They are lists of facts.

They usually offer you new information, but provide no reasons for their truth and provide no reasons to believe that they are true. All they do is provide information.

A description differs from an argument since an argument tries to convince you of something and a description does not.

A description differs from an explanation since an explanation tells you why something is the way it is and a description simply tells you that things are a certain way.

Example Iggy Pop was one of the first popular Punk musicians in North America. When I saw him on my 20th birthday, the people in the front row continuously spat on him.

This is a straightforward description. The speaker is not trying to convince us of anything, nor is he trying to explain anything about Iggy Pop.

Example Sartre and Kierkegaard believed that we define ourselves through our actions. In their view, beyond being metaphysically free or self-determining beings, there is no such thing as a common human nature.

This is a Description. It simply describes what Sartre and Kierkegaard believed.

Example I tell you that God is in his heaven and all is well. I can only say that the life of faith is a joyous one.

This is not likely an explanation, since the other plausibly explains neither claim. However, the context might make a difference as to whether it is an argument or a description.

If the speaker has been trying to convince us that the life of faith is happier than a life without faith, then knowing that God is in heaven and that all is well (if one could know that) might justify this claim. In this case, we would have an argument.

Alternatively, the speaker could be trying to describe what a life of faith is like, in which case, knowledge (or belief) about heaven is just another fact in the list and plays no justificatory role.

What would the Principle of Charity suggest about how we ought to interpret this passage?

This is better characterized as a description, since there are much more

effective ways to justify the claim that the life of faith is a joyous one.

For instance, one could speak of one's sense of moral accomplishment and satisfaction, one's sense of personal security, etc

Example The odds against two snowflakes being identical are so great as to approach certainty. A snowflake consists of about 1018 water molecules. As the snowflake gets larger, molecules attach themselves to it essentially at random. The number of ways that 1018 molecules can be arranged into six-sided crystals is astronomical—a great deal larger than the number of snowflakes that have ever fallen on earth.

This seems like an explanation. Why? Because most people already accept the claim that no two snowflakes are identical. Given that, it seems as though the rest of the passage explains why this is so. But is the main point of the passage that no two snowflakes are identical, or is it something slightly different?

The main point of the passage is that we can be certain that no two snowflakes are identical. The rest of the passage provides support for this claim. Hence, we have an argument.

Propositions

When we begin to analyse and standardize arguments, it will be important to be able to identify premises and conclusions, and to break arguments down into their simplest components. Sometimes one premise of an argument supports one part of an argument and another premise a different part. To reveal the logical structure of an argument we first need to be able to identify all the parts that make up the argument. These parts are called “propositions.”

A proposition is a statement or assertion. One of the defining features of a proposition is that any proposition must be either true or false.

“It is raining outside” is a proposition. It assets something about the world (a fact or state of affairs), and it is either true that it is raining outside or it is false.

“I hate jazz” is also a proposition and, depending on the actual preferences of the speaker, is also true or false.

“Shut the door” is not a proposition. This claim is an imperative or a command. It does not assert or describe a state of affairs, but tries to make someone else do something or change the world in some way. While it can be true or false, for instance, that “Geoff shut the door,” the imperative “Shut the door” itself is neither true nor false.

“Ouch!” is not a proposition either. This is simply an expression of someone's feelings. While “I hate jazz” also expresses someone's feelings toward jazz, “I hate jazz” can be true or false. “Ouch” is neither true nor false. In fact, we can't even imagine how we would test whether or not “ouch” were true.

Simple and Compound Propositions

There are two kinds of propositions: Simple and compound.

A simple proposition expresses a single, complete thought. A compound proposition expresses more than one complete thought.

Simple Propositions

A simple proposition contains 1 subject and 1 predicate.

“John is tall” is an example of a simple proposition. Its components are as follows:

Subject: John Predicate:is tall

Notice that in order to have a complete thought we require a subject and a predicate. If I say, “Is tall,” I don't make any sense. You will want to ask me, “Who is tall?” This is because I have not expressed a complete thought. Similarly, if I say, “John,” I don't appear to be making sense either (unless I'm trying to get

John's attention, in which case I'm not uttering a proposition). You would likely ask me, “What about John?

Compound Propositions

A compound proposition expresses more than one complete thought because it contains more than one subject or predicate, or both.

“I love you and you love me,” is an example of a compound proposition.

This can be broken down or analyzed into 2 simple propositions:

“I love you” AND “You love me”

It is also important to note that the same proposition can be expressed in a variety of ways. Each alternative way of expressing the same proposition is said to be equivalent, or to have the same meaning. For example, “We are in love,” is the same proposition as “I love you and you love me.” “I love you,” is equivalent to “Je t'aime.”

Why break down compound propositions?

When we standardize arguments we need to break the supporting premises into their simplest components so we can see if each part of the claim is supported or plausible. Any compound proposition must therefore be analyzed into simple propositions.

Standardizing Arguments

 

Once you can recognize an argument there are some things you need to be able to do before you can evaluate it. To evaluate an argument one requires an understanding of the logical structure of the argument. To see this structure one must be able to identify the premises and conclusions and show how they are related to one another. That is, which premises support which claims. This is what is called “standardizing” an argument. Doing this is helpful because once one can clearly see which premises support which conclusions, one is in a better position to evaluate the argument. Think of it this way. If I build a mousetrap you cannot say whether it is a good or a bad mousetrap or offer ways to improve the design unless you have some understanding of how my mousetrap works. Similarly, unless you understand how someone's argument works, you cannot offer a useful criticism of that argument.

The first step in standardizing an argument is to identify the conclusion.

Here are a few hints to help you identify conclusions.

1. Look for indicator words associated with conclusions.2. The conclusion is usually the main point of the passage.3. The conclusion usually appears at the beginning or at the end of the

passage.

We will employ the diagram method for our standardizations. This involves the use of boxes and arrows. Identify the conclusion of the argument. Put it at the top of your page in a box. Identify the supporting premises by listing them below, each premise in its own box, with an arrow illustrating that the premise supports what is above it.

  The Diagram Method

  Schematically, we arrive at a diagram that looks something like this:

Let's try an example.

Philosophy is one of the best subjects one can study at university because it teaches you how to think clearly.

The place to start is by identifying the conclusion of the argument. The conclusion is: “Philosophy is one of the best subjects one can study at university.” This is the main point of the passage and seems to be a claim the truth of which the speaker wishes to convince the reader.

The rest of the passage is made up of the following proposition: “Philosophy teaches you how to think critically.” Notice the indicator word “because” (which is associated with premises) that precedes this proposition. This therefore serves as a premise in support of the conclusion.

The standardization of this argument would look like this:

Let's try another example.

Since Pat was a professional soccer player, and since she is a born leader, she should be the captain of the team.

What is this passage trying to convince us about? The main point it wants to convince us about is that Pat should be the captain of the team. This is therefore the conclusion. The other two claims, that Pat was a professional soccer player and is a born leader, each lend

independent support to the conclusion and thus are intended to be separate premises. The standardization of the argument will look like this:

  Subarguments

 

Subarguments are used to support one or more of the premises of an argument.

When an argument contains a subargument, it has a “mini-argument” within it to justify one or more of the premises used to support the main conclusion.

Schematically, an argument containing a subargument might look like this:

Here everything represented inside the dotted line is a subargument. The conclusion of the subargument is premise 1, of which subpremises 1 and 2 are the premises.

An argument can frequently be made stronger by adding subpremises. If any of the main premises are questionable, then it is a good idea to support them. This is the function of a subargument.

Let's take our argument about Pat, the soccer player. If I want to convince you that she should be the captain of the team and offer the reasons mentioned above, it might not be obvious that she is a born leader. To make my argument stronger I would provide a subargument the conclusion of which is that she is a born leader. For instance, I might say that when lost in the woods with her friends she took charge and kept everyone calm until the park rangers found them.

By adding this subargument we would need to amend the standardization above in the following way:

Let's try a few more examples.

Example

Jones took it. Frank knows Jones did it because he saw the whole thing on the surveillance tape.

Here we have three propositions:

Jones took it

Frank knows Jones did it

Frank saw the whole thing on the surveillance tape

When you are asked to standardize an argument, sometimes it can be helpful to write each proposition down on a scrap piece of paper. This way you can try alternative standardizations until you find one that best represents the structure of the argument.

The main point of the passage seems to be that Jones took it, so this proposition would be the conclusion. How are the other propositions related to the conclusion and to each other?

The proposition Frank knows Jones did it certainly seems to support the conclusion, that Jones took it, but so does the third proposition.

Here you need to ask yourself whether the proposition about the surveillance tape makes the argument stronger by supporting the conclusion directly, or by functioning as a subpremise supporting the claim about Frank's knowledge. If we are given reasons to believe that it is true that Frank knows Jones did it, then that would make for a stronger argument than if we were just told that Frank knows this without any support. Hence, it looks as though

the argument contains a very simple subargument and should be standardized like this:

Now let's try a much more complicated example.

Boston is a more interesting city than Toronto. It has more interesting architecture and there is more to do in the Boston area. There are many terrific shops and beautiful places to visit nearby.

This time, let's look at the standardization and then discuss why it is an accurate way of representing the argument.

It should be reasonably clear that the conclusion is the proposition Boston is a more interesting city than Toronto. This is the main point of the passage and appears at the beginning of the paragraph. Why are the other propositions arranged in this way?

First, let's look at the claim that Boston has more interesting architecture. Clearly this does not support the claim that Boston has many terrific shops or that there are many beautiful places to visit near Boston. Shops are not ordinarily considered to be terrific because of their architecture, and the claim about Boston's architecture is a claim about Boston itself, not about

places near Boston.

Could this premise be thought of as supporting the claim that there is more to do in the Boston area?

This sounds plausible but is not the best way to standardize the argument for two reasons. First, the conclusion is about how interesting Boston is relative to Toronto, and saying that Boston is architecturally more interesting than Toronto gives this conclusion direct support. Second, the fact that Boston is architecturally more interesting than Toronto does not necessarily support the claim that there is more to do in Boston. A city can be full of beautiful buildings, yet there might be nothing to do in that city.

What about the rest of the argument? It seems pretty clear that having places to shop and beautiful places to visit nearby are things to do, and hence, are best thought of as supporting the claim that there is more to do in the Boston area. Clearly, the claim that there is more to do in Boston does not support the claim that Boston has more interesting architecture, but is directly related to the conclusion. If one city offers more things to do than another, then it is probably the more interesting city.

 

Kinds of Premises

 

We have already seen that there is more than one kind of premise. There are premises and subpremises. Premises support a conclusion directly, and subpremises are used in subarguments to support either premises or other subpremises.

There is another difference between premises that concerns their logical relationship to the propositions they support. Premises can be either convergent or linked.

 

Convergent Premises

 

Convergent premises work independently to support the conclusion.

By “independently” the idea is that a convergent premise supports its conclusion without requiring the truth of other premises. So far, all of our examples have involved convergent premises.

Consider the previous example. The claim that there are more terrific shops in Boston than Toronto supports the claim that there is more to do in Boston than Toronto all by itself; it does not need to be accompanied by the claim that there are many beautiful places to visit near Boston.

Similarly, in order for the claim that there is more to do in the Boston area to support the conclusion that Boston is a more interesting city than Toronto, it does not have to be true that Boston has more interesting architecture. Each claim gives the conclusion independent support.

  Linked Premises

  Linked premises are interdependent and must work together to support the conclusion.

This means that if two premises are linked, they must both be asserted to support the conclusion. Neither premise supports the conclusion at all without the other.

When we standardize an argument with linked premises, we represent linked premises by connecting them with a line or a bar. Schematically, such an argument will look like this:

Example

If Jesse makes that shot, then I'll be a monkey's uncle. Jesse made the shot. I'm a monkey's uncle!

The conclusion of this argument appears at the end of the passage. It is supported by the other two propositions that appear as linked premises. The reason they are linked is because neither one gives the conclusion any support unless the other is asserted as well. The claim that Jesse made the shot does not support the claim that I'm a monkey's uncle unless we are also told that if Jesse makes the shot, then I'll be a monkey's uncle.

The same is true of the other premise. The claim that if Jesse makes the shot, then I'll be a monkey's uncle does not give any support to the conclusion (I'm a monkey's uncle) unless we are also told that Jesse made the shot. Hence, these are linked premises.

Let's look at another example.

Example

Either we go to the movie or we go out for dinner. We can't afford to go to dinner, so we should go to the movie. We don't have much cash because we don't get paid until next week.

  Counterarguments

  A counterargument is an argument that responds to another argument. Counterarguments have the goal of denying the conclusion of the original argument, either by offering new premises in support of a different conclusion, by undermining the premises used to support the conclusion, or by showing that the conclusion of the original argument does not follow from the premises offered to support it.

To help you identify counterarguments, look for the following indicator words:

but, however, on the other hand

When standardizing a counterargument, one should first identify and standardize the original argument it is responding to. It is very important to standardize it properly. Otherwise, it is difficult to evaluate the counterargument. Once you have done this, standardize the counterargument below the argument.

Example

Some argue that Ridley Scott is a better Director than Stanley Kubric. They point out that Scott has already made more films than Kubric, and that experience is the key to being a good director. But experience does not always make one a good director. Ed Wood made many films, all of which were awful.

First, identify the argument this passage is responding to. The argument seems to be that Scott is a better director than Kubric because Scott has made more films than Kubric and experience is the key to being a good director.

Now let's standardize this argument:

Notice that the two premises are linked. Unless both premises are asserted together neither one supports the conclusion.

Now, let's identify the counterargument.

Notice the indicator word “but”. This introduces the counterargument: But experience does not always make one a good director. Ed Wood made many films, all of which were awful.

Before we go any further we need to consider the purpose of the counterargument. Recall that we saw above that the aim of any

counterargument is to deny the conclusion of the argument to which it is responding. What was the conclusion of the original argument? It was this: Ridley Scott is a better Director than Stanley Kubric. The conclusion of the counterargument must be a cautious denial of this claim: Ridley Scott is not necessarily a better director than Kubric.

Why is the conclusion this rather than say, Ridley Scott is not a better director than Kubric or, Kubric is a better director than Scott?

In this case, and this will be true of many counterarguments, the aim of the speaker is only to show that the conclusion of the original argument does not follow from the premises offered. This does not mean that the conclusion is false. It might still be true that Scott is a better director than Kubric, but the argument has not given us good reason to believe this is true.

When you reconstruct counterarguments you will often need to formulate and add the conclusion of the counterargument yourself. When you do, remember that you should do so cautiously. Don't make the conclusion stronger than it needs to be or stronger than the premises warrant.

In light of all this, the counterargument is something like this:

Ridley Scott is not necessarily a better director than Kubric. Although Scott has made more films than Kubric, experience does not always make one a good director. Ed Wood has a lot of experience as a director, but all of his films were awful.

The standardization of the counterargument should look like this:

Notice here that the premises are all linked rather than convergent. Once again, the reason for this is that the linked premises depend on each other. Without also saying that all of Ed Wood's films were awful, the claim that Ed Wood had a lot of experience as a director does not lend any support to the claim that experience does not necessarily make one a good director.

Example

Sure, I see the merit in raising taxes next year. As you say, it will fund some needed social programs, but we already pay too much tax in Canada. In fact, we pay the highest amount in taxes of any G7 nation. Taxes should come down, not go up.

Argument

Counterargument

  Counterconsiderations

  Counterconsiderations are claims or propositions that count against the conclusion. These differ from counterarguments in the following way. Counterconsiderations are not used as premises to support an opposing argument. They merely serve as an acknowledgement that there exist points the author is aware of that tend to detract from or weaken the author's conclusion. Identifying counterconsiderations in one's own argument is like giving a nod to the opposing side or saying the opposition has a point, but without surrendering what is important in one's own views. It is like saying, “I am aware of certain problems with this argument, but these problems are not serious enough to undermine my conclusion.”

There are certain indicator words that tend to be associated with counterconsiderations and can help you identify them:

although, it is true that, on the other hand, despite

When we standardize an argument with counterconsiderations, we list them underneath the standardization of the argument.

Example

Despite the fact that the fetus is genetically human, abortion early on in a pregnancy is not equivalent to murder. What is important is the status of the fetus as a moral being or a person, and a fetus does not become a person until the third trimester.

Example

Although Durkheim provided convincing arguments to show that the concept of God emerged as an inevitable mechanism of social control, these arguments do not prove that God does not exist. Durkheim merely identifies possible origins of the concept of God. The idea of something can have social origins and yet exist in reality as well.

  Missing Premises and Conclusions

  Often arguments have missing premises, conclusions, or both.

This can happen under the following conditions:

1. The speaker asks a rhetorical question (one that anticipates a particular answer).

2. The speaker has simply failed to make all the premises (or conclusions) explicit.

Example

You shouldn't eat that Whopper. What about your diet?

Here the conclusion is that you shouldn't eat that Whopper. The premises used to support this conclusion are implied but have not been made explicit. The question about the diet suggests that the person being addressed is on a diet, so one of the premises is something like:

You are on a diet.

There must be more to this argument, however. It seems there is also a missing premise about Whoppers being the wrong sort of thing to eat when on a diet.

Each Whopper contains 42 grams of fat (or something similar) would be a suitable premise to motivate the conclusion.

So we can rephrase the argument more explicitly as follows:

Since you are on a diet and each Whopper contains 42 grams of fat, you shouldn't eat that Whopper.

Now that the premises have been made explicit we can standardize the argument.

Now let's look at an example that is missing other elements.

You're not going to wear that outfit tonight, are you? It's a formal function.

In this example the first thing you should notice is that the conclusion is

missing. We can figure out what it is from the question “You're not going to wear that outfit tonight, are you?” The expected answer when someone asks a question like that is “No.” So the conclusion of the argument must be You shouldn't wear that outfit tonight.

The fact that the event in question is a formal occasion, by itself, gives no support to the conclusion. Hence, there must be an additional premise that is also implied and which needs to be made explicit.

That outfit is inappropriate for a formal occasion is a good candidate for this role, and is clearly implied by the question that starts off the argument.

So the argument, in expanded form, is this:

It is a formal occasion tonight and that outfit is inappropriate, so you shouldn't wear that outfit tonight.

Often, when the speaker fails to make all of the premises explicit, we can ask the speaker for more details and he or she can then provide us with the missing premises or conclusion.

Example

It is Sharon's birthday tomorrow. Therefore, Bob should buy her a present.

One thing we will want to know to evaluate this argument is whether or not there is a special relationship between Bob and Sharon.

If the speaker tells us that Bob and Sharon are married, then this should be used as a further premise to support the conclusion.

Other times we can't ask the speaker to give us more information (perhaps you are reading an article). In such cases we must fill in the missing premises ourselves. On occasions like this we must use the principle of charity.

1. The added premises must help make the argument as strong as possible.

2. We should not attribute to the speaker claims that are too strong to be plausible.

3. Strike a balance between these two guidelines.

Example

High crime rates are caused by the widespread use of probation and suspended sentences. Therefore, we should amend the Criminal Law to provide for mandatory prison sentences for all crimes.

The conclusion of the argument is:

We should amend the law to provide for mandatory prison sentences for all crimes.

This is clearly supported by the following premise:

High crime rates are caused by the widespread use of probation and suspended sentences.

What are some additional premises that are implied but have not been made explicit in this passage?

Here are two possibilities:

1. A policy of mandatory prison sentences for all crimes will lead to a reduction in crime rates.

2. A policy of mandatory prison sentences for all crimes is likely to lead to a reduction in crime rates.

Which of these two premises does the principle of charity suggest we should adopt?

(2) because (1) is too strong to be plausible whereas (2) will support the

conclusion but is less contentious (but can still be questioned). The reason (1) is implausible is that it claims that a certain policy will have definite results. (2) states that a certain result is likely, but offers no guarantee about what will happen. Since one can't predict the future, claims about what will happen are more plausible if they are qualified to say what will probably happen.

 

Assumptions and Presuppositions

 

Assumptions and presuppositions are premises that are not stated but are assumed by the speaker.

These differ from the examples we have looked at so far because these assumptions are not implied claims that the speaker meant to identify but forgot. These are claims that motivate the speaker's argument without the speaker's awareness. Assumptions or presuppositions are often a problem because they serve as premises in an argument without the speaker's awareness and are usually contentious claims, claims that, if they were brought to our attention, we would likely reject.

Example

Philosophers make the best lovers because being attentive to one's partner is essential to being a good lover.

What assumption is being made here? What are the possible missing premises? The claim must be something to the effect that philosophers are attentive people. Here are two possibilities:

1. Philosophers are always attentive people.2. Philosophers tend to be attentive people.

(1) is implausibly strong. To disprove it all one needs to do is find one instance of an inattentive philosopher (not very hard to do, in my opinion) to render the argument ineffective. Without that premise, the conclusion cannot follow. According to the principle of charity, we ought to adopt (2) as the missing premise.

 

Categorical Logic 1

 

What is Categorical Logic?

Logic is the science of inference, or the study of how premises support conclusions in arguments.

Categorical Logic is a branch of logic that studies the categorical syllogism. The word “syllogism” means “argument”. Hence, a categorical syllogism is a special kind of argument. Think of the word “category”. A category is like a heading under which objects can be collected or subsumed. Another way of talking about categories is in terms of classes. A class of objects is a group of things that share a particular property or characteristic. For example, toy is a category. Included in the class of toys are things like tops, video games, model airplanes, and so on. Categorical arguments are ones that are based on relations of class membership.

Syllogistic logic is only a small part of formal logic. If you would like to explore more of what formal logic can do you might like to look at some of the following books. These are just a few of the many good books on logic you can find in the library.

Wilfrid Hodges, Logic (Penguin, 1977) John Nolt, Logics (Wadsworth, 1997) Kent Wilson, The Essentials of Logic (Research and Education Associates, 1997) Ian Hacking, An Introduction to Probability and Inductive Logic (Cambridge, 2001) John L. Bell, David DeVidi, and Graham Solomon, Logical Options: An Introduction to Classical and Alternative Logics (Broadview, 2001)

A class is a group of objects that share a particular characteristic. Dogs is a class of objects that contains all dogs, regardless of what kind of dogs they are. Things with hair, is a larger class of objects that includes the entire class of dogs within it as well as the class Cats, Hamsters, Humans, and so on. Things that are faithful is another class that may include all dogs, some humans, but not cats or hamsters. Any one thing can be a member of many different classes. For instance, my dog is a member of the class of pets, of things with hair, things that smell, things that eat, and many other classes.

  Categorical Statements

  The basic element in categorical logic is the categorical statement. A categorical statement is an assertion in which one identifies a relationship between items in terms of whether or not they are members of certain groups or classes of objects.

Example

All philosophers are attractive

This says something about the relationship between the members of two classes: philosophers and things that are attractive. In particular, the claim says that all of the members of the class philosophers, are a part of the class things that are attractive.

Four components of categorical statements

All Categorical Statements have a certain form. They always contain the following four elements:

1. A Subject Term The subject term is what kind of thing the statement is about. In the above example the statement is saying something about philosophers. Hence, the subject term is “philosophers”.

2. A Predicate Term This is what is being said about the Subject Term. What is being said about philosophers in the above statement? We are being told that philosophers are attractive. The predicate term, then, is “attractive”.

3. A Scope Word The scope word tells us how many members of the class of the subject term we are talking about. Above we are told something about members of a class of objects. The class is philosophers. How many members of this class are we being told something about? All of them. Hence, “all” is the scope word.

4. A CopulaThe copula connects the Subject Term and the Predicate Term. This can be any of the words “is”, “is not”, “are”, “are not”. In the above example the copula is “are”.

Let's look at a few examples.

Example

Some rodents are good pets.

Subject term:rodents

Predicate term: things that make good pets

Scope word:some

Copula: are

Affirmations and Negations

All Categorical Statements are either Affirmative or Negative.

Affirmative Categorical Statement

An affirmative categorical statement is a positive statement that says that some or all of the members of the Subject Class belong to the Predicate Class.

Example

All furniture at Ikea is made of particleboard.

This categorical statement tells us something positive about all of the furniture at Ikea; that it is made of particleboard.

Negative Categorical Statement

A negative categorical statement is one that says some or all of the members of the Subject Class do not belong to the Predicate Class.

Example

No scanners are difficult to operate.

This tells us something negative about the subject class “scanners”; that none of them belong to the class of “things that are difficult to operate”.

Sometimes you can tell from the copula whether a categorical statement is affirmative or negative.

The categorical statement is usually negative if the copula is any of the following: is not, are not.

The categorical statement is usually affirmative if the copula is any of the following: is, are.

You can't always rely on the copula to determine whether a categorical statement is affirmative or negative.

Example

No dogs are philosophers.

Here the copula is “are” but the statement is negative because of the scope word “no”. To tell whether a categorical statement is affirmative or negative, first see if it starts with the scope word “no”, then check the copula.

Universal and Particular

Positive and negative categorical statements are always either Universal or Particular. The Scope Word determines whether the statement is universal or particular.

A categorical statement is universal if the scope word is either “all” or “no”. If a categorical statement tells us something about all members of a class, then the statement is universal.

A categorical statement is particular if the scope word is “some”. If a categorical statement tells us something about only some members of a class, then the statement is particular.

Example

All dogs are philosophers.

This is universal because it tells us about all members of the subject class, “dogs”.

Example

Some dogs are philosophers.

This claim is a particular categorical statement because it only tells us something about some members of the subject class, dogs.

When we combine the fact that categorical statements can be universal or particular, affirmative or negative, we end up with four possible kinds of Categorical Statements. Below, the schematized forms of each are provided, where S stands for any subject class and P stands for any predicate class.

1. Universal Affirmation: All S are P2. Universal Negation: No S are P3. Particular Affirmation: Some S are P4. Particular Negation: Some S are not P

Each of these forms is given a name from a vowel in the Latin words for “I affirm” (affirmo) and “I deny” (nego).

  UNIVERSAL PARTICULARAFFIRMO A : ALL S IS P I : SOME S ARE P

Affirmative NEGO

Negative E : NO S ARE P O : SOME S ARE NOT P

  Distinguishing Categorical Statements

 

Often, when you encounter categorical statements, they are not expressed in standard categorical form. In order to recognize what kinds of statements they are, what their components are, and how to deal with them, it is useful to be able to translate statements into standard categorical form. We often have to change the predicate statement into a class or group. Usually this takes the form of “things that…”

Example

All pubs in Ireland serve Guiness.

All pubs in Ireland are things that serve Guiness.

Example

All banana peels are slippery.

All banana peels are things that are slippery.

We also often have to change the verb in the sentence into a copula or else add a copula to the existing sentence.

Example

Some cats have fleas.

Some cats are things that have fleas.

Example

All things that are poison will make you sick.

All things that are poison are things that will make you sick.

Sometimes we also need to change the subject term in order to translate a categorical statement into standard form.

Example

Nobody with a face like that is a killer.

No person with a face like that is a thing that is a killer.

Example

Several children have colic.

Some children are things that have colic.

Example:

The French are snotty.

All people who are French are things that are snotty.

Example

The Frenchman is snotty.

All people who are the Frenchman are things that are snotty.

Why is this example translated as a universal categorical statement? It is a rule that whenever a statement is about one particular individual, that individual constitutes an entire class of its own. Any categorical statement about one specific individual, then, will always be a universal claim.

Subject and predicate terms are said to be either distributed or undistributed. Learning to recognize when a term is distributed or undistributed is very important for being able to tell whether or not a categorical syllogism is valid.

 

Distributed Terms

 

A subject term is distributed when the categorical statement tells us something about all of the members of the subject class.

Subject Terms are distributed in Universal Affirmations and Negations (A Statements and E Statements).

Example

All mosquitoes are pests.

Here the subject term, “mosquitoes” is distributed because we are learning something about the whole class of mosquitoes: that they are pests.

Example

No collection agencies are friendly.

Here we learn something about the entire class of collection agencies: that no members of that class belong to the class of things that are friendly, or that all members of the class collection agencies are excluded from the class of things that are friendly.

A predicate term is distributed when the statement tells us something about all members of the predicate class or about the whole class.

Predicate terms are distributed in Negations (E Statements and O Statements).

Example

No pianists are fingerless.

In this case the predicate class things that are fingerless is distributed because we have learned that the entire class of things that are fingerless is excluded from the class of pianists.

Example

Some birds are not scavengers.

It is often very difficult to understand why predicate terms are distributed in particular negations. What is it that we learn about the whole class of things that are scavengers? This is not obvious. The reason we do learn something about the entire predicate class is this: If we needed to find out whether or not some birds are not scavengers we would need to examine the entire class of scavengers and see what is included and what isn't included. Since we have had to look at the entire class, we learn something about the whole class.

  Undistributed Terms

  A subject term is undistributed when the categorical statement only tells us something about some of the members of the subject class. Subject terms are undistributed in particular affirmations (I statements) and particular negations (O statements).

Example

Some magazines are naughty.

In this example we learn only about some members of the subject class magazines: that they belong to the class of things that are naughty.

Example

Some movies are not for children.

Again, in this case we are being told something about some of the members of the class movies. Since we are not learning about the whole class, the subject term is undistributed.

A predicate term is undistributed when it tells us only about some members of the predicate class. Predicate terms are undistributed in Affirmations (A Statements and I Statements).

Example

Some fish are big.

The predicate term is undistributed because this tells us only about

some members of the predicate class things that are big: that some big things are fish.

Example

All penguins are cute.

The predicate term is undistributed because this tells us only about some members of the class things that are cute: that some cute things are penguins.

An easy way to remember rules of distribution is that subject terms are distributed in Universal Statements and undistributed in Particular Statements.Predicate terms are distributed in all Negations and undistributed in all Affirmations.

Let's practice dealing with categorical statements. If you see a claim and need to know which terms are distributed and undistributed, but the claim is not in standard form, translate it into standard categorical form

first.

Example

The phone is ringing.

First, put this into standard form:

All things that are the phone are things that are ringing.

What is the subject term?

All things that are the phone (this is about a particular individual)

Is it distributed or undistributed?

The subject term is distributed because the scope word is “all”. This is a universal claim.

What is the predicate term?

Things that are ringing.

Is it distributed or undistributed?

The predicate term is undistributed because the categorical statement is an affirmation, and predicate terms are only distributed in negations (E and O statements).

  Categorical Logic 2

 

Drawing Inferences

Inference is the process of moving from (possibly provisional) acceptance of some propositions to the acceptance of others. There are two kinds of inferences we need to clarify for talking about categorical arguments: immediate inferences and mediate inferences.

Immediate Inferences

Immediate inferences are ones that can be made on the basis of a single categorical statement without any additional premises. These are possible because there are fixed logical relations between different categorical claims. Many of these relations are captured in what is called the “square of opposition”.

The Square of Opposition

The square of opposition gives us a schematic picture of these logical relationships. Let's look at each of these in more detail.

 

Contradictories

  One of the most powerful tools in argumentation is the counterexample.

A counterexample is a case that proves an assertion false. This is a powerful tool because it can be used to do more than prove that a claim is questionable or without support. It can show that the claim is false. Counterexamples are represented in the square of opposition by contradictories. There is a contradictory for every kind of categorical statement (A,I,E,O). The logical relation that holds between contradictories is specified in terms of relations of truth and falsity. Two claims are contradictories if they can't both be true and they can't both be false.

Suppose that I said, “Nobody loves me”. If you wanted to show that what I said is wrong, how would you achieve that? You would probably argue with me by pointing out that there are, in fact, people that love me, such as my parents and close friends. If you could establish this, you will succeed in proving what I said to be untrue.

What you are doing in this case is using a counterexample by appealing to the truth of the contradictory of my original statement. Let's look at this more closely and technically.

Example

Nobody loves me

The easiest way to show I am wrong is to find it out what the contradictory of this claim is, and show that the contradictory is true.

First, put the claim into standard categorical form:

No person is a thing that loves me.

This is a universal negation (E statement).

Next, identify its contradictory. This would be an I statement. The subject class is people and the predicate class is things that love me. So the contradictory would be:

Some people are things that love me (some S are P).

If you could show that this is true, you will have succeeded in proving my original claim false.

Since contradictories cannot both be true and cannot both be false, if we know that one of them is true, then there can be no doubt that the other is false.

Example

All cartoons are funny (All S are P).

If this is true, then we know that its contradictory must be false. What would be the contradictory? Since All cartoons are funny is an A statement, the contradictory must be an O statement:

Some cartoons are not funny (Some S are not P).

Example

No dog hair makes a good paintbrush.

If this is false, then what can we say must be true? It would be the contradictory of this claim. The above claim is an E statement. So its contradictory will be an I statement. Hence, we know that the following claim is true:

Some dog hair is a thing that makes a good paintbrush (Some S are P).

Example

Some chickens are not things that make good pets (Some S are not P).

Suppose we know this is false. What can we conclude is true? Its contradictory:

All chickens are things that make good pets (All S are P).

 

 

 

Contraries

 

The second set of fixed logical relations captured by the square of opposition is contraries. Contraries are claims that cannot both be true but can both be false. This relationship can hold only between universal affirmations and universal negations (A and E statements).

Example

All cartoons are funny.

If we know that this claim is true, then we know that its contrary must be false. Its contrary would be an E statement since all cartoons are funny is an A statement.

Hence we know it is false that no cartoons are funny.

If we know that it is false that all cartoons are funny, we cannot conclude from this that no cartoons are funny. Both of these claims might be false. This would be so if it is the case that some cartoons are funny, or if some cartoons are not funny (if we have an I or an O statement).

This means that the only time you can draw an inference using contraries is if you know that an A or an E statement is true. If you know this, then you know its contrary is false. If you know that an A or an E statement is false, its contrary could be either true or false, so you cannot actually draw an inference in this case.

Example

All philosophers are freaks.

If you know that this is false, then it is possible for its contrary to be either true or false. Its contrary would be:

No philosophers are freaks.

Clearly, if it is false that all philosophers are freaks, this could be because no philosophers are freaks, or it could be because some philosophers are freaks. Knowing the original claim is false does not tell us which of these possibilities is true, so we cannot draw an inference.

 

Subcontraries

 

The third set of logical relations in the square of opposition is subcontraries. Subcontraries cannot both be false but can both be true. This relationship holds only between particular categorical claims (I and O statements). This means that if we know an I statement is false, its subcontrary must be true. However, if we know an I statement is true, we cannot conclude that its subcontrary is false. It could be either true or false.

Example

Some philosophers are freaks.

The subcontrary to this is:

Some philosophers are not freaks.

If we know it is false that some philosophers are freaks, then it must be true that some philosophers are not freaks. However, we can't conclude from the truth of the claim that some philosophers are freaks that it is true that some philosophers are not freaks. This is because if it is true that some philosophers are not freaks it might be the case that no philosophers are freaks.

Other kinds of immediate inferences that are possible with categorical statements are called “conversion”, “obversion”, and “contraposition”. These are different categorical statements that are equivalent.

  Conversion

  In conversion we switch the subject and predicate terms in a categorical statement. This is only possible in Particular Affirmations (I-Statements) and Universal Negations (E-Statements).

Some S are P Converse Some P are

SNo S are P Converse No P are SExample

No fish are mammals.

The converse is: No mammals are fish.

Example

Some potatoes are things with eyes.

The converse is: Some things with eyes are potatoes.

Example

No things with feathers are humans.

The converse is: No humans are things with feathers.

Example

Some games are fun.

The converse is: Some things that are fun are games.

Notice that truth is always preserved in conversion. If your original claim is true, then its converse is also true. If the original claim is false, then its converse is also false. This is what we should expect if we are making equivalent statements. Conversion is a matter of saying something equivalent in a slightly different way. If you are saying something equivalent by stating the converse, then the truth-value of the claim must remain constant.

Notice that if you try conversion with other kinds of categorical statements, truth is not necessarily preserved. This is why conversion is invalid with A and O statements.

Example

All dogs are things with four legs.

If you tried conversion with this claim, which is an A statement, you

would end up with:

All things with four legs are dogs.

The original claim is true but the converse is obviously false since cows and cats and plenty of other animals have four legs aside from dogs. In this case the converse does not state something equivalent to the original statement.

  Obversion

  In obversion we change the statement to its opposite (affirmative or negative) and replace the predicate term with its complement. This is valid for all forms of categorical statement (A,E,I,O).

The complement of a class is made up of all things that do not fall within the identified class. For instance, the complement of the class philosophers is non-philosophers. This includes everything that is not a philosopher. Schematically we represent the compliment of a class P by adding the prefix “non” to end up with non-P

Obversion can take the following forms:

All S are P Obverse No S are non-PNo S are P Obverse All S are non-PSome S are P Obverse Some S are not non-PSome S are not P Obverse Some S are non-PExample

All frogs are reptiles.

Obverse: No frogs are non-reptiles.

Example

Some animals are appetizing.

Obverse: Some animals are not non-appetizing.

Sometimes the compliment class reads awkwardly, as it does above. In those cases it is permissible to represent the compliment class using the prefix “un” instead. So one might write:

Some animals are not unappetizing.

Either form is correct.

Example

No Pygmies are tall.

Obverse: All Pygmies are non-tall.

Example

Some boxer shorts are not comfortable.

Obverse: Some boxer shorts are uncomfortable (or non-comfortable).

Example

All feathered animals are non-human.

Obverse:

Clue: The complement of non-humans is non-non-humans. When this happens, the two “nons” cancel each other out.

No feathered animals are human.

 

Contraposition

 

In contraposition what we do is switch the subject and predicate terms and replace each with its complement. This is permissible only with Universal Affirmations and Particular Negations (A-Statements and O-Statements.)

All S are P Contrapositive All non-P are non-SSome S are not P Contrapositive Some non-P are not

non-SExample

All logic students are brilliant.

Contrapositive: All non-brilliant people are non-logic students.

Example

Some Canadians are not hockey players.

Contrapositive: Some non-hockey players are not non-Canadians.

Example

All rain is wet.

Contrapositive: All non-wet things are non-rain.

Notice again that when these inferences are valid (in A and O statements) truth is preserved. Let's see what happens when we try contraposition with an E statement.

Example

No cats are things that like dogs.

Contrapositive:No non-things that like dogs are non-cats.

This is extremely awkward. What it asserts is that there isn't anything that doesn't like dogs that aren't cats. Although the original E statement was true, its Contrapositive is false. There are all kinds of things (including some people) that don't like dogs but that aren't cats. Since truth is not necessarily preserved (though it might happen to be sometimes), contraposition is invalid for anything other than A and O statements.

  Mediate Inferences

 

Mediate inferences are ones where we need additional information (i.e., more than one non-equivalent categorical statement) to draw a conclusion. Mediate inferences occur in categorical arguments (syllogisms).

Every categorical argument contains at least two premises and a conclusion. We will limit our examination to categorical arguments with two premises.

Every categorical argument also contains the following three elements:

1. A major term: the predicate of the conclusion. 2. A minor term: the subject of the conclusion.3. A middle term: a term that appears in both of the premises but

not in the conclusion.

Example

Some dogs have fleas.

All dogs are cute.

Therefore, some cute things have fleas.

Major term: having fleas

Minor term: cute things

Middle term: dogs

Arguments of this form are said to be valid or invalid, sound or unsound.

Validity

An argument is valid if it has proper logical form. This means that if the premises are true, the conclusion must be true.

An argument is invalid if it lacks proper logical form. It is possible for the premises to be true but for the conclusion to be false.

Soundness

An argument is sound if the premises are true and is unsound if any of its premises are false.

It is important to recognize that an argument can be valid but unsound.

Example

All men are potatoes

Socrates is a man

Therefore, Socrates is a potato.

This argument is valid. If the premises were true, it would have to be true that Socrates is a potato. However, it is unsound because the first premise is false. It is not true that all men are potatoes.

  Testing Validity

  There are three rules for evaluating the validity of categorical syllogisms. This is where the ability to discern whether or not subject and predicate terms are distributed becomes important.

1. At least one premise must distribute the middle term.2. If a term is distributed in the conclusion, it must also be

distributed in at least one of the premises.3. The number of negative claims must be the same in the premises

and conclusion.

Example

All men are potatoesSocrates is a manTherefore, Socrates is a potato

First, identify the middle term.

Middle Term = men

Is it distributed in at least one premise?

Yes. In premise 1. All men are potatoes is an A statement (universal affirmation) and subject terms are distributed in A statements.

Is a term distributed in the conclusion?

The conclusion is an A statement (remember, if a categorical statement is about a particular individual, it is a universal statement. Since the conclusion is an affirmation, it must be an A statement.

In the conclusion the predicate term is potato. Predicate terms are undistributed in A statements.

The subject term is Socrates. It is distributed since subject terms are always distributed in A statements.

Subject term = Socrates

Is the subject term distributed in at least one of the premises?

Yes. In premise 2, (Socrates is a man) the term is distributed (for the same reason above).

Now we can move on to rule three.

Do the number of negative terms in the conclusion equal the number of

negative terms in the premises?

Yes. There aren't any. The argument is therefore valid. If the premises were true, the conclusion would have to be true.

Example

All men are mortalSocrates is smartTherefore, Socrates is mortal

First, identify the middle term.

There is no middle term.

This argument fails to satisfy the first test of validity and is therefore invalid.

Let's try a few more examples.

Example

Some alligators do not make good wallets.Nothing that makes a good wallet is delicious.Therefore, some alligators are delicious.

Rule 1

Middle term = things that make good wallets

Is it distributed in at least one premise?

Yes. In fact, it is distributed in both premises. Both premises are negations and predicate terms are always distributed in negations.

Rule 2

Is there a term that is distributed in the conclusion?

No. The conclusion is an I statement (particular affirmation). No terms are distributed in I statements. We can therefore move on to rule 3.

Rule 3

Is there the same number of negative statements in the premises as in the conclusion?

No. The conclusion has none and the premises have two. The argument therefore fails the third test and is invalid. The conclusion of the argument does not necessarily follow. It is possible for the premises to be

true but for the conclusion to be false.

Here's a useful tip:

There are two conditions under which it is really easy to see that a categorical argument is invalid.

1. If the premises are all I statements. This is because if the premises are I statements no terms are distributed in them, meaning that the middle term cannot be distributed, rendering the argument invalid.

2. If the argument contains negative premises and a positive conclusion, or positive premises and a negative conclusion. If either of these is true, the argument cannot pass the third test.

Let's try a couple more examples.

Example

Some cows are not black at night.All cows are herbivores.Therefore, some herbivores are not black at night.

Rule 1

The Middle Term is: cows

Is it distributed in at least one premise?

Yes. In premise 2. All cows are herbivores is an A statement. Cows is the subject term and the subject term is always distributed in A statements.

Rule 2

Is a term distributed in the conclusion?

The conclusion is an O statement (a particular negation). Subject terms are not distributed in O statements but predicate terms are.

Now we have to see if this term is distributed in at least one of the premises.

The term that is distributed in the conclusion is things that are black at night. The only place this appears in the premises is as the predicate term of the first premise. The first premise is also an O statement, so the term is distributed there as well. The argument passes the second test.

Rule 3

Are there the same number of negative claims in the conclusion as there

are in the premises?

Yes. There is one in the conclusion and one in the premises.

The argument is therefore valid.

Sometimes following the third rule can be tricky. Be careful when an argument employs obverse statements.

The obverse of affirmations (A or I statements) are positive statements even though they contain words we associate with negation.

Example

Some Friends fans are non-brainless people.All people with brains are people with a good sense of humor.Therefore, some Friends fans are people with a good sense of humor.

Here it is more difficult to identify the middle term. In this case we want to use the obverse of premise 1 to make the argument easier to evaluate.

Some Friends fans are non-brainless people is equivalent to the obverse:

Some Friends fans are people with brains.

Now, rewrite the argument with the first premise restated as it is above:

Some Friends fans are people with brains.All people with brains are people with a good sense of humour.Therefore, some Friends fans are people with a good sense of humour.

Rule 1

Middle term = people with brains

Is it distributed in at least one premise?

Yes. It is the subject term in the second premise, which is an A statement. Subject terms are distributed in A statements.

Rule 2

Is a term distributed in the conclusion?

No. The conclusion is an I statement. None of its terms is distributed. We can therefore jump to rule 3.

Rule 3

Are there the same number of negative statements in the conclusion as in the premises?

Yes. There are none in the conclusion and none in the premises. The argument is therefore valid.

Notice that if we had left the first premise the way it was, not only would we have had a difficult time identifying the middle term, but we would have had trouble with the third test of validity because it looks like a negative claim even though it is not.

 

Necessary and Sufficient Conditions

 

Many arguments you are likely to encounter can be analysed, understood, and evaluated in terms of what are called “necessary” and “sufficient conditions”. Learning to identify necessary and sufficient conditions is therefore a very powerful tool since it will enable you to recognise bad arguments quickly, and enable you to ensure that your own arguments are good ones.

The most common type of argument that employs necessary and sufficient conditions is the conditional argument. A conditional argument contains at least one premise that is what is called a “conditional statement”.

 

Conditional Statements

 

A conditional statement is one in which it is claimed that something is or will be the case provided that some other situation obtains. These are also sometimes called hypothetical statements because they say what would happen if, hypothetically, something else were to happen.

Most conditional statements take the following form:

If x then y

where x and y each stand for particular propositions.

Example

If I win the lottery, then I will retire to the Bahamas.

This asserts that, on the condition that I win the lottery, something else will happen; namely, I will retire to the Bahamas. This claim can be true even if I never do win the lottery. All that matters is that if the first thing were to happen (I win the lottery) we know for sure that the second thing will happen (I'll retire to the Bahamas).

The part of the conditional claim that follows the word “if” (I win the lottery) is called the antecedent (meaning “comes before”), and the second part, that follows the word “then” (I will retire to the Bahamas) is called the consequent (meaning “comes after”).

When I say that if I win the lottery, then I will retire to the Bahamas, I am saying that there is a special logical relationship between these two propositions:

I win the lottery

I will retire to the Bahamas.

The nature of this logical relationship is expressed in terms of necessary and sufficient conditions.

What we are saying in the conditional claim is that my winning the lottery is enough to ensure that I will retire to the Bahamas. We express this by saying that my winning the lottery is sufficient for my retiring to the Bahamas. We are also saying that my retiring to the Bahamas is a necessary consequence of my winning the lottery, or that my retiring to the Bahamas is necessary for my winning the lottery.

  We can define necessary and sufficient conditions as follows:

  Sufficient Conditions

A sufficient condition is a state of affairs that, once true, is enough for something else to be true.

If X is sufficient for Y, then if X is true, Y is true.

Necessary Conditions

A necessary condition is a state of affairs that must be true in order for something else to be true but is not enough to make something else true.

If X is necessary for Y, then if X is not true, Y is not true.

Let's look at a different example to illustrate these concepts.

Example

Being a bachelor is a sufficient condition for being male.

If we know that something is a bachelor, then we also know with absolute certainty that it is a male. Since there can be no doubt about this, it is enough (i.e., sufficient) to know that something is a bachelor to know that it is also male.

If we know that someone is male, can we draw the conclusion that he is a bachelor? No. Just because Tom, for instance, is male, this does not give us an absolute guarantee that he is a bachelor because he might be married. So, while it is true that in order to be a bachelor you must be male, being male isn't enough for being a bachelor.

We would say, then, that being male is necessary for being a bachelor, but is not sufficient for being a bachelor. That is, if Dan is a bachelor, then it is a necessary consequence that he is male (we know this for sure). But if all we know about Dan is that he is male, we don't know whether or not he is a bachelor. Being male, then, is not sufficient for being a bachelor.

Let's say we know that Allan is a bachelor. What else can we say about Allan with absolute certainty? We know that Allan must be male and we also know that he must be unmarried. In other words, being a bachelor is sufficient for being male and is sufficient for being unmarried.

We've already seen that being male, although necessary for being a bachelor, is not sufficient for being a bachelor. What is the relationship between being unmarried and being a bachelor? Is being unmarried sufficient for being a bachelor? No. Keitha is unmarried but isn't a bachelor because she is a woman. Being unmarried, then, is necessary but is not sufficient for being a bachelor.

When do we know for sure that someone is a bachelor? Only when we know that person is both male and unmarried. Hence, being male is necessary for being a bachelor, being unmarried is also necessary for being a bachelor, and being male and unmarried are jointly sufficient for being a bachelor.

All of these relationships can be expressed in the form of the following conditional claims:

1. If John is a bachelor, then John is male. This means John's being a bachelor is sufficient for John's being male.

AND

John's being male is necessary for John's being a bachelor.2. If John is a bachelor, then John is unmarried.

This means John's being a bachelor is sufficient for John's being unmarried.

AND

John's being unmarried is necessary for John's being a bachelor.

  Classes

 

These logical relationships can also be understood in terms of the relations between classes of objects. A class is a group of objects that share a particular characteristic. Dogs is a class of objects that contains all dogs, regardless of what kind of dogs they are. Things with hair, is a larger class of objects that includes the entire class of dogs within it as well as the class Cats, Hamsters, Humans, and so on. Things that are faithful is another class that may include all dogs, some humans, but not cats or hamsters. Any one thing can be a member of many different classes. For instance, my dog is a member of the class of pets, of things with hair, things that smell, things that eat, and many other classes.

A simple way to represent the relationship between classes is in terms of the following diagram:

 

B

 

A

 This diagram represents the claim that the entire class of objects A is included within the class of objects B.

Above, we said that the class Dogs, is included within the class of objects Things with hair. We can represent this with a similar diagram:

 

Things with Hair

 

Dogs

 This shows us that while everything that is a dog is a thing with hair, not everything that is a thing with hair is a dog.

Most people don't express this idea so awkwardly. Usually people say

something like “All dogs are hairy”. This is a more natural way of saying exactly the same thing.

This also expresses a relationship between things that can be understood in terms of necessary and sufficient conditions. To say that all dogs are hairy is to say that being a dog is sufficient for being hairy, and that being hairy is necessary for being a dog. In our diagrams above, being a member of the class represented by the smaller circle is always sufficient for being a member of the class represented by the larger circle, and being a member of the larger circle is always necessary for being a member of the smaller circle.

 

Necessary Condition

 

Sufficient Condition

 We saw earlier that being male is necessary for being a bachelor and that being a bachelor is sufficient for being male. This can also be expressed by saying “All bachelors are male”. We can now represent this claim using a diagram like the ones above:

 

Males

 

Bachelors

 Sometimes one might express this idea in a different way. Instead of saying “All bachelors are male,” one might say, “Only men are bachelors”. Once again, even though the words used are different, this is saying exactly the same thing. To say that only men are bachelors is to say that there are no bachelors that are not men, or that the class of bachelors is entirely enclosed within the class of men.

If you find it helpful to use these diagrams to determine necessary and

sufficient conditions, remember this simple rule:

All inside; only outside.

 

Only

 

All

 

  Other Forms of Conditional Claims

  We saw earlier that conditional claims usually take the form

If x then y

where x (the antecedent) is sufficient for y (the consequent) and y is necessary for x.

Sometimes conditional claims take a slightly different form from this. Look at the following example:

I'll tear you a new one if you keep talking.

Notice that this does not have the standard form if x then y. The word “if” appears in the middle of the sentence and the word “then” doesn't appear at all. Nevertheless, this is still a conditional claim. What follows the word “if” is still the antecedent and is also still the sufficient condition. The rest is the consequent and the necessary condition.

Thus, we have the following relationships:

Your keeping talking is sufficient for my tearing you a new one.

My tearing you a new one is necessary for your keeping talking.

The only time what follows the word “if” in a conditional claim is not the sufficient condition is when the word “only” precedes the word “if”.

Another form of conditional claim, then, is this:

x only if y

Example

I'll laugh only if you wear those pants.

Your wearing those pants is necessary for my laughing.

My laughing is sufficient for your wearing those pants.

Negation

Often a conditional statement will contain a negation. There are two rules you should learn to help you deal with negation.

Rule 1

If A is necessary for B, then not A is sufficient for not B

Example

If being male is necessary for being a bachelor, then not being a male is sufficient for not being a bachelor. Anything that isn't a male cannot be a bachelor.

Rule 2

If B is sufficient for A, not B is necessary for not A.

Example

If being a bachelor is sufficient for being a male, then not being a bachelor is necessary for not being a male.

Unless

Some conditional claims include the word “unless.” I am going to diverge from the textbook here and give you a much easier and more reliable method for dealing with these kinds of claims. What LeBlanc tells you in the textbook is fine, but it will often lead you into trouble because it frequently requires additional steps involving negation. So make it easy for yourself and use the following method. Since I use this myself, my questions on the quiz are most easily resolved using this approach (hint, hint).

If the premise of an argument employs “unless,” the easiest way to identify the necessary and sufficient conditions is to translate the statement into standard conditional form (if x then y).

Here are two simple steps to help you do this.

1. Take what follows “unless”, negate it and make it the antecedent in the new conditional claim.

2. The rest of the original claim takes the place of the consequent.

Example

You can't go outside unless you put on your pants.

What follows “unless” is “you put on your pants”. So we take this, negate it and make it the antecedent in the new conditional claim as follows:

If you don't put on your pants, then

Now, take the rest of the original claim, just as it is (don't change anything), and make it the consequent in your new conditional claim by placing it after the word “then”. You end up with this:

If you don't put on your pants, then you can't go outside.

Now that the claim is in standard conditional form it is much easier to identify the necessary and sufficient conditions.

Your not putting on your pants is sufficient for your not going outside.

Your not going outside is necessary for your not putting on your pants.

You can use these two steps to deal with any conditional claim including “unless”. Here are all of the possible equivalences:

A unless B If not B then AA unless not B If B then ANot A unless B If not B then not ANot A unless not B If B then not AUnless A then B If not A then BUnless A then not B If not A then not BUnless not A then B If A then BUnless not A then not B If A then not BExample

Unless John does not hurl, we'll be thrown out of the bar.

To identify the necessary and sufficient conditions, first put this into standard conditional form.

If John does hurl, then we will be thrown out of the bar.

John's hurling is sufficient for our being thrown out of the bar.

Our being thrown out of the bar is necessary for John hurling.

Example

You can't keep your kneecaps unless you pay your debt.

Put this into standard conditional form using the method outlined above:

If you do not pay your debt, then you can't keep your kneecaps.

Your not paying your debt is sufficient for not keeping your kneecaps.

Your not keeping your kneecaps is necessary for not paying your debt.

Example

You can't have any dessert unless you eat your meat.

Since this contains the word “unless”, translate it into standard conditional form.

If you don't eat your meat, then you can't have any dessert.

Not eating your meat is sufficient for your not having any dessert.

Not having any dessert is necessary for your not eating your meat.

Definition and Identity

Sometimes a single condition can be both necessary and sufficient. In this case A is both Necessary and Sufficient for B, and B is both Necessary and Sufficient for A.

If Batman is identical to Bruce Wayne, then being Bruce Wayne is both necessary and sufficient for being Batman, and being Batman is both necessary and sufficient for being Bruce Wayne.

Similarly, if water is defined as H2O, then being water is sufficient for being H2O and being H2O is sufficient for being water.

Definitions and identities are sometimes expressed as conditional claims using the phrase “if and only if”.

Examples

X is water if and only if X is H2O.

X is Batman if and only if X is Bruce Wayne.

  Conditional Arguments

 

Now that we have seen how to identify necessary and sufficient conditions in a variety of statements, let's see how these claims are used in arguments.

Arguments that contain conditional claims as at least one premise are called “conditional arguments”.

The kinds of conditional arguments we will be concerned with are called “deductive” arguments. What deductive arguments all share is that their conclusions are always implicitly present, but hidden, in their premises. Part of how a deductive argument is defined is in terms of the concept of validity, so let's look at this first.

Validity

Validity is a technical term in logic that is used in the evaluation of deductive arguments. While you have likely heard people refer to an argument or opinion as valid, this differs significantly from the technical understanding of the term. In common usage a “valid” argument or opinion usually means that it is one worth holding or one we should respect. In logic, an argument's validity is a function of its logical form or structure. More specifically, validity refers to the relationship between the premises of an argument and its conclusion.

An argument is valid if and only if the conclusion necessarily follows from its premises.

Another way this is expressed is as follows:

An argument is valid if it is impossible for its premises to be true and for its conclusion to be false.

This means that if an argument is valid, and if its premises are true, there is an absolute guarantee that the conclusion is true as well. Hence, valid deductive arguments are extremely powerful tools to use if you want to convince someone of a certain claim.

It is important to note, however, that the premises of a deductive argument need not actually be true in order for the argument to be valid. What matters is whether or not it is possible for the conclusion to be false if the premises were true.

Example

All men are made of peanut butterAlice is a manTherefore, Alice is made of peanut butter

This argument is deductively valid. Even though both of its premises are in

fact false, if they were true, the conclusion would also have to be true.

Does the truth of the premises of a deductive argument matter? Of course it does. If you want to use the above argument to convince me that Alice is made of peanut butter, it had better be true that Alice is a man and that all men are made of peanut butter. That is, if the conclusion of a valid deductive argument is true and follows from the premises of the argument, those premises need to be true.

Soundness

The soundness of an argument is a function of the truth of its premises. An argument is sound if and only if it has all true premises. If any of the premises of an argument are false, then the argument is said to be unsound.

Hence, the above argument about Alice is valid but unsound. Good arguments are both valid and sound. These are the kinds of arguments you should strive for. There are, however, bad deductive arguments that may be sound but are invalid. You need to be able to spot these when you encounter them.

We will examine four common types of conditional argument. Two of these are valid forms of argument and two are invalid.

  Valid Conditional Arguments

 

Modus Ponens

The first and most common form of valid conditional argument goes by two names: modus ponens and affirming the sufficient condition. Modus ponen is Latin for “mood that affirms”.

The form modus ponens takes is as follows:

Premise 1: If p then q

Premise 2: p

Conclusion: therefore q

“p” and “q” stand for any proposition. Plug in any proposition you want and the conclusion will always follow.

Notice that the first premise is a conditional claim. The second premise affirms part of the conditional. That is, it says that p is in fact the case. We saw earlier that this part of a conditional claim is called the antecedent and is always the sufficient condition. This explains why this form of argument is sometimes called “affirming the sufficient condition”. Finally, the argument draws a positive conclusion. It affirms the other part of the conditional. Since everything the argument does after the first premise is an affirmation, it is also sometimes called by the Latin for “mood that affirms” (modus ponens).

An Important Note About Affirming

p and q can stand for any proposition, even a proposition that says something is not the case (a negation), which can sometimes make it hard to determine whether or not p is affirmed in the second premise. Consider the following example:

If you don't put your pants on, then I'll call the police.

You didn't put your pants on.

Therefore, I called the police.

It is tempting here to say that p is denied in the second premise because the claim You didn't put your pants on expresses a negative statement. This is actually not the case as we can see if we break the first premise down into its two components:

If you don't put your pants on,

then I'll call the police.

P Q

Sufficient Condition Necessary Condition

As we can see, p is what is expressed in the entire first part of the above conditional claim. It is the proposition you don't put your pants on. To determine whether the second premise in a conditional argument like this affirms or denies p, you need to compare what is said in the first premise with what is said in the second. The second premise says You didn't put your pants on. This is saying the same thing as what was stated in the first part of the first premise (except for a change in tense, but you can ignore that in conditional arguments altogether). That is, they both express the same proposition or state of affairs: you haven't put your pants on. Since the second premise says the same thing as p in the first premise, p is affirmed. We therefore have an example of modus ponens. The argument is valid.

Example

If Janet gets the job, then I'll resign from the board.

Janet got the job.

Therefore, I'll resign.

Standardizing Modus Ponens

Modus ponens is always standardized as it is above. The conditional claim (the first premise) is linked with the second premise (in which the sufficient condition is affirmed). Together these support the conclusion, which is the other half of the conditional claim.

Example

Jill will only win the award if she doesn't offend the judges.

Jill won the award.

Therefore, Jill didn't offend the judges.

Is this an example of modus ponens? The first thing you should notice about this example is that the first premise is a conditional claim containing “only if”. Recall the rule about conditionals with “only if”: “only if” introduces the necessary condition. So, does the second premise affirm the sufficient or the necessary condition?

In premise 2 we are affirming the sufficient condition. Hence, this is an example of modus ponens and is a valid argument.

Modus Tollens

The second common form of valid conditional argument is modus tollens, which is Latin for “mood that denies”.

The argument takes this form:

If p then q

Not q

Therefore, not p

The argument is called “mood that denies” because both the second premise and the conclusion are negations. This form of argument is also called “denying the necessary condition” because this is what happens in the second premise. When we have a conditional claim if p then q, q is necessary for p. So if we say “not q” we are denying the necessary condition. Since q is a necessary consequence of p, we know that if q didn't happen, p must not have happened. Hence, from these two pieces of information we can draw the conclusion that p didn't happen or is not the case.

An Important Note About Denying

We saw above that you need to be very careful to be clear about what p and q express in order to tell whether a proposition is affirmed or denied in a conditional argument. Just as it can be hard to tell when a proposition is affirmed, it can be difficult to tell when a proposition is denied. Consider the following example:

If you put your pants on, I won't call the police.

I called the police.

Therefore, you didn't put your pants on.

It is tempting to say that premise 2 (I called the police) affirms something, because it is a positive statement. However, if we examine the first premise more carefully, we will see that this is not so.

If you put your pants on, I won't call the police.P

Sufficient Condition Q

Necessary ConditionAs we can see, q is what is expressed in the entire second part of the first premise: I won't call the police. To determine whether q is affirmed or denied in the second premise of the argument, we need to compare what is said in the first premise with what is said in the second. The second premise says I called the police. This is clearly different from the proposition expressed by q. It is, in fact, the negation of q. In effect, I called the police is equivalent to saying it is not the case that I won't call

the police. Hence, the second premise denies q, and so we have modus tollens. This is a valid argument.

Let's look at a few examples:

Example

If you work out, then you will feel tired.

You don't feel tired.

Therefore, you didn't work out.

The first premise is a conditional claim. The first thing you should notice about it is that it does not contain words like “only” or “unless”, which means it is easy to identify the necessary and sufficient conditions. From the conditional we can tell that working out is sufficient for feeling tired and that feeling tired is necessary for working out. The second premise, then, is denying the necessary condition. So far, so good. Has the correct conclusion been drawn?

Yes. The argument concludes by denying the rest of the conditional claim (remember “mood that denies”).

Let's think about the argument more concretely. If we assume that the conditional claim is true, meaning that every time you work out, you feel tired, and we also know that you don't feel tired, then we know that, among other things, that you must not have worked out (otherwise you would feel tired).

Standardizing Modus Tollens

We standardize modus tollens the same way we standardize modus ponens. The two premises are linked and support the conclusion as illustrated below.

The reason the premises are linked is that both are required to motivate the conclusion. Without the other, neither premise gives the conclusion any support.

Example

I can only go to the mountains if I can get a ride.

I didn't get a ride.

Therefore, I can't go to the mountains.

In this case notice that the conditional claim contains “only if”. Remember that “only if” always introduces a necessary condition. This means that my getting a ride is necessary for my going to the mountains.

The second premise, then, is denying the necessary condition. It is saying that it is not the case that I can get a ride to the mountains. The conclusion denies the other half of the conditional claim, so we therefore have an example of modus tollens.

A handy way to remember which forms of argument are valid is to make use of the following rule:

AFFIRM THE SUFFICIENT CONDITION & DENY THE NESSECARY CONDITION.

Anything else is invalid.

  Invalid Conditional Arguments

  There are two invalid conditional arguments that are often confused with the valid forms we just looked at. As long as you can identify necessary and sufficient conditions and remember the rules just mentioned, you shouldn't have any trouble recognizing these invalid forms of argument.

Denying the Antecedent

The first form of invalid conditional argument is called “denying the sufficient condition” or “d enying the antecedent”. Like the previous valid forms of argument, these names are derived primarily from what happens in the second premise of the argument.

This argument has the following form:

If p then q Not p Therefore not q

Why is this invalid? The reason is that from the information we are given in the premises, we cannot actually draw the conclusion that q is not the case. Even though p entails (i.e., leads to or implies) q, or has q as a necessary consequence, if p does not happen this is no guarantee that q didn't happen or will not happen. The main reason for this is that something else other than p could lead to q.

Let's examine this more with the help of an example.

Example

If you take off your clothes, I'll laugh. You did not take off your clothes. Therefore, I didn't laugh.

First, let's consider the form of the argument. The conditional claim tells us that your taking off your clothes is sufficient for my laughing, and that my laughing is necessary for your taking off your clothes.

The second premise of the argument is denying the sufficient condition (the antecedent). Hence, the argument is an example of denying the antecedent, which is invalid.

Why can't we draw the conclusion that I didn't laugh from these two premises?

Even if it is true that I will, without fail, laugh if you take off your clothes, this is not the only thing that can make me laugh. Perhaps I am thinking about a funny joke someone told me earlier. Other things might make me laugh besides your undressing, so we can't rule out the possibility that I will laugh from the premises provided.

Example

If it rains, then the streets will be wet. It didn't rain. Therefore, the streets aren't wet.

What does the second premise of this argument do? It denies the antecedent or the sufficient condition. Hence, we know the conclusion does not necessarily follow. This does not mean that the conclusion is false. It might very well be true that the streets aren't wet. But that is not the issue. The question is, “What can we conclude for certain, given what we do know?”

The reason we can't conclude that the streets aren't wet from these two premises is that the streets can be wet for a number of other reasons (e.g., broken water mains, the street washer, snow).

Affirming the Consequent

The second common form of invalid conditional argument is called “affirming the consequent” or “affirming the necessary condition”.

This argument has the following form:

If p then q q Therefore, p

The reason this is invalid is that, once again, from the premises provided we have no guarantee that the conclusion is true. It might be true, but it could equally well be false. Even though p must, necessarily lead to q, we cannot conclude that if q happened, p must have happened. The reason for this is similar to the problem with denying the antecedent. Other things, besides p can lead to q.

Example

If it rains then the streets will be wet. The streets are wet. Therefore, it rained.

Even though it is true that if it rains the streets must get wet, we can't conclude from this and from the fact that the streets are wet that it did in fact rain. Maybe it snowed, or maybe a dam burst. Because the argument does not provide a guarantee that the conclusion is true, it is invalid. Notice also the structure of the argument. The second premise is an affirmation, and what it is affirming is the necessary condition.

Example

If you bring some chicken, then we'll have a barbeque.

We had a barbeque. Therefore, you brought some chicken.

The conditional claim tells us that your bringing some chicken is sufficient for our having a barbeque, and that our having a barbeque is necessary for your bringing some chicken. The second premise says we had a barbeque, and so is affirming the necessary condition or the consequent. The argument is therefore invalid.

Now that we've seen four forms of conditional argument, let's look at a few examples to practice identifying them.

Example

You can't go outside unless you put on your shoes. You didn't put on your shoes. Therefore, you didn't go outside.

This is a considerably trickier example. Notice that the conditional claim contains the word “unless”. The best way to deal with this is to reformulate this claim in standard conditional form. Recall that we do this by taking what follows “unless”, negating it, and making it the antecedent in the new conditional claim. The rest of the original claim takes the place of the consequent. What we end up with is this:

If you don't put on your shoes, then you can't go outside.

Now, replace the first premise of the above argument with our new conditional. The argument should look like this:

If you don't put on your shoes, then you can't go outside.

You didn't put on your shoes.

Therefore, you didn't go outside.

Now that we have rewritten the argument with the first premise in standard conditional form, it is much easier to identify the necessary and sufficient conditions. Your not putting on your shoes is sufficient for your not going outside, and your not going outside is necessary for your not putting on your shoes.

The argument therefore is an example of modus ponens. It is valid since the conclusion necessarily follows from the premises.

Example

If you pee into the wind, you'll get your shoes wet. You didn't pee into the wind. Therefore, you didn't get your shoes wet.

Your peeing into the wind is sufficient for your getting your shoes wet and your getting your shoes wet is necessary for your peeing into the wind. The second premise is thus denying the sufficient condition. The argument is invalid. Why? Because the conclusion could be false. Your shoes might have gotten wet for some other reason.

Example

Unless he tells me otherwise, I'll paint his room pink. I painted his room pink. Therefore, he didn't tell me otherwise.

This conditional claim contains the word “unless”. Rewrite the argument with the first premise in standard conditional form.

If he doesn't tell me otherwise, I'll paint his room pink.

I painted his room pink.

Therefore, he didn't tell me otherwise.

Here the second premise affirms the necessary condition (the consequent). The argument is therefore invalid .

Example

Only if you paid me would I go to see Patch Adams. I didn't go to see Patch Adams. Therefore, You didn't pay me.

This conditional claim contains “only if”. “Only if” introduces a necessary condition. So this argument is denying the sufficient condition and is therefore invalid.

Example

If Tamara doesn't call her mother, then her mother will cry. Tamara calls her mother. Therefore, her mother doesn't cry.

The first premise of this argument is a standard conditional claim. What happens in the second premise? Be careful here. It is doing something with the sufficient condition. Is it affirming it or denying it? It is denying it. The antecedent in the conditional is Tamara doesn't call her mother . If the second premise were affirming this, it would just repeat it: “Tamara doesn't call her mother”. The proposition has instead changed from negative to positive. This is the result of denying the proposition Tamara doesn't call her mother . Denying this proposition is like saying the following:

It is not the case that Tamara doesn't call her mother.

This is equivalent to:

Tamara calls her mother.

This argument therefore denies the sufficient condition (the antecedent) and is therefore invalid.

 

Language and Definitions

 

One of the most important things we need to do when we argue for a claim or view is to ensure that we are not misunderstood. If I want to convince you of the truth of a proposition p, then I had better make sure you understand p the way I intend p to be understood.

For example, suppose I want to prove to you that God exists. If, at the end of my argument you say, “You have proved the existence of something , but that's not God” then I have failed. To succeed we need to agree from the start what God is like.

The best way to ensure understanding is to define the key terms in your argument.

There are several different kinds of definitions one can use.

  Kinds of Definitions

  Reportive or Lexical

A reportive or lexical definition is a dictionary definition. It describes the way a word is ordinarily understood and used.

Stipulative

A stipulative definition establishes a new meaning of a word for a particular purpose. Usually this involves modifying the established lexical meaning of a term in some way. Such modifications can be very slight or can involve significant changes in meaning.

Usually, when we make use of definitions in arguments we employ stipulative definitions. This is because when we argue for a conclusion we need our key terms to mean something very specific; usually something more specific than a lexical definition can provide.

If you make use of a stipulative definition there are three criteria the definition should meet. Any good stipulative definition will satisfy these criteria.

1. The definition must not be too broad. It shouldn't include things that should be excluded.

Suppose I want to argue about the mind. “Mind” is a very broad term that can mean all kinds of things. Since I want “mind” to mean something quite specific I might provide the following stipulative definition: a mind is anything that can take in information, process it, and respond to it.

This definition might be broader than I want. It is too broad if the definition allows for the possibility of things having minds that shouldn't. According to this definition, my computer and my thermostat have minds, as do plants and all kinds of other things. If I did not intend for these things to be considered minds, then my definition is too broad and needs to be adjusted to exclude these things.

2. The definition must not be too narrow. It shouldn't exclude things that should be included.

When making adjustments to a stipulative definition there is a risk of going too far in the opposite direction. I might make it too narrow. For instance, if I define having a mind as having the ability to formulate and entertain propositions, then this might mean that things I believe do have minds are excluded by the definition. Animals probably have minds, but it is doubtful that they formulate and entertain propositions. Since my definition of mind is too narrow, it needs to be widened to include things like animals.

3. The definition must not be both too broad and too narrow, including things that shouldn't be included, and excluding things

that shouldn't be excluded.

Finally, a definition can be both too broad and too narrow. If I say that having a mind is a matter of possessing rationality, this might exclude things that clearly do have minds (such as children or irrational individuals) and might include things like computers and thermostats.

Operational

A third type of definition that is frequently used in arguments is called an “operational” definition. Because operational definitions usually specify meanings that are more specific than lexical definitions, they are a kind of stipulative definition.

In operational definitions, a word is defined in terms of when a specified operation yields a specified result. An “operation” is just a procedure needs to be followed. The operation gives us certain measurable criteria that define the term, or specifies necessary and sufficient conditions for it.

Example

Drunkenness is a relatively imprecise term. We might say someone is drunk when he or she slurs their words, or when they fall down and pass out. Obviously, if you are to be charged with drunk driving, the police cannot rely on such an unclear definition of drunkenness. They use a legal definition that is an operational definition.

The legal definition of drunkenness is an operational definition. It defines drunkenness in terms of blood-alcohol content (BAC). There is a procedure that we have to go through that involves testing blood for BAC. The operation or procedure involves the use of a breathalyser. When the breathalyser indicates a particular result, you are drunk.

Persuasive Definitions

Persuasive definitions are another kind of stipulative definition. These are disguised stipulative definitions used in arguments as premises. These are sneaky attempts to redefine terms in ways that are inappropriate (because they are too broad, too narrow, or both).

One way to help you identify persuasive definitions is to look for the following indicator words. Remember that indicator words are only a general guide and do not guarantee the presence of what they indicate.

Indicator words

Authentic, genuine, real, true

Example

A real man can drink at least sixteen beers before he gets drunk.

A true Canadian plays hockey.

A genuine leader is someone who can think on his or her feet.

Persuasive definitions are just one example of what is called “persuasive language”.

 

Persuasive Language

 

The goal of using persuasive language or definitions is to influence the listener to accept a particular point of view or to make an argument seem stronger than it is.

Such language may be effective in getting people to agree with you, but the agreement is not rationally motivated. This means that persuasive language does not actually make an argument stronger. It only seems to.

The language that is used to formulate an argument can be regarded as being located on a spectrum. At on extreme is what is called “emotionally charged language” and at the other is what is called “euphemism”. Emotionally charged language and euphemism are both examples of persuasive language. Good arguments use rational persuasion rather than emotion to convince others of a conclusion. Hence, good arguments should be formulated using neutral language.

EmotionallyCharged <----------

Standard or

Neutral ----------> Euphamism

Emotionally Charged Language

Emotionally charged language involves t he use of words with additional emotional force to influence the listener's or reader's emotions.

Example

John Smith is guilty of the senseless slaughter of innocent children. He is a butcher who preys on the helpless.

Here the words “senseless,” “slaughter,” “innocent,” “butcher,” “preys,” and “helpless” all function as emotionally charged language, casting John Smith in an extremely negative light.

Emotionally charged language need not always elicit negative feelings. It can also work by producing positive or sympathetic feelings in the listener.

Example

Mr. Jones, a fine, upstanding citizen, with ties to the community, and father of three, is just the innocent victim of circumstance. He represents a low flight-risk.

Here the phrases “fine, upstanding citizen,” “innocent victim,” “father of three,” and “ties to the community,” are introduced to elicit sympathy for him.

  Ambiguity and Vagueness

  Ambiguity

A word, phrase, or sentence is ambiguous when it has more than one meaning. All of the alternative meanings are perfectly clear, but from the context we don't know which one we should use.

Semantic Ambiguity

A single word can be taken to have more than one plausible meaning in a single context.

Example

Bank:

This can refer to an institution that deals with money, the edge of a river, or a shot used in billiards (to name a few possibilities).

Usually, the context in which a word is used eliminates any ambiguity about its meaning. If I say, “The robbers are coming out of the bank,” I probably intend to use the first meaning of “bank” mentioned above. If the context does not narrow down the meaning of a word, then we have semantic ambiguity. In the case of semantic ambiguity, one or more words is used in a way that is ambiguous, leading to more than one plausible meaning in the context.

Example

I'm afraid that there are bugs in my room.

This can mean either that there are insects in my room, or listening devices used for surveillance.

Note that the ambiguity in this case stems from the uncertainty about the meaning of one word in the above sentence: “bugs”.

Example

She awoke with a jerk.

This can mean either that she woke up with a jolt, or that she woke up next to someone of questionable character. Again, the ambiguity arises because a single word in the sentence has more than one plausible meaning in the given context.

Syntactic Ambiguity

Syntactic ambiguity occurs when an entire sentence can be taken to have several distinct meanings a result of the grammatical structure

of the sentence. This is also called “amphiboly”. In this case it is the way the sentence is formulated that leads to the ambiguity, and not because of the fact that one word in the sentence has multiple meanings.

Example

Noted UFO fanatic Peter Smith will talk to us tonight about sexual experiences with aliens in the student center.

This can mean either:

Peter Smith will talk to us tonight about sexual experiences people have had with aliens, and that these experiences took place in the student centre.

Or

Peter Smith will talk to us tonight in the student center about sexual experiences people have had with aliens.

Example

Two Sisters Reunited after 18 Years in Checkout Line.

This can mean either:

Two sisters who haven't seen each other for 18 years meet by chance in a checkout line.

Or

Two sisters were in a checkout line for 18 years and were finally reunited after getting out of line.

These kinds of ambiguities can be amusing, but are rare in arguments. Sometimes, however, a speaker can slide between two or more meanings of a word in an argument without realizing it. When this happens the argument is a bad one. It is guilty of a fallacy called “equivocation”.

  Fallacy of Equivocation

  A word is used in two different senses in an argument. The only reason that the premises appear to support the conclusion is because the different senses of the word are not distinguished.

Example

Nothing is better than a million dollars. Leftovers are better than nothing. Therefore, leftovers are better than a million dollars.

This argument commits the fallacy of equivocation: distinct meanings of “nothing” are being used in the premises. For the argument to be valid the same meaning of the word must be used throughout the argument.

In the first premise “nothing” is being used to mean, “There isn't anything I would like more.”

In the second premise “nothing” is being used to mean, “Not having anything to eat.”

Notice that, despite the improbability of the conclusion, the argument looks valid until we distinguish between the different meanings of the word “nothing” at work in the premises.

Here's another example.

Example

Darwin's theory of evolution is just a theory. A theory is speculation, not fact. Our schools should teach facts, not speculation. Therefore, our schools should not teach Darwin's theory of evolution.

This argument is also guilty of equivocation. The problem in this case is subtler than it was in the previous example. In this case, the argument is sliding between two meanings of the word “theory”.

A theory can be understood as either:

(a) A consistent explanatory account of a given phenomenon, often grounded on general principles, used in science and elsewhere for prediction and explanation. Although theories are not proven, they are generally well founded and reliable.

(b) Fanciful speculation as in “this is one of my pet theories.”

In the argument the first premise uses meaning (a) and the second premise uses meaning (b). Since different meanings of the word “theory”

are used in the argument, the argument is invalid.

To avoid equivocation, words must be used univocally . That is, they must be used with a consistent meaning throughout the argument.

  Vagueness

  Vagueness is like ambiguity since both are a problem with clarity of meaning. We saw that a word, phrase, or sentence is ambiguous when it has more than one plausible meaning in a single context. With ambiguity each of these meanings is perfectly clear. By contrast, a word, phrase, or sentence is vague when it has no definite meaning at all. This means that we can't pick which meaning to use. Instead, there is no clear meaning at all .

Some words are intrinsically vague in all contexts.

For example, “bald”, “sick” and “good” are all vague terms. We cannot specify necessary and sufficient conditions for being sick, bald, or good. Arguably, one is sick when one has cancer and when one has a blister.

Some words are intrinsically vague, but can nevertheless have quite specific meanings in the appropriate context. For example, “small,” “medium,” and “large” are vague terms but have quite clear meanings in the context of sorting eggs or buying a soft drink at the movies.

Two kinds of terms that are always vague and that should always be avoided in your own arguments are what are called “useless modifiers” and “relative terms”.

Useless Modifiers are words and phrases like these:

“Very,” “so much,” “a lot,” “kind of,” “sort of”

These are words that a speaker employs when he or she cannot be bothered to find out the true extend of something. If I think that Stockwell Day is out of favour among the members of the Canadian Alliance Party, but don't know how many members of the party want him to step down, I might say, “He is sort of unpopular.” To say that Day is sort of unpopular does not actually tell us anything informative. One should be more precise than this, especially in an argument.

Relative Terms are words like these:

“Big,” “small,” “tall,” “short,” “fast,” “slow,” etc.

“A big car” is vague unless we specify more about it. “A big car for four 250 pound men” is much more precise. We need to know what it is big in relation to in order to have a statement that isn't vague.

Arguments can employ vague terms, phrases, or sentences. When they do, they are bad arguments. This is because if a term in one of the premises is vague, it has no definite meaning.

If I say, “John is sort of smart,” or, “John is big” I am not saying anything specific about John. If I say, “John is smart” or “John is big for a 9 year old”, then I am saying something specific. In arguments we need to say

things that are specific, not vague. If a premise has no definite meaning, then it cannot be true or false and so cannot support any particular conclusion.

Recognizing Vagueness

The best way to determine whether or not words or claims are vague is to determine whether or not there are clear truth-conditions for using them. To determine this, ask yourself. “Under what circumstances, and how could we tell if the claim is true?” If you can't imagine how to answer this question, then the claim is vague.

Example

The psychic hotline can help you achieve personal growth by reaching into your soul.

This is a fine example. How would you know that it is true that the psychic hotline reached into your soul? The soul, if it exists, is certainly not something we can observe or measure. Hence, this claim is vague and should not be used or accepted as part of an argument.

Finally, it is important to recognize that a passage can be ambiguous and vague at the same time.

Example

Even after our long walk in the rain together, Joseph was still rather dry.

The phrase “long walk” is vague, as is “rather dry”.

The sentence is also ambiguous. Saying that Joseph was rather dry could mean that he didn't get wet, that his sense of humour remained sardonic, or that he was thirsty. Since these alternative meanings arise as a result of the single word “dry” having multiple meanings, these are examples of semantic ambiguity. The word “our” is also ambiguous. It could mean “me and Joseph” or “me and someone other than Joseph”.

 

Accepting Premises

 

Most of what was discussed in the previous section concerned the status of the premises of an argument. As we saw, to support a particular conclusion premises must not be vague or ambiguous, should not be phrased in emotionally charged language, and should make use of definitions where necessary to prevent misunderstanding.

Even if one has taken all of these steps, the premises of an argument will often still require support. In this section we will examine several methods used to support premises.

Provide an Argument

The best way to ensure a premise is acceptable is to provide an argument to show that it is true. In this case, one is formulating one or more subarguments to support premises that might not be readily accepted.

Example

John could not have stolen the painting. The painting was taken from the gallery at 10:35. Darren has told us that at that time he was talking to John in the library. Darren is a Bishop and wouldn't lie about that.

In this case the conclusion of the argument is that John could not have stolen the painting. The main argument is that John was elsewhere when the painting was stolen. The reference to John's conversation with the Bishop is intended as support for one of the central premises in the main argument. If we were to standardize this argument, its logical structure becomes clear.

 

Common Knowledge

 

A claim is said to be common knowledge if most people in the relevant group know the claim to be true.

Sometimes the audience can be different from the group to which the information would be considered common knowledge.

For example, most people in the United States know that George W. Bush is the President, but most people in the United States do not know that Jean Crétien is the Canadian Prime Minister. If the audience is not a part of the relevant group (the group for whom the information is common knowledge), then the premise needs additional support.

If the audience requires additional support, then be prepared to offer a subargument in support of the premise that is contentious.

When appealing to common knowledge, it is a good idea to pause and ask, “Is it really knowledge?” Sometimes items of information make their way into a group and are widely accepted as true but are in fact false.

An extreme example of this can happen when we acknowledge the relativity of common knowledge. What is regarded as common knowledge is relative not only to groups of people, but to times as well.

Example

It was not always common knowledge that information about our physical traits is encoded in our DNA.

Example

Before Freud, the concept of the subconscious was not widely accepted, but now it is.

So, when you appeal to common knowledge there are three things to beware of:

1. Make sure that the audience is likely to be part of the group for whom the information is common knowledge.

2. Make sure you can offer other evidence in support of the premise. 3. Make sure that the claim that you think is common knowledge

actually is knowledge, and not merely shared false belief.

Another very common way of justifying the use of premises in arguments is to appeal to testimony. In this case we are relying on the report of the facts as observed by someone else.

  Testimony

  We can define testimony as the communication of someone's own personal experience.

How do we know that John was in the Library at the time of the theft? Because the Bishop says he saw him there. We are relying on the Bishop's testimony.

The weight we can give to testimony will depend on a number of things. One of these is the importance of the conclusion. Obviously, the more that is at stake, the closer we need to scrutinize appeals to testimony.

There are three criteria that need to be met for testimony to be an acceptable reason for accepting the premise of an argument.

1. Plausibility

A claim is plausible if it could be true and if it fits with what you already know.

If John claims that he couldn't have stolen the painting because at the time of the theft we was suddenly sucked into an alternative dimension, we probably don't want to base his innocence on his testimony alone. Things like this just don't happen, so the testimony is very implausible.

On the other hand, if john says he was in conversation with the Bishop at the time of the robbery, and we know that John and the Bishop are old friends who chat when they get the chance, then the testimony is plausible and should be given some consideration.

2. Reliability

Is the person giving the testimony trustworthy? If not, or if he or she has an earned reputation as a liar, then their testimony should not be given much weight. In our example, since Bishops usually tell the truth, his testimony as to John's whereabouts during the theft is reliable.

3. Restricted to Personal Experience

Finally, testimony must be based on personal experience. Think about what happens in a trial when a witness gives testimony. The witness is always directed to testify only about events he or she saw first hand. Otherwise, the testimony is called hearsay and is thrown out by the judge.

Sometimes we claim to know something is true and declare so when it is in fact beyond our own experience. Since we believe something so firmly, we think we have first-hand knowledge when we do not. When this happens testimony might seem to be reliable, but in fact is not.

Suppose I watch NYPD Blue religiously and say, “NYPD Blue is the best show on television.” This might seem like reasonable testimony, but is probably not. It is likely that this claim actually extends beyond my personal experience, even though I might not realize this. The problem is that unless I have watched everything else on television I am not really in a position to say that NYPD Blue is better than all of the other shoes on TV.

When you see an appeal to testimony in an argument, ask yourself whether or not the claim under discussion is actually within the bounds of the witness offering the testimony.

 

Authority

 

A third method of supporting premises is the use of experts or authorities. We often need to make claims about things we don't know that much about in our arguments. When this happens we appeal to someone else who knows more than us about the subject under discussion.

An authority is someone who knows more about a subject than most people.

Appealing to authorities is a useful means of supporting premises in arguments, but doing so must accord with certain rules. If these rules are not met, then the appeal to authority is fallacious, and the argument becomes a bad one.

1. The authority must be identified

Who are the authorities being appealed to? Unless we know that, we cannot evaluate whether or not the authority really is an authority or is worth taking seriously. Think about those ads for toothpaste in which it is claimed that eight out of ten dentists recommend a particular brand over others. Who are these dentists? How do we know they are good dentists, or have had access to other brands of toothpaste? We don't, so we should not accept what they say as supporting anything.

2. The authority must be respectable

What is at issue is the authority's caliber as an expert, not as a person. One's calibre as an expert is measured in different ways depending on the field of study. Academics are often evaluated by where they studied and how much they publish in the field. An angler's expertise might be measured by how many years she has been fishing.

3. The matter must be in the authority's field of expertise

The expert must be an authority on what is being discussed. There is no point appealing to what a geophysicist thinks about Russian cinema to support the claim that Eisenstein was a superior filmmaker to Pudovkin. Find someone who specializes in cinema, or better, Russian cinema.

4. The matter must be one on which there is a consensus of experts

There is no point appealing to an authority to support a premise if that particular individual is the only one, or one of only a very few experts, who endorse the claim in question. One should avoid using rogue scholars as authorities.

 

Fallacies Resulting From Bad Premises

 

Dichotomy Arguments

A dichotomy argument is one in which one of the premises is a disjunction or where one is explicitly or implicitly forced to choose between options. “Dichotomy argument” is somewhat of a misnomer for the kind of arguments we will look at in this section. The word “dichotomy” means “division in two”, which suggests that in a dichotomy argument we are faced with only two options. The understanding of dichotomy argument we will use involves facing options, but this will frequently include more than two alternatives. Dichotomy arguments can be good or bad arguments. Not all dichotomy arguments are bad, and not all of them are good.

  Disjunctions

 

A disjunction is a statement with the word “or” in it, where the reader is presented with two or more possibilities.

Example

We can go to the movies or we can go out for dinner.

This sentence is a disjunction. It can be broken into parts, which are called “disjuncts”. Each disjunct is a proposition that is presented as a choice or option. A disjunction can have an unlimited number of disjuncts. In the above example there are two:

We can go to the movie

And

We can go out for dinner

In dichotomy arguments we are usually presented with a disjunction of some sort in which we are presented with several alternatives (the disjuncts). The other premises in the argument rule the other disjuncts out except for one.

We can standardize these arguments schematically as follows:

 

Notice that the main premises above are linked. The disjunction is always linked with the premises that rule out particular disjuncts. This is because all of these premises need to be asserted together to support the conclusion. The premise A, B or C does not support the conclusion B unless we also have the other premises Not A and Not C .

Example

We can go to the movies, we can stay home, or we can go to the pub. We can't afford to go to the movies and we've been banned from the pub, so we'll have to stay home.

Here the first premise is a disjunction with three disjuncts (going to the movies, staying home, and going to the pub). The additional premises rule out two of the three disjuncts, so we are left with only one alternative as the conclusion: staying home.

The standardization for this would like this:

Notice that this argument includes a subargument. There are subpremises that are used to support the premises in which disjuncts are eliminated.

A bad dichotomy argument is guilty of a fallacy of false dichotomy . To understand this we need to clarify something about disjunctions. An interesting logical feature of disjunctions is that any disjunction is true if one or all of its disjuncts are true.

Example

Mike or John committed the murder.

This is true under any of the following conditions:

1. Mike committed the murder. 2. John committed the murder. 3. Mike and John both committed the murder together.

This claim is false only if none of its disjuncts are true. This would be the case if neither Mike nor John committed the murder.

The fallacy of false dichotomy can happen in two ways. The first way is if the disjunction is treated as an exclusive disjunction but is really an inclusive disjunction .

 

Exclusive Disjunctions

 

A disjunction is exclusive if only one of the disjuncts can be true.

Ordinarily, if you order a sandwich and are asked, “Do you want fries or salad with that?” you are being presented with an exclusive disjunction. It is understood that you can't have fries and salad or a third , unnamed item, but must choose between the two.

Example

I can either drive us to the airport or we can take a cab.

Since it would be very difficult both to drive and take a cab to the airport, this should be understood as an exclusive disjunction. The disjuncts, or choices, are mutually exclusive.

Inclusive Disjunctions

A disjunction is inclusive if two or more of its disjuncts can be true.

Although we tend to think that when we see a disjunction we have to choose between alternatives, this isn't always the case. Consider the claim, “You can run or you can miss your bus”. This is a disjunction but it is possible for both disjuncts to be true. Haven't you ever run and yet still missed your bus?

Sometimes arguments will present you with a disjunction and treat it as though it is an exclusive disjunction when it is in fact an inclusive disjunction. This is a fallacy because it assumes we can rule out disjuncts or possibilities that we in fact cannot rule out.

Example

Cheryl has come into some money all of a sudden. Either she won the lottery, or she received an inheritance. She won the lottery. Therefore, she didn't receive an inheritance.

In this argument we are presented with two possibilities (winning the lottery and receiving an inheritance). We are told in one of the premises of the argument that one of these possibilities (disjuncts) is true, and are asked to draw the conclusion that the other disjunct is false.

Can we draw this conclusion? No. We can draw this conclusion only if the disjunction is exclusive, since this would mean that only one of the disjuncts could be true. The problem is that although it is extremely unlikely, it is possible for both disjuncts to be true. Winning the lottery does not preclude receiving an inheritance or vice versa. Cheryl could have done both.

 

Non-Exhaustive Disjunctions

 

The other kind of false dichotomy occurs when the disjunction is not exhaustive. This means that other plausible alternatives have not been mentioned or considered.

Sometimes the options are not presented but are implied, as in the “all or nothing” version of the dichotomy argument.

Example

There is no way we can afford to fix everything that is wrong with our car, so we might as well not spend any money fixing it up.

This is a fallacy because we are asked to choose between fixing everything that is wrong with the car and fixing nothing. Obviously we could spend some money on the more serious problems and ignore the others. Notice that this example, although it contains a disjunction, does not include the word “or”. Not every dichotomy argument has the word “or” in it.

Sometimes other options are not even implied although they exist.

Example

Opera is not for everyone. You either love it or hate it.

Clearly there are other possible reactions to opera than these. If this were part of an argument we would be forced to choose between false alternatives since the other possibilities are not mentioned.

  Begging The Question

  Another fallacy that is associated with bad premises is called “begging the question”. This is also known as making a “circular” argument. This happens when one assumes what it is one wants to prove is already true. A rule of argumentation is that premises must always be more certain than the conclusion. Begging the Question breaks this rule since one of the premises is identical to the conclusion.

The more technical definition of begging the question is as follows:

Using a proposition P as a premise or an assumption in an argument used to support P as a conclusion.

There are three general ways in which an argument can beg the question.

1. When a premise and the conclusion are the same proposition expressed in different words.

ExampleHuman beings must be more than physical beings, because we all have immaterial souls.

In this example the conclusion is just the same as saying that human beings have a nonphysical aspect in addition to their physical bodies. This is exactly what the premise about immaterial souls says. What this argument amounts to saying is that human beings are not completely physical because they are not completely physical. Saying this twice does not give the claim any logical support.

Example Capital punishment should be required of all convicted drug dealers because they should be given the death penalty.

Since capital punishment is the same thing as the death penalty, this argument begs the question in the same way as the previous example.

2. When a subargument relies on a missing premise or an assumption that is identical to the conclusion of the main argument.

Example In revealed theology, the word of God is revealed in the Bible. It states very clearly in the Bible that God exists. Since the contents of the Bible are true, God exists.

The missing premise is that the contents of the Bible are true because they are the word of God.

The argument begs the question because the existence of God is used to justify the claim that what the Bible says is true, and that

is used to justify the claim that God exists. Again, we have argued in a circle. This argument boils down to saying that God exists because God exists.

3. Using a theory that is being argued for to refute a counterexample to the theory.

Example A: I deserve a larger salary than you because as sales manager my job is more important to the company. B: That's not true. As production manager my job is just as important as yours. A: No it isn't. My job is more important because I get paid more than you.

Here the debate is about whose job deserves the higher wage. A and B agree that this should be determined by whose job is more important to the company. When A and B disagree about that, A appeals to the fact that she makes more money than B to support her claim that her job is more important. Since this is the very point under discussion, A's argument becomes circular.

 

Fallacies of Relevance

 

In this section we will investigate another problem that can arise in arguments due to problems with premises. Fallacies of relevance are errors in reasoning that are linked to the use of irrelevant premises in an argument. In such arguments there are premises that are presented as though they have a bearing on the issue in question, or support the conclusion, but they do not.

There are 3 kinds of relationships that a premise can have to a conclusion.

1. A premise can be positively relevant to the conclusion.

In this case the premise supports the conclusion. This is what we want from a good argument.

2. A premise can be negatively relevant to the conclusion.

In this case the premise disproves the conclusion. Negatively relevant premises usually appear in counterarguments. Recall that in a counterargument the aim is to formulate an argument that undermines the conclusion of the original argument.

3. Finally, a premise can be irrelevant to the conclusion.

An Irrelevant premise neither proves nor disproves the conclusion. It bears no interesting logical relationship to the conclusion. An irrelevant premise is often called a “non-sequitur”, which is Latin for “does not follow” because conclusions do not follow from irrelevant premises.

Now let's examine some of the more common fallacies of relevance.

 

Straw Person Arguments

 

The straw person argument is typically associated with counterarguments. The fallacy consists in misrepresenting an argument when countering it. A straw person is, literally, something that looks like a person but is made out of something that is not very substantial: straw. It is a caricature of a real person. A straw person argument involves representing someone else's argument as weaker, or less substantial, than it really is; it is a caricature of the other person's argument. This is a bad argument because it responds to an argument no one actually holds or accepts.

Example

The feminist claim that we should adopt an ethics of caring and response is untenable. When I see my doctor I want her to fix what's wrong with me, not kiss my boo-boo.

Here the speaker is attacking a caricature of a feminist view of health care ethics. No feminist would think that their view of health care requires doctors to kiss injuries better. Hence, the speaker is guilty of a straw person fallacy.

Example

What I object to most about those people who oppose capital punishment is that they think that the lives of the convicted murderers are more important than the lives of their victims.

This is another straw person argument. It is unlikely that those who oppose capital punishment do so for the mentioned reason.

When you see arguments like these and wonder if they are straw person arguments, ask yourself if it is true, or even just plausible, whether or not people would really accept the view as it is described in the couterargument.

 

Red Herring Fallacy

 

A related fallacy is called the “red herring fallacy”. The term “red herring” is used to describe a tactic to take people off of the trail of something. Red herrings in arguments are an attempt to distract one's opponent from the real issue. Usually this involves introducing extraneous subject matter into the discussion, but it can also involve things like using humour and changing the subject.

Example

I disagree with you. Capital punishment is wrong for all sorts of reasons. Remember that episode of Law and Order where everyone witnesses the execution? That's a great show, isn't it? But I prefer Ben Stone to Jack McCoy.

Here the speaker is responding to someone else's views on capital punishment, but has neglected to offer any arguments of her own at all. Instead, she has just shifted attention to a television show.

  Ad Hominem Arguments

  “Ad hominem” means “to the person”. In an ad hominem argument one is attacking one's opponent rather than his or her argument. Usually this involves trading insults, or otherwise making fun of the other person.

Ad hominem arguments are divided into two categories. There are circumstantial ad hominems and there are abusive ad hominems.

Circumstantial

In a circumstantial ad hominem one refers to the situation or circumstances of one's opponent rather than the opponent's argument.

Example

Of course Charles would say that everyone should have a pet. He runs a pet store and wants to drum up business.

In this case the speaker is attacking Charles' contention that everyone should have a pet. The fact that Charles is in a position to benefit from having his views of pet ownership adopted by others in no way undermines the reasons Charles might have given to support his view. His argument might have been a good one. The speaker is not addressing any argument, and hence is guilty of the circumstantial ad hominem.

Abusive

In the case of an abusive ad hominem one simply attacks one's opponent's personality or intelligence. This can be done by ridiculing or insulting. This is a fallacy because trading insults does not address the quality of an opponent's argument.

Example

What the reverend has to say about the labour dispute is not worth listening to. He's a jumped up little twerp.

Whether or not someone is a twerp is irrelevant to the quality of that person's argument, and so cannot be used to dismiss it.

Example

According to the supporters of capital punishment, the death penalty is an effective deterrent against murder. This is nonsense. These people are not interested in deterrence. They want vengeance. They are the kind of people who flock to Dirty Harry movies.

This argument is actually guilty of two fallacies of relevance. It is an abusive ad hominem because it does little but attack those with a different opinion about the death penalty. It is also an example of a straw

person because it offers a caricature of the opposing view. It is extremely unlikely that those who support the death penalty do so only because they are interested in vengeance.

It is common for an argument to contain more than one fallacy of relevance. In fact, it is rare to find arguments that are guilty of only one fallacy of relevance.

Tu Quoque Fallacy

This is Latin for “you too”. The tu quoque fallacy involves accusing one's opponent of hypocrisy. The fact that someone who offers an argument is a hypocrite is irrelevant to the strength of his or her argument or the truth of his or her conclusions.

Example

Why should I take your advice? You never listen to anybody.

Just because the person in question never takes advice does not mean that the advice he or she has to offer is not worth following.

Example

John: You cheated on your income tax. Don't you realize that's wrong?Martha: Hey! You cheated on your income tax last year. Or have you forgotten about that?

The fact that John cheated on his income tax last year does not mean that it is permissible for Martha to do it this year. It might be equally wrong for both of them to cheat.

 

Fallacious Appeal to Authority

 

Earlier we saw that one way to support the premises of an argument is by appealing to an authority, someone who knows more about a particular subject than most people. We saw that certain criteria had to be met in order to use authorities effectively in arguments. If these criteria are not met, then we have a fallacious appeal to authority.

Here are the conditions under which this can happen:

1. We don't know who the expert is.2. The authority isn't recognized and respected as an authority in

the field.3. The authority doesn't work in the relevant field.4. The authority is a rogue scholar who is in the extreme minority in

advancing his/her views.

Example

4 out of 5 experts agree. Soapy brand soap gets your whites their whitest.

This is another fallacious appeal to authority. This time the problem is that we don't know who the experts are. This means we can't tell if they are experts in the relevant field, if they have solid credentials, aren't in the minority among experts, and so on.

Other Examples

Television advertisements contain many examples of such fallacies. These happen when doctors or professors attest to the quality of a long-distance phone plan, when firefighters endorse an abdominal exerciser, or when a figure skater recommends a vitamin supplement. Endorsements like this are common on television. When you see them, ask yourself if the person pushing the product is really an expert with knowledge relevant to the product being sold. More often than not, they aren't.

 

Appeal to Tradition

 

An appeal to tradition assumes that because something has been believed for a long time, that it is true, or that because something has been practiced a certain way for a long time, that it is a good idea to continue to do so. If, in an argument someone says, “Because it's always been that way” to justify a particular claim, it is probably an appeal to tradition.

Appealing to examples of the practice of slavery, denying women suffrage, etc., usually shows why such are problematic. It doesn't follow from the fact that something has been done a certain way for a long time that we should keep doing it that way. Maybe the practice in question has always been a bad one, or maybe a change would be for the best.

Example

We can't start using the schools all year round as a response to the board's new budget. Children have always had two months off in the summer.

Again, the fact that children have always had two months off does not mean they should continue to do so. Perhaps the education system needs to change in light of the quality of education and the financial pressures the government has placed on schools.

Example

Think of how many commercials you have seen in which it is claimed that the product in question is made “the old fashioned way.” Such commercials are usually guilty of the appeal to tradition.

 

Appeal to Ignorance

 

To claim that since there is no evidence against a particular claim, it is true, or to claim that since there is no evidence to support a particular claim, that it must be false.

This is a fallacy because a lack of evidence cannot be used to establish anything . Only positive evidence can be used to support a conclusion. Imagine if this weren't the case and you were on trial for murder. There is no evidence that you performed the criminal act, yet there is no evidence that you didn't do it either. Would it make any sense at all to convict you for murder? Of course not. A lack of evidence or proof establishes only that we don't know whether something is true or false. It cannot be used to establish that something is true or false.

Example

Since there is no physical evidence that aliens have actually abducted people, no one has ever been abducted by an alien.

A lack of physical evidence of alien abduction does not mean that abductions don't happen. They might happen in a way that does not leave evidence. All the lack of evidence in this case can show is that we can't prove alien abductions actually happen. This is not the same thing as proving they do not happen.

Example

There's no way to prove that God doesn't exist, so God exists.

Similarly, just because no one is smart enough, or because it is impossible to prove God does not exist, it doesn't follow that God actually does exist. What does or does not exist in the world is independent of what we can or cannot prove. It might very well be that even though no one can formulate a compelling argument to prove God does not exist that God doesn't actually exist.

 

The Gambler's Fallacy

 

The idea that when it comes to events that are purely probabilistic , the odds that a particular result will occur next time the event happens are likely to change depending on what has happened in the past.

Example

The last 10 times I've flipped this coin it has come up heads. Therefore, the next time I flip this coin it is more likely to come up heads than tails.

Assuming the coin is not a trick coin, this conclusion doesn't follow. Whether a coin lands heads or tails always has an equal chance. Previous flips of the coin do not affect future outcomes, so in fact there is still an equal chance of the coin coming up heads or tails despite the previous flips.

Don't confuse the gambler's fallacy with induction. Induction is the process of making inferences about the future on the basis of what has happened in the past.

If you have seen your English professor arrive at class with the same pair of brown shoes on all term, you can draw the inference that she will probably have the same shoes on at the next class and you will probably be correct. In this case past events do make particular events in the future more likely to happen.

The difference between this case and the coin flipping is that it is not a matter of chance which shoes your professor wears while it is a matter of chance whether a coin land heads or tails. She probably owns only a few pairs of shoes and has a favourite comfortable pair that she likes to wear to class. So, with induction we are not making reference to genuinely random events, in which case repeated occurrences of a result do make it more probable that the same result will happen again in the future.

 

Appeal to the Majority

 

To argue that a proposition is true because “everyone” or “the majority” of people believe it is true. This is also sometimes called the “bandwagon fallacy”.

Remember all the times your mother said to you: “I suppose if everyone thought it would be a good idea to jump off a bridge you would think so too” in response to the claim, “But mom, everyone's doing it.”

The idea here is simply that agreement cannot be taken to be a reliable guide to truth. The fact that a lot of people, or even all of them, think that a proposition is true is doesn't make it true.

Remember that the vast majority of people in the western world believed that the Earth was flat. The majority was mistaken in this case.

 

Appeal to the Select Few

 

The appeal to the select few is like the appeal to the majority in reverse. To invoke this argument is to claim that a proposition is true because not everyone believes it.

Because only a few wealthy or beautiful people can afford or are able to use a certain product, we are to think that it is worth having. But that has nothing to do with whether or not the product in question is a good one, is worth having, or is something that we should want or desire.

Affluenza is a good illustration of this fallacy. It is the desire to have the newest, so-called best stuff because that's what the few, our betters, are using. We want to stand out from “the herd” and so want what the few have.

 

Arguments From Analogy

 

The argument from analogy draws a conclusion about one thing by comparing it with another. In virtue of the similarities, something that is true of the one is likely to be true of the other.

All arguments from analogy involve an analogy. An analogy is a comparison between two or more things.

The way an argument from analogy works is that it compares two things, A and B, and points out that A and B are similar. For instance, A and B share properties p, q and r. In virtue of these similarities the argument suggests that A and B are probably similar in a further respect, s.

What do arguments from analogy prove?

Even when analogies are employed in arguments, they do not prove anything. No argument from analogy can support a proposition with absolute certainty. All they can do is show that the conclusion is probably true or likely to be true.

Because of this, arguments from analogy are not evaluated as true or false, valid or invalid, sound or unsound. Instead, they are evaluated as weak or strong.

A weak analogy does not give us much reason to think that the conclusion is true.

A strong analogy gives us good reason to think that the conclusion is probably true.

  Components

 

Every argument from analogy has the following components:

1. A Primary Subject The thing the conclusion of the argument tells us about.

2. The AnalogueWhat the Primary Subject is being compared to.

3. The SimilaritiesThe respects in which the primary subject and the analogue are being compared, or the features they have in common.

4. The Target PropertyWhat is said about the primary subject in the conclusion.

To better acquaint us with analogical arguments, let's employ an example. William Paley offered an argument for the existence of God that is sometimes characterized as an argument from analogy.

Imagine that you had never seen a watch before. Certain features of the watch would tend lead you to the conclusion that it has an intelligent designer. The clockwork perfection and complex organizational structure of the watch are features that we associate with the idea of intelligent design. These features make it seem more probable that an intelligent designer is responsible for the watch than the idea that the watch came to be by accident. While it is not impossible for the watch to have been created by chance, it seems very improbable.

Now consider the world. It is a very complex thing too. The elements of ecosystems all exist in a perfect balance and harmony. The human body has the ability to regulate itself through a variety of fantastically complicated mechanisms. Animal species have just the right features required to survive in their environments.

Paley thought that in light of these observations, the world is a lot like a watch. Since we would conclude from the complexity and organization of a watch that the watch was designed, we must conclude that the universe was also designed.

Let's identify the parts of this argument

The primary subject:

In this case the primary subject is the world. This is what the conclusion of the argument is about.

The analogue:

The analogue is the thing the primary subject is compared to. The watch in Paley's argument plays this role.

The similarities:

The similarities are all of the respects in which the primary subject and the analogue are alike. These include the idea that both are complex and highly organized systems.

The target property:

This is what is said about the primary subject in the conclusion. Being designed or having an intelligent designer is the target property. This is the characteristic that is extended from the analogue to the primary subject.

  Evaluating Arguments from Analogy

  Evaluating arguments from analogy

Remember that analogical arguments are evaluated as being either weak or strong arguments.

A strong analogy has a large number of relevant similarities and a small number of relevant dissimilarities.

A weak analogy has a small number of relevant similarities and a large number of relevant dissimilarities.

Because the number of similarities and differences is always relative, arguments from analogy can only be probably true. They can never give us absolutely certain grounds on which to accept a conclusion.

The first thing to ask when evaluating an argument from analogy is whether or not there are really similarities between the primary subject and the analogue.

Example

Fishing is like meditating. Hence, fishing is very relaxing.

This is a bad analogy. No similarities have been identified between the primary subject (fishing) and the analogue (meditating). Although there might in fact be some similarities, in an analogical argument the speaker must provide these similarities in order to motivate the analogy.

In the case of Paley's argument from design, there are identified similarities between the primary subject (the universe) and the analogue (a watch). They are both complex, highly organized, and behave in a regular manner.

The second question you should ask is whether or not the similarities are relevant.

This question must always be answered by considering what is at issue. The identified similarities used to motivate the analogy must be ones that reinforce the main point.

If Paley said that the world is a lot like a watch because both are round, this would not be a relevant similarity. It is not in virtue of watches (or anything else) being round that we think they were designed. It is in virtue of other features. The similarities Paley did identify do, in fact, seem to be relevant ones. It is in virtue of complexity and precision (in part) that we think watches have designers. Hence, Paley does identify relevant similarities.

Third, one should ask whether or not the identified similarities treated

univocally.

In providing an analogy, the identified similarities must be understood in the same way, within an acceptable range. The arguer should not equivocate, or treat features that are really quite different as though they were the same.

Example

Batman is like abortion. Batman and abortion are both complicated. Since abortion is immoral, so is Batman.

To say that abortion is complicated is to say that it is a complex issue; that the concepts involved are difficult ones to understand, that there are many good arguments both for and against abortion.

When Batman describes himself as complicated, he uses the word “complicated” in a different sense. He means that his personality contains many facets, that his life is very involved and complex.

The word “complicated” then, is not understood univocally in the above argument. Because of this, the analogy is extremely weak and the conclusion is highly improbable.

In Paley's argument the use of the words “organized,” and “complex” seem to be used univocally, or at least the same within acceptable limits. Often this will be a matter of judgement and will not be straightforward.

Finally, you should ask whether or not the identified similarities outweigh any relevant dissimilarities.

This is usually the most reliable place to examine an analogical argument. Try to identify differences between the analogue and the primary subject that tend to detract from the idea that we can treat them in similar ways.

Traditionally, Paley's argument is attacked in just this way. Many philosophers have argued that the sort of complexities and regularities identified in the natural world can be adequately explained in other ways than by appeal to an intelligent designer (e.g., natural selection), whereas the features of a watch cannot.

Furthermore, the kind of complexity of a watch and of an ecosystem is different in a number of ways. The watch involves a mechanical complexity of the orientation of its parts, whereas an ecosystem involves a balance between resources needed for species to survive.

These observations can, at best, weaken the analogy. Unless one can show that the two things being compared are different in every conceivable way, it is impossible to prove that an analogical argument is

completely unmotivated, or that its conclusion is false.

Finally, as was pointed out earlier, the question of whether or not the relevant differences between a primary subject and an analogue outweigh the relevant similarities is not an exact science. It will always be a matter of judgement and there will always be room for discussion in this matter.

We would standardize Paley's argument as follows:

 

Fallacies of Analogy

 

These are bad arguments that make use of comparisons or analogies.

Fallacy of Two Wrongs

To argue that because one bad case is permitted, similar bad cases should be permitted too.

Example

People who have tenure don't write half as much as sessional instructors and don't put any work into teaching. When I get tenure I'm going to slack off too, stop doing research, and stop caring about my classes.

The fact that tenured professors might “slack off” does not mean that the speaker should do the same when he or she gets tenure. Consistency demands that if it is wrong for tenured professors to act this way, it would be wrong for the speaker to act this way too.

Example

The last time I saw Tom he was incredibly rude to me. Why should I have to be polite when he isn't? If he's at the party this weekend I'm going to give him a taste of his own medicine.

The problem here is the same as it was in the previous example. The fact that Tom was rude to the speaker does not mean that he now has the right to be rude toward Tom. Rudeness is poor behaviour regardless of who started it.

Slippery Precedent

The slippery precedent is also called the “slippery slope argument”. The basic pattern of argument here is that it is claimed that if A happens, B will happen. Since B is undesirable, we should not allow A to happen in the first place. Sometimes there are further intermediate steps in slippery precedents. It might be claimed that A will lead to B, B will lead to C, C will lead to D, and that D is undesirable. Not all slippery precedents are fallacies. Some of these arguments are good ones and some are bad ones. Before we draw this distinction, let's look at another difference between kinds of slippery slope arguments.

There are two kinds of slippery slope argument. There is a logical version and an empirical version.

    The logical version

If we allow the initial action A (which seems permissible), we are logically committed to allowing another action B (which is impermissible).

It is thought that allowing A entails allowing B because, although there are differences between A and B, there is no relevant conceptual difference between A and B.

Example

If we allow passive euthanasia, then we will have to allow active euthanasia too. There is no real difference between allowing someone to die through the cessation of treatment and killing them through active means. In either case the intention of the physician is the death of the patient, and in either case the effect, the death of the patient, is the same.

In this example it is said that if we allow passive euthanasia (A), then we will have to allow active euthanasia (B), because there is no relevant difference between active and passive euthanasia. Because the argument is saying that active and passive euthanasia are equivalent, this is an example of the logical version of the slippery slope argument.

The empirical version

The empirical version of the slippery precedent is a little different. This version does not claim that A and B are equivalent in any significant way. Rather, it claims that due to the social forces and beliefs at work in the relevant group, allowing A (which is permissible) is in fact likely to lead to allowing B (which is impermissible). In the logical version, then, A and B may look different, but are not. In the empirical version A and B are different, but A will lead to B.

Example

Although passive euthanasia is permissible, we should not adopt active euthanasia as an acceptable practice. Allowing active euthanasia of the terminally ill might be morally permissible, but it will have disastrous effects. The pressures to cut health costs and make more resources available could lead physicians to administer active euthanasia more liberally. Also, the elderly and handicapped might feel undue pressure to ask that their lives be ended through active intervention.

Notice how this argument differs from the first one. It claims that allowing active euthanasia will lead to certain unacceptable consequences. These consequences are not inevitable or necessary, but are likely given social attitudes toward the elderly and handicapped and given the financial problems with the health care system.

It is important to emphasize that an argument like this claims B is only likely to follow from allowing A, not that it necessarily will. Whether or not B will follow A depends on a variety of factors, the effects of which are

difficult to predict accurately. Provided the argument acknowledges that it is only probable that the bad effects will follow, the argument does not commit a fallacy.

When are these kinds of arguments fallacies?

The logical version of the fallacy occurs if the actions in question (A and B) are not logically equivalent, but are treated as if they are . If letting die and killing are presented as logically equivalent, when in fact they are not, then the argument would commit the slippery slope fallacy. This version of the fallacy also occurs if the speaker simply assumes A and B are conceptually equivalent without offering any reasons to think that they are.

To evaluate logical versions of slippery slope arguments, ask if the items under discussion really are equivalent. The more relevant dissimilarities you can identify between A and B, the more likely the argument commits the fallacy.

The empirical version occurs if the argument simply assumes that the negative consequences will result, or if the social factors it appeals to are irrelevant to whether or not the unwanted consequences are likely to follow.

Example

Sure, raising taxes next year will pay for some important social programs. But if we let the government raise taxes next year, they'll raise them again and again in the years to come and soon we'll be paying outrageous taxes.

This is a fallacious version of the empirical slippery slope argument. It claims that allowing the government to raise taxes this year will lead to further tax increased in years to come. The argument is fallacious because it merely assumes that these later tax increases will happen. No justification is given to think that this is in fact likely.

Example

This is ridiculous. What is affirmative action but a form of discrimination?

This would be an example of the fallacious version of a logical slippery slope argument. Notice that the speaker is suggesting that there is no real difference between affirmative action policies and discrimination. That explains why it is the logical version. It is a fallacy because the speaker does not give us any reason to think that these two things are in fact equivalent.

 

Slippery Assimilation

 

This occurs when one ignores the fact that many small differences that are insignificant on their own can, taken together, constitute a significant difference.

Example

Killing a foetus is just as much an act of murder as killing an infant. There's no real difference between a three-month-and-one-day-old foetus, or a three-month-and-two-day-old fetus, and so on. So where do you draw the line between a three-month old fetus and an infant?

What the argument neglects is that, while there are no individual differences that, from one day to the next, mark a significant difference between a fetus and an infant, many small changes can, taken together over a long period of time, constitute an important difference.

To evaluate arguments like these, that appeal to grey areas, or claim that it is difficult to “draw the line”, ask whether, despite these difficulties, clear distinctions can be made.

One might not notice the change in hair colour of the guy who uses Just For Men hair colouring from one day to the next, but that doesn't mean there isn't a difference between his having grey hair and his having black hair.

 

Negative Analogy Arguments

 

These arguments rely on a disanalogy between two things. In light of a set of differences between the primary subject and the analogue, it is argued that there is likely to be a further difference.

Negative analogy arguments contain almost all the same elements as arguments from analogy, with one difference. Instead of identifying similarities between the primary subject and the analogue, the argument appeals to differences.

Example

Fish are unlike us since they have small brains and are not mammals. We feel pain, but it is likely that fish do not.

Primary subject:

Fish

Analogue: Us (human beings) Differences: We have large brains and fish have small brains. We are

mammals and fish are not.Target Property:

Feeling pain

In the case of a negative analogy argument, the identified differences should be negatively relevant to the possession of the target property.

In the example above, it is plausible to say that brain size has something to do with the ability to feel pain.

Example

My boyfriend is nothing like yours. Yours has lied to you throughout your relationship, whereas mine has always been honest with me. Furthermore, since your boyfriend was a real ladies' man and mine has always been shy, it is unlikely he has cheated on me.

Primary subject:

The speaker's boyfriend

Analogue: The other person's boyfriendDifferences: The speaker's boyfriend has been honest while the other's

has not. The speaker's boyfriend is shy while the other's is a ladies man.

Target property:

Not cheating on his partner

Negative analogy arguments are standardized just like arguments from analogy, except that the differences are used to support the claim that the primary subject and the analogue are not alike.

 

Arguments from Experience

 

Arguments from experience involve the attempt to justify a general conclusion on the basis of observations, or make particular predictions about the future in light of what has happened in the past.

Like arguments from analogy, arguments from experience can have conclusions that are only probably, not certainly true.

 

The Universal Generalization

 

The first kind of argument from experience is called the “universal generalization”. A universal generalization appeals to the experiences someone has had of some members of a class of objects to support a conclusion about all or most members of that class. Remember that a class is simply a group of things that share a particular characteristic.

Example

All of the hot dogs I have ever eaten have made me sick so all hot dogs make me sick.

Example

All of the hot dogs I have ever eaten have made me sick so most hot dogs make me sick.

Both of the above examples are universal generalizations. Generalizations like the second are less likely to be falsified, since the claim is about most , but not all of the members of the class hot dogs . The conclusion is therefore weaker in the second claim but is thereby more likely to be true. This is because the first alternative would be falsified if there were even one hot dog that didn't make me ill when I ate it. The second formulation of the generalization allows for some counterexamples and so is not so easily falsified. As a general rule, universal generalizations of the second type are preferable for this reason.

 

The Generalization to a Particular

 

A second, related argument from experience is called the “generalization to a particular”. The generalization to a particular appeals to the experiences someone has had of many members of a class to support a conclusion about a single, unexperienced member of that class. While the universal generalization draws a conclusion about a lot of things, the generalization to a particular draws a conclusion about only one thing: something that has not yet been experienced.

Example

All of the movies starring Pauley Shore I have ever seen have been awful. This movie stars Pauley Shore. Therefore, this movie will be awful.

Notice that in this case the conclusion that is drawn is about one thing (a particular film).

Both kinds of arguments contain the following necessary elements:

The Sample

The sample is made up of all the things we have experienced or know about that belong to a particular class or group of objects. In our examples so far the samples are all the kinds of hot dogs I have ever ingested or all the movies starring Pauley Shore I have seen.

The Population

The population is made up of the things we have yet to experience. In our first example that would be all of the kinds of hot dogs I have never tried. In the second it would be the Pauley Shore movie I am about to see.

The Category

The category is the respect in which the sample and the population are similar. This is like the similarities in an analogical argument. In the first example the category is hot dogs and in the second the category is Pauley Shore movies .

Target Property

The target property is the characteristic that is being extended from the sample to the population. In the first example this is the property of making me sick, and in the second it is the property of being awful. The target property is always the thing you are saying about an object or class in the conclusion of a generalization.

Evaluating Generalizations

As with analogical arguments, there are certain things to look for, or questions to ask when you evaluate generalizations.

Is the sample adequate?

The first thing you should ask about is the sample size. The larger the sample, the more likely it is that the conclusion is true. The smaller the sample, the less likely it is that the conclusion is true.

If I were to say, “ All of the hot dogs I have ever eaten have made me sick so all hot dogs make me sick” but have only ever eaten one hot dog in my entire life, it is not very likely that the conclusion of my argument is true. It is quite possible that my experience with that one hot dog was unusual, or that other kinds of hot dogs might not effect me in that way. On the other hand, if I said the same thing and had eaten hundreds of hot dogs, my conclusion would seem a lot more probable.

A similar question to this is the following:

Is the generalization hasty?

A generalization is hasty when it is based on few experiences, or when the population is too small to support the generalization. Making such an error often occurs when one employs what is called “anecdotal evidence.” This involves providing testimony that extends beyond the personal experience of the speaker.

Example

Calgarians hate people from Toronto. I've met a number of native Calgarians who have become antagonistic toward me once I have told them where I'm from.

This involves a hasty generalization because my own experience is very limited. To be more plausible I'd have to have had many such experiences, such as having entire classes of students boo when I say that I'm from Toronto.

Is the category appropriate?

Does the category bear an appropriate relationship to the target property? If not, then the generalization makes use of a bad category and is more likely to be false. If so, then it uses a good category and the conclusion is more likely to be true.

Example

Everybody I've met who is named Tom is a jerk. Therefore, all Toms are probably jerks.

This conclusion is not given very strong support because there is no real

connection between what name a person has and what their character is like. We do not wait to see how our children behave and then give them names that reflect certain character traits. This example makes use of a bad category, and hence, the conclusion is very weak.

  Statistical Arguments

  The Statistical Generalization

The statistical generalization uses knowledge about how one or more characteristics are distributed among an experienced group to draw a conclusion about how those characteristics will be distributed among the members of an unexperienced group.

This differs from the universal generalization and the generalization to a particular because it is concerned with how frequently a property or characteristic is likely to appear in the population. Statistical generalizations do not attempt to say anything about all members of a group or about an individual member of a group.

Example

The last five times Jessica taught this course 5% of the students failed each time. The next time she teaches this course we can expect that 5% of those students will receive Fs.

The Elements of the Statistical Generalization

Because statistical arguments are a kind of generalization, they contain similar elements. In every statistical argument there is:

The Sample

This is made up of the experienced cases.

In our example this would be the last 5 classes Jessica taught.

The Population

The population is made up of the unexperienced cases. The population is always what you want to learn something about in a statistical argument.

In our example this is the next class that Jessica will teach.

A Target Property

This is the characteristic or group of characteristics extended from the sample to the population. This is usually expressed as a percentage.

In our example it is that 5% of the students will fail the course.

A Similarity

Instead of a category, statistical arguments invoke a similarity. This is because the sample and the population must be alike. The kind of similarities identified are extremely important because they have a direct

bearing on the strength of the conclusion. This is expressed by saying that the sample is representative of the population. The idea is that there won't be important differences between the sample and the population that would undermine the conclusion of the argument.

In our example about Jessica the sample is representative only if the kind of students she will teach next year do not vary in certain ways from the kind of students she has taught before. If the university has raised its admission standards this year, then the quality of the students she will have should be better, and this has a good chance of affecting the distribution of the grades in her class.

  Evaluating Statistical Arguments

  Questions About the Sample

When you encounter statistical arguments there are questions you should ask about the components of the generalization and about the way the data were collected.

Is the sample representative?

As we saw above, it is very important that the sample be representative of the population. If a study wants to learn something about men's attitudes toward their prostates, then the study shouldn't be made up of interviews with ten year old girls.

Was the sample big enough?

The larger the sample is, the stronger the conclusion of the argument. If the sample is sufficiently large, it will reflect any relevant differences between the people asked. This is partly why random selection is so important. The selection is random when each member of the population has an equal chance of being selected.

Imagine that you decide to poll university students to determine what percentage of them thinks tuition is too expensive. If you stand outside the Dean's office and poll ten people, it is possible that you might, by chance, have come across ten people who are on their way to the Dean's office to raise a complaint about the cost of tuition. Because you have stumbled upon a very specific segment of the population made up of university students, your results will not likely be representative.

What kinds of individuals compose the sample?

If you are conducting a study on whether people prefer vegemite or marmite , a population of people from Waterloo is probably not the best sample to use, since most people in that population won't know anything about these.

Is the sample a homogeneous group or a diverse one?

If the conclusion you want to draw is about a very broad group, like North Americans, then your sample needs to reflect the heterogeneity of that group.

Stratified Sample

A sample that is already known to reflect certain classifications or groups of people in a population and will therefore be representative of the group in question.

Measuring the Data

There are also questions you should ask about how the data were measured.

What was the measuring instrument used?

Were the instruments interviews, questionnaires, etc? If interviews, were they conducted face to face? Were identities kept anonymous?

These factors can have a profound effect on the results. Approximately 50 years ago Alfred Kinsey conducted research on the sexual activities of people in the United States. The data were collected by means of anonymous questionnaires. The results showed that a large number of men and women had experimented with same-sex relations as well as multiple partners. Had Kinsey relied on interviews with subjects face to face, you can imagine that people might have been more reluctant to be open and honest about their sexual experiences.

Is the instrument reliable?

A reliable instrument is one that provides consistent results under the same conditions. The results must be repeatable, much like a scientific experiment. Scientific experiments are often performed several times to ensure that the end results are the same. The goal is to make sure that the instrument used to detect the result is working properly.

Is the instrument valid?

An instrument is valid if it actually measures what it claims to. Comparing the results of different tests using different instruments on the same subjects tests this.

An example of an instrument the validity of which people frequently question is IQ testing. IQ tests purport to measure intelligence. However, a number of people have suggested that IQ tests involve so many cultural biases and assumptions (in terms of the kinds of questions asked and the expected “correct” responses) that they don't actually measure intelligence. They measure something more specific, like a white, middle class, male conception of intelligence.

What kinds of questions were asked?

Questions must be specific and as unambiguous as possible. Important concepts must be operationalized (i.e., the researcher must provide an operational definition for any key concepts.

Suppose you want to test the drinking habits of university students. Imagine if you used a questionnaire that asked the following question:

Do you consider yourself to be a light, moderate, or heavy drinker?

The problem with this question is that the key terms are not defined. This

means that the individual filling out the questionnaire must define what it is to be a light, moderate, or heavy drinker. Individual conceptions of alcohol consumption might differ significantly from yours. To prevent this, you must operationalized these concepts and ensure that the subjects work with the same understanding of what it is to be a light drinker as you. For instance, you might specify how many drinks a light, moderate, or heavy drinker consumes on average in a week. By providing an operational definition of the main concept in a questionnaire (e.g., being a light or a heavy drinker), the results of the survey will not depend on how the subjects interpret what it is to be a light or a heavy drinker.

Avoid loaded questions. Loaded questions are ones that are tailored to encourage a particular response.

Example

You're not going to have another drink, are you?

That is a loaded question. Clearly I am trying to encourage a negative answer. Questionnaires and interviews can, in more subtle ways, use loaded questions.

Example

Is your spouse/living partner supportive of your career?

Yes_______ No_______

How does he show his support?

The problems with this question are as follows. First, it offers only a “yes” or “no” response to what is a fairly complex question. There are many ways in which one's spouse may be both supportive and unsupportive. Second, the follow up question assumes an affirmative answer to the first question, which has the effect of encouraging a “yes” response to the first part. Finally, notice that the second question asks, “How does he show his support?” If this question was not intended only for female subjects, it will seem as though the questions are oddly skewed to male respondents.

The effects of loaded questions can be numerous. People may take offense to the assumptions that have been made by the researcher and not respond, or respond falsely, or people may be led to answer in the way they are expected to, rather than honestly.

If a researcher has not taken care to avoid such problems, the data becomes unreliable. Hence, in evaluating a statistical argument, one should ask whether all of these criteria have been met.

 

Causal Arguments

 

The final kind of argument we are going to look at is the causal argument. A causal argument draws the conclusion that one thing (or group of things) lead to another thing (or group of things).

The Nature of Causal Relations

Before we look at causal arguments, we should clarify a few things about the nature of causal relationships.

It is generally thought that in causal relationships effects follow upon their causes. This means that effects can occur either after their causes, or simultaneously with them, but they cannot precede their causes in time.

Second, the sorts of things that can be causes or effects are usually thought to be events. Although we frequently talk about causal relationships as holding between objects, this is not quite correct. If I say, “The brick caused the window to break” I am describing a causal relationship. I seem to be picking out two objects: a window and a brick. The problem is that it isn't just the brick as such that makes something happen; it is the impact of the brick against the window that causes the window to break. Both of these things (the impact of the brick and the breaking of the window) are changes that involve the identified objects. The changes are usually referred to as “events”. Hence, one event (the impact of the brick against the glass) caused another event (the shattering of the window).

Third, causes and effects are correlated. When two things are correlated we see them happening together. To say this, of course, assumes that we are talking about two kinds of events that happen lots of times. Hence, if we think A causes B, then events like A must be correlated with events like B.

These are necessary conditions for a causal relation. If A is the cause of B, then A and B must be correlated, and B must follow upon A.

Repeated correlations are important for justifying the claim that one thing caused another. If we witness an event A and see that it is followed by another event B, we cannot conclude with any certainty that A in fact caused B. To assume that it did is to commit what is called the “post hoc fallacy”.

 

Causal Fallacies

 

Post Hoc Fallacy

The name for this fallacy is taken from the Latin post hoc ergo propter hoc , menaing, “after this because of this.” Simply because one event follows another in temporal sequence doesn't necessarily mean they are causally connected.

Example

Just because three babies were born with three eyes after the plastics factory burned down is not itself sufficient reason to conclude that the burning of the factory caused the birth defects. There might be other factors responsible for the defects that happened to coincide with the fire.

To argue that A caused B we need more than the observation that B happened directly after A. We need to see that events like A are always followed by events like B. In other words, we need to see that A and B are correlated. Even this can fail to be enough to justify the claim that A and B are causally related, however.

Jumping from correlation to cause

Another common fallacy in causal arguments is the fallacy of jumping from correlation to cause.

Before we explore this problem, let's say a little more about correlations. Earlier we saw that two things are correlated if they happen together. Let's make this more precise by employing the following definition:

Two properties or events are correlated if and only if occurrences of or changes in one are accompanied by occurrences of or changes in the other.

  Kinds of Correlations

  There are two kinds of correlations

1. Positive Correlations There are more occurrences of A among members of B than among non-Bs.

Example If there are more occurrences of breast cancer (A) among Canadian women (B) than among American women (non-Bs), then A and B are positively correlated.

2. Negative Correlations There are fewer occurrences of A among members of B than among non-Bs.

Example If prostate cancer (A) occurs rarely in male children (B) but frequently in men over 50, then being a child is negatively correlated with having prostate cancer.

So now that we've seen what it means for two things to be correlated, and what kinds of correlations there are, why can't we conclude that if there is a correlation between A and B, A caused B?

There are three principle reasons for this.

1. In the case of many positive correlations, there might very well be a causal relationship between A and B, but it could be that A caused B, or that B caused A. Without further information there is no way to decide between these two possibilities.

Example Drug use and poverty are positively correlated, and there may be a causal relation between them, but poverty might cause drug use or drug use might cause poverty. Either one is possible.

2. In any correlation between A and B there might be a third factor, C, that causes A and B, in which case A neither causes B nor is caused by B.

ExampleManual dexterity is correlated with intelligence, but it is unlikely that one causes the other. They might both owe their occurrences to a third factor (a common cause) such as brain development.

3. In the case of any correlation, the correlation might be a coincidence. For instance, the myth that the stork delivers babies is based on such a correlation. Cycles of births in a town just happened to coincide with the migration of storks through the area. Because these two things happened together many times, people began to suggest that these events weren't just correlated, but that one caused the other. Of course, we know that storks don't deliver babies.

It is very difficult to establish that two events are causally connected rather than merely correlated. To make things worse, identifying a genuine correlation is itself a difficult task. It is not enough to notice that two things happen together frequently to have a correlation that will support a causal connection.

Example "Research shows that while alcohol is neither a sufficient nor a necessary cause for violence, alcohol and violence do co-exist.  They do go together.  The consumption of alcohol at the societal level does contribute to the incidence and prevalence of violence among certain individuals."  (From: Testimony before the Parliamentry Committee of Violence Against Women).

This is a prime example of the fallacy of jumping from correlation to cause. The above passage asserts that because alcohol and violence “go together” or “co-exist” that alcohol consumption causes violence. The reason that alcohol and violence “go together” could be explained in a number of other ways besides saying the first causes the second.

Establishing a correlation

To establish a positive correlation between X and Y we need to see that Y occurs more frequently among members of X than among non-members of X.

Example

Is there a correlation between women with silicone breast implants and women who develop connective tissue disorder? Even if many women with breast implants develop connective tissue disorder, this might not establish a genuine correlation.

We need to determine whether or not connective tissue disorder occurs in high numbers of women without breast implants.

This requires a comparison between two groups:

1. A Test Group The members of the test group possess the property whose causes or effects we want to study. In this case it would be women with silicone breast implants.

2. A Control Group A group that does not possess the property whose causes or effects are under investigation.

The control group must be as similar as possible to the test group, with the exception of lacking the property being studied.

For a study on breast implants, the control group will not consist of men,

or five year old girls, but women in the same age-group as those with breast implants, of the same general level of health as the women before they had their implants, and so on. If the participants in the study differ in significant ways, it is difficult to establish that it is the property in question that is responsible for different results between the test and control groups, and not some other factor.

If we discover a significantly higher occurrence of connective tissue disorder among the test group than the control group, then we have a correlation between having breast implants and developing connective tissue disorder.

In any causal argument, just like an argument from experience, or an analogical argument, the conclusion can only be shown to be probably true, not certain. The results of such a study can show that it is likely that breast implants can cause connective tissue disorder, not that it does for certain.

  Types of Studies

  Depending on the kind of study that has been done, there are different questions we should ask to evaluate causal arguments.

Correlational Research

In the case of correlational research the researcher does not control any of the conditions. This kind of research simply involves collecting data.

This is most commonly used when it would be unethical to expose research subjects to the causal factor under consideration, since it might be harmful. For instance, if you wanted to study whether or not the use of cellular phones causes brain cancer, you cannot gather test subjects, expose them to cell phone microwaves and then see if they develop brain cancer. Instead, you need to find people who already use cell phones on a regular basis and monitor their health, or find out how many people who have developed brain cancer used cell phones.

Controlled Laboratory Experiment

In this kind of experiment the researcher controls all of the conditions.

These kinds of experiments are only performed on non-human animals, such as rats. This involves a tremendous level of control over every aspect of the lives of the test and control groups. It is not feasible or ethical to give experimenters that much control over human beings.

Control Group/Test Group Experiment

The researcher controls the causal factor (the substance the causal effects of which are the object of the study). Other conditions are not controlled. The group of subjects is divided into the test group and the control group. The test group is given the causal factor and the control group is not. All participants must be made aware of any potential risks created by exposure to the causal factor.

The participants in the study (both in the test and control groups) must be representative of the population. If the drug is one like Viagra, then there isn't much point in having women participate in the study.

Also, the members of the control group must be as similar as possible to the members of the test group to ensure that it is the causal factor, and not something else, that gives rise to differences between the two groups later on.

Replication

For the results of an experiment to be reliable, the results must replicable. The experiment is one that can be repeated with the same results under the same conditions. If the results cannot be replicated, then it is likely that some of the conditions were not properly controlled

and that these affected the results.

There are a number of way in which experimenters control experimental conditions.

Blindness

In a blind experiment, participants do not know whether they belong to the control group or the test group.

The purpose of blind experiments is to prevent subjects from affecting the results because of their expectations. The main aim is to avoid the placebo effect . This occurs when someone who receives a placebo (an inert substance given to the control group) reports feeling certain effects because he or she believes they are receiving the causal agent.

You might have experienced this when you were younger. Perhaps you saw one of your friends given something that he or she was told was alcohol but wasn't. Your friend nevertheless began acting drunk. This was because of your friend's expectations, not because he or she was actually caused to be drunk by the substance in question.

Double-blindness

In a double-blind experiment neither the participants nor the experimenters know who is in the control group and who is in the test group.

This is to prevent the placebo effect among the test subjects, and to prevent experimenters from tainting results either by cuing test subjects or by looking at data with a set of expectations.

Experimenters can cue test subjects in very subtle ways, from the kinds of questions they ask, to their body language. A famous example of such cuing is the case of Clever Hans . Clever Hans was a horse that was thought to be able to do arithmetic by being asked a problem and stamping out the solution with one of his hooves. Many skeptics were convinced when they tested the horse's abilities. It took a long time before one researcher discovered that Clever Hans was receiving very subtle cues in body language not only from his owner, but from other experimenters as well, to stamp his foot the correct number of times.

  Evaluating Causal Arguments

  When you encounter a causal argument, here are the kinds of questions you should ask in order to appreciate how the argument works:

1. What is the causal claim being tested? 2. What is the sample? 3. What is the population? 4. What kind of study is involved? 5. What is the test group? 6. What is the control group? 7. Are the test and control groups similar? 8. How are the results measured?

Let's try an example.

Example

Pop music may help schoolchildren pass exams. In a nationwide British study, 11,000 students in 250 schools were randomly split into three groups. They listened to either Mozart, the pop group Blur, or a radio chat show, while taking a test on spatial reasoning.

The students who listened to the pop group scored 56%; the other two groups, 52%. The difference approached significance. The author of the study cited a California study in which adults performed better on a similar test while listening to Mozart, and said that this may show that adults process music differently.

The Causal Claim Being Tested

That pop music may help students pass exams.

The Sample

11,000 Students.

The Population

Students.

This should be more specific. Grade school students? High school, university?

Kind of Study

Control group/test group experiment.

Test Group

Students who write the test while listening to Blur (though the other two groups could each be the test group as well).

Control Group

Any two groups serve as a control group for the third. In this case, given the causal claim tested, the groups that listen to Mozart and talk-radio are the control groups.

Are the Test Group and Control Groups Similar?

This is difficult to say. We have not been given any information about this. They are similar to the extent that they are all students of the same nationality, but we know nothing of their ages, gender, etc.

Measuring Instrument

The scores on tests on spatial reasoning.

Finally, in light of all this, you should be able to offer an overall evaluation of the causal argument:

Overall Evaluation

The size of the sample is good. It is quite large, and the number of schools that participated in the study is high enough to be representative of schoolchildren in general.

One problem we have already seen is that neither the sample nor the population is well defined in terms of age. So we should wonder about how representative the sample is of the population.

We should wonder about the control groups used. The results might be more plausible if a silence condition were used in one. Perhaps the students scored more poorly than they would have without any background noise at all, but since they probably like Blur , were less distracted by it than by Mozart or talk-radio.

Only one kind of test was administered. It is unlikely we can generalize to all kinds of tests (exams) on the basis of how the students score on spatial reasoning.

Does the study give the conclusion strong support?

It seems not, in light of the above problems. Furthermore, it was claimed that the differences between the test and control groups merely approached significance. Without a more definite result there is little reason to think that there is a causal relationship between music and passing exams.

What about the claim about the differences between adults and children?

Do the test results suggest that adults and children process music differently?

Probably not. It is more likely that adults are more familiar with Mozart than with Blur, in which case what the study more plausibly shows is that adults are less distracted by Mozart than students are.