The Basics of Arguments

 

We are constantly called on to make decisions that enact certain values and depend on certain beliefs – what kind of career we want, who we will vote for, to vote or not, what kind of products to buy, and even what we will eat.  Many of these decisions are made without reflection, but when we become aware of our actions, we search for reasons for our choices.  At the same time, people give us their own reasons to persuade us to act in certain ways.  In so far as we think critically, we rely on arguments.  The most practical value of philosophy is that it teaches how to argue more effectively and how to evaluate the arguments of others.  From a philosophical perspective, the goal of an argument is not simply to persuade another, but rather to find the truth.  That is why “logic,” the study of argumentation and reasoning, is different from “rhetoric,” the study of persuasion.

We all make and evaluate arguments already, and some have more of a “knack” for it than others, but we all can engage arguments more effectively by examining different kinds of arguments and their structures.  That requires defining some terms.  A “proposition” is the technical name for a statement that asserts or denies something about the world and can be affirmed as true or denied as false.  Statements of fact are examples of propositions.  Questions, exclamations, and commands are not.  An argument is a collection of propositions organized so that one proposition (the conclusion) is based on the other propositions (the premises).  That is, the premises are given to support or justify the conclusion.  Usually, the conclusion is a proposition about which there is disagreement, while the premises are more widely accepted.  The maker of the argument hopes you will see that if you accept the premises, you should also accept the conclusion. 

All this sounds obvious, but it is not as simple as it seems.  We usually read arguments in a vague way, without distinguishing the different premises and without seeing how they fit together.  We evaluate them by gut reaction, relying on uncritical assumptions.  In addition, most arguments are poorly written, so it is difficult even to determine what the conclusion is.  Often, by simply analyzing how an argument functions, we immediately see its flaws or gaps.  The way premises fit together can be very complex.  An argument can have just one premise.  It can have several separate premises, or it can have several premises that are interdependent and together give one reason for the conclusion.  An argument can also have several steps, where some premises are given to support a conclusion, which then functions as a premise for a further conclusion.  Here are some examples:

A) Watching TV is fun and relaxing.  It teaches you about pop culture, and if you don’t watch it, you won’t know what your friends are talking about.  So watch more TV.

 

B) Animals do not have rights.  Only rational beings have rights, and no animals are rational.

 

C) You should study computers, because you can get a job making good money and money is extremely important.  In this world, money brings prestige, security, and, of course, lets you buy what you want.

Argument A gives three separate premises (it’s fun and relaxing; it teaches pop culture; your friends talk about it) for its conclusion (watch more TV).  If you eliminate one of the premises, it would be weaker, but would still be an argument.

Argument B gives two premises (only rational beings have rights; animals are not rational) that if taken together, support the conclusion (animals have no rights).  If one premise is taken alone, it does not support the conclusion.

Argument C is really two arguments.  The first is similar to argument B, giving two interdependent premises (you’ll make money; money is important) to support its conclusion (study computers).  But maybe you don’t accept the premise that money is important.  A second argument is given to support this premise, where three separate premises (prestige, security, buying stuff) support the conclusion (money is important).

Take a moment and reflect on each of these arguments to consider their weaknesses and where they could be strengthened.

Notice that an argument is only as strong as its premises.  These arguments depend on the truth of propositions such as: animals are not rational, money brings prestige, TV is fun and relaxing, etc.  Because premises matter so much, sub-arguments are often given to support the premises, as in example C.  It is difficult if not impossible to absolutely prove your premises.  One can always ask, why should I believe that?  In practice, an argument usually works when the conclusion is based on premises on which everyone involved agrees.  Since the goal of constructing arguments, however, is to discover the truth (not just reach agreement), it is crucial to question assumed premises, even if they are widely assumed.  For example, we might all agree with the proposition “only rational beings have rights,” but when we question this assumed premise, we find it difficult to justify.  Probably we never even thought about it before.  Perhaps the greatest value of analyzing an argument is precisely to reveal propositions we are assuming without justification.  This fault is so common that philosophy is often presented simply as questioning things.

Note also that premises can be good yet present an incomplete picture.  For example, argument C is strong, but incomplete, since while money is important, other factors are important as well, such as enjoying your work and having your work effect the world in certain ways.  Argument A is similarly incomplete, since while TV brings these benefits, other activities might bring more benefits.  So in making or analyzing arguments, one goal is to question assumed premises but another goal is to search for suppressed or ignored premises that give a more complete view.

In practice, the most common way to evaluate arguments is to evaluate the premises.  A second point for evaluation, though, is how the premises relate to the conclusion.  That is, it could be that even if the premises are true and relatively complete, the conclusion is still not proven.  “Logic” focuses on this second issue – how the conclusion follows from the premises.  From this perspective, we can distinguish two kinds of arguments – deductive arguments and inductive arguments.  In brief, a deductive argument is one in which the conclusion follows necessarily from the premises, while an inductive argument is one in which the conclusion follows with more or less probability from the premises.  Note that the distinction has nothing to do with whether or not the premises are true or how we come to know the premises.

Deductive Arguments 

A deductive argument asserts that its premises absolutely prove its conclusion.  For example:

All animals need oxygen.  Cats are animals.  Therefore, all cats need oxygen.

If the two premises are true, then the conclusion must be true.  There are many forms of deductive arguments, but three common ones are a categorical syllogism, a hypothetical syllogism, and a disjunctive syllogism.  A categorical syllogism has at least two premises, each of which places things in categories.  The preceding argument is one example.  Another would be:

All humans are rational.  Some animals are human.  Therefore, some animals are rational.

A hypothetical syllogism takes the form of “if . . .  then . . .”  For example:

A disjunctive syllogism takes the form of “either . . . or . . .”  For example:

Either God exists or life is meaningless.  Life is not meaningless.  Therefore, God exists.

In general, we intuitively recognize whether a deductive argument is good or not, once we have analyzed it into its parts.  Logicians will translate arguments into to symbols in order to make the form even clearer.  The crucial aspect of analyzing a deductive argument is to distinguish between its form and the truth of its premises.  An argument whose form is correct, where the conclusion follows necessarily from the premises, is called valid.  An argument whose form is incorrect, where even if the premises are true the conclusion is not guaranteed, is called invalid.  This distinction is made regarding the form of the argument only, with no regard for the truth of premises.  A second distinction is between a sound argument and an unsound one.  A sound argument is one that is valid and whose premises are true.  Therefore, the conclusion of a sound argument must be true.

Here are some examples to clarify the distinctions:

E) Everyone who cares about the environment always recycles.  She cares about the environment.  Therefore, she always recycles.

This is a valid argument (a hypothetical syllogism), so if the premises are true, the conclusion must be true.  The first premise, however, is probably not true, since there are probably some people who care but don’t always recycle.  Thus the argument is valid but unsound.

F) Everyone who recycles saves resources.  She recycles.  Therefore, she saves resources.

This argument is valid, with the same form as the first (hypothetical syllogism), but its premises are true, so it is valid and sound.  Necessarily, then, its conclusion is true.

G) Everyone who recycles saves resources.  She saves resources.  Therefore, she recycles.

Is this argument valid?  It might seem so, but it is a common mistake in reasoning (called affirming the consequent).  There are many ways that she could save resources without recycling.  For example, she might not use a car yet not recycle.  Thus the premises would be true while the conclusion would be false, which means that the argument must be invalid and unsound..

H) Everyone who cares about the environment recycles.  She recycles.  Therefore she cares about the environment.

In this example we find the same mistake but in addition, the first premise is false.  It is unsound (and invalid).

A good question would be, why care about this distinction?  All that really matters is if the argument is sound or the conclusion is true.  Distinguishing between the form of the argument and the truth of its premises allows us to more clearly see possible mistakes in the argument.  It is a way of focusing our attention.  Also, it can save time.  It is usually easier to judge the form of an argument than to judge the truth of its premises, so before making a complicated investigation of the truth of a premise, first see if the argument is valid.  If it is invalid, it does not matter if the premises are true.

Argument B above is a deductive argument (a categorical syllogism):  Only rational beings have rights.  No animals are rational.  Therefore, no animals have rights.  The argument is valid, so if the premises are true, then the conclusion must be true.

Inductive Arguments

An inductive argument is one in which the premises provide only partial support for the conclusion.  If the premises are true, the conclusion is supported, but not guaranteed.  In general, inductive arguments move from particular cases or instances to a new case.  They thus depend on the similarity between the initial cases and the new case, and they depend on the range of cases used.  Arguments A and C above are inductive arguments, where the conclusions are supported but not guaranteed by the premises, and where the completeness of the premises is at issue.

There are many forms of inductive arguments, but the three basic forms are arguments by analogy, arguments from statistics, and arguments concerning cause and effect.  Arguments by analogy rely on similarity between two cases.  For example:

I took a course with this professor last year and it was good.  You should take his course this quarter, it will be good too.

How does this argument work?  You have two similar cases (courses taught by the same professor).  The argument says that what is true of the first case (it was good) will be true of the second case (it will be good).  The conclusion is only probable.  The crucial point in arguments by analogy is that similarities strengthen them, and differences weaken them.  So, if it was not only the same professor but the same course, then the argument would be stronger.  If it is a very different course, such as an introductory rather than an advanced course, the argument is weaker.  In any case, the argument is never perfect, because there are always some differences (such as the mix of students in the class).  Arguments by analogy are very common and often subtle.  The “War on Drugs” is an excellent example, since the fight against drugs has both similarities and differences with war.  The strength of the analogy depends on what conclusion is being drawn.  For example: In war it is okay to kill some innocent people.  The attempt to fight drug abuse is like a war.  Therefore, it is okay to kill some innocent people to stop drug abuse.

Arguments from statistics are familiar to everyone.  At their best they are only probable:

70% of U.S. citizens support the war in Afghanistan.  He is a U.S. citizen.  Therefore, he supports the war.

At its best, the argument support the conclusion with some probability (70%), but statistics are much more complicated.  We must also know, how many people were asked?  Who were they?  How was the question phrased?  Were alternatives given?  Statistical arguments are notoriously unreliable because these kinds of questions are almost never answered, yet they greatly effect the argument.  For example, statistics about teen opinions are often done in malls, thus limiting the pool to teens who gather in malls.

Arguments concerning cause and effect can achieve close to certainty, but they are inductive and only probable.  Take the following example:

You wake up early in the morning terribly sick.  You call a friend and find she is similarly sick, and you ate dinner together last night, with three other people.  The food at the restaurant must be the cause, you decide.  You call one of the other friends, but he is not sick.  Your argument becomes weaker.  You call the other two and find that of the five who ate together, three are sick.  What could be the cause?  You discuss what each of you ate and find that all three ate the same seafood dish, while the other two did not.  Therefore the seafood caused you to be sick.

This argument is strong, but is still only probable.  Perhaps the three of you ate or drank something else in common, or perhaps it was a flu from a few days earlier.  The argument would be weakened if you found someone else who ate the seafood but did not get sick, and would be strengthened if you found someone unconnected with you who also ate the seafood and got sick.

Fallacies

Fallacies are common mistakes in reasoning.  Awareness of these common errors will help you avoid them in your own arguments and recognize them in the arguments of others.  Countless fallacies have been described and named, but here are some of the most important.  For a while it was common to know them by their Latin names, so I have given some of those in parentheses.

I. Fallacies of Relevance

These are fallacies where the premises are not relevant to the truth of the conclusion.  The premises may or may not be true, but the do not matter for the conclusion.  Here are several well-known fallacies of relevance:

1) Appeal to Inappropriate Authority (Argumentum ad Verecundiam)

In many situations, it is reasonable to appeal to an authority with knowledge in the relevant areas; this kind of argument becomes a fallacy when the authority is inappropriate for the conclusion.  Obvious examples are celebrity spokes-people who recommend foods, products, insurance, and so on.  This fallacy is often less obvious and more dangerous.  A geneticist is not necessarily an appropriate authority to speak on the ethics of genetic engineering.  An economist speaking on international affairs may not by the appropriate authority, if human rights are at issue.

2) Attack on the Person (Argumentum ad Hominem)

This fallacy occurs when one attacks the person making an argument rather than the premises for the argument.  So, if Bill Clinton gave marital advice, and one responded – “That can’t be right, he’s Bill Clinton!” that would be an ad hominem fallacy.  If someone gave an argument against the death penalty, and you responded by saying, “But he’s on death row!” that would be the same fallacy.  An attack on the person can be useful in making us question an argument – an energy policy formulated by energy executives should raise suspicions – and can be used to counter appeals to inappropriate authority.  Nonetheless, it is a fallacy because even a person with bad motives and no qualifications can make a good argument.  The only relevant issue is whether the premises are true and if they support the conclusion.

3) Appeal to the Masses (Argumentum ad Populum)

This is sometimes called an appeal to emotion, and is any attempt to convince someone by appealing to what everyone else thinks or does.  Arguments from “peer pressure” would be a good example.  Arguments which appeal to a group identity fall in this category as well, such as, “if you . . ., then you are not a true American.”

4) Appeal to Pity (Argumentum ad Misericordiam)

The appeal to pity is an attempt to allow feelings to dominate over argument.  Here is one I have heard:: “I need to get an B in this class, or else my parents will be furious.”  This is a fallacy of relevance.

II. Fallacies of Presumption

These are fallacies that include a hidden assumption, that is, they presume part of what they claim to prove.  They often work by setting the terms of an argument in a biased way.

5) Begging the Question (Petitio Principii)

This fallacy uses circular reasoning, where the premise is a rephrasing of the conclusion.  For example, “Teachers should be better paid because they deserve more money.”  That is an obvious example, but often an argument has many premises where one is a confusing restatement of the conclusion.

6) Complex Question

“Are you always such a liar?”  However you answer the question, you confess to being a liar.  The question is thus set up to lead to one conclusion.  A similar case is sometimes called a “false dilemma:” either you love philosophy or don’t understand it.  This is a fallacy because it presents only two options, while there could be many more (you could understand it and dislike it).  This form of the fallacy is common, for example, saying that you have to choose between prosperity and protecting the environment.

7) False Cause (Post Hoc Ergo Propter Hoc)

This fallacy is a poor inductive argument for cause and effect.  One assumes that because one event followed another, that event was caused by the other.  I once found a five dollar bill on the beach, and the next day I found a desperately needed summer job and the next week I found a job teaching in China.  I still have the five dollar bill in my wallet, for “good luck.”  That is an example of this fallacy.

8) Slippery Slope

In this fallacy, an argument is made against something on the threat that it will lead to more and more things; it will start us down a “slippery slope.”  A common example is against gun control: registering or licensing guns is the first step that will lead to restricting gun use more and more, until finally the government takes away our guns.  A slippery slope argument can be good, but it becomes a fallacy when no reasons are given for the slippery slope.  That is, if one could make an argument about why licensing guns will lead to taking them away, then it would be a good argument.  It becomes a fallacy when the slope is assumed.

9) Straw Man

A common fallacy in which a caricature of an opposing argument is given and then disproved.  One of the most effective ways to make an argument is to explain and address opposing arguments.  This fallacy works by giving the appearance of doing this, while really only addressing a weakened and simplified opposing argument.

III. Fallacies of Ambiguity

These fallacies depend on unclear writing, where the meanings of certain terms shift in different parts of the argument.

10) Equivocation

This fallacy occurs when the same word or phrase is used in different senses in the same argument.  This fallacy occurs most often with vague, emotionally charged words, such as freedom, justice, democracy, etc.  It is avoided by clearly defining terms.

11) Composition

The fallacy of composition happens when we reason from the attributes of the parts to attributes of the whole, or attributes of individuals to attributes of the group.  If we said every part of a car is well made, therefore the car is well made, we would have this fallacy, since the parts might all be good but put together poorly.  A less obvious example would be when attributes of employees (that they are kind people) are attributed to a corporation (that it acts kindly).

12) Division

The fallacy of division is the reverse of the fallacy of composition, where we reason from attributes of the whole to attributes of the parts.