| Basic Logic |
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Evaluating Arguments:
Some Helpful Concepts
. Jeremy Anderson Contents: 1. Defining
"argument" and related terms
2. The two types of arguments: inductive and deductive 3. Evaluating inductive arguments 4. Deductive arguments 5. Evaluating deductive arguments 6. Further reading 1. Defining the term "argument" The word "argument" has different meanings in different contexts. Often it means "a verbal dispute," as in "Joe and Ray had an argument over money." In mathematics it can mean "an independent variable in a function." In literature it may refer to the plot of a play or book. In philosophy, we use "argument" somewhat differently. Philosophers, like other people, try to get you to believe things: that animals have (or don't have) rights, that we should be virtuous, that the universe consists of minds and ideas and nothing else, and on and on. To get you to believe something, philosophers give you reasons--we call them premises: some statement or statements that are supposed to show you why some other statement (called the conclusion) is true or likely true. Premises and conclusion together make an argument. To give you a precise definition (which you should memorize and remember forever after): In philosophy, an argument is a set of two or more
statements. One of the statements is called the conclusion, and the
other(s) are called premises.
The premises of
an argument are supposed to support, or give us
reason(s) to believe, the conclusion. That is, premises are
supposed to show the conclusion is true or likely true.
(Whether the premises succeed
in showing the conclusion is true or likely true
is another story. But even if they try to and fail, the
set of statements is still an argument.)[1]
Sometimes in philosophical discussions, "argument" refers only to the premises, as in "You think X? What's your argument for that?" But usually "argument" refers to the premises and the conclusion they're supposed support. Below you will find several examples of arguments with their premises and conclusions neatly labeled. Very often, however, arguments do not come in such plain form. To understand philosophy you must find the arguments in what people say and write. You must, in other words, identify what it is they want you to believe, and what reasons they give you to believe it. It's not that hard to do, but it takes practice. As you read philosophical (and other) works, just keep asking yourself what the author is trying to persuade you of. What is the main point being made? And what reasons are being offered in favor of it? Once you find the arguments, you must then evaluate them; that is, check and see whether they're good. The point of this reading is to help you identify the two main types of arguments--inductive and deductive--and give you tips on evaluating them. Because most of the arguments we will encounter in this course are deductive, we will focus most on how to evaluate deductive arguments. 2. The two types of arguments: inductive and deductive To evaluate an argument, it is helpful to notice is what type of argument it is. There are two main types of arguments: inductive and deductive. First we'll take a quick look at inductive arguments and how to evaluate them, and then move on to deductive arguments. In inductive arguments,
the premises, at best, show the conclusion is likely
(or probablyj) true.
Here's an example of an inductive argument: 1 (premise): This crow is black.
2 (premise): That crow is black. 3 (premise): Every crow I've ever seen is black. 4 (conclusion): Therefore, all crows are black. Notice that the premises of this argument do not prove that its conclusion is true. Maybe I've only seen one flock of crows in my whole life! This is a weak inductive argument. An inductive argument is
weak when its
premises fail to show its conclusion is likely (or
probably) true.
Also notice that we can strengthen the argument by adding more premises, like this: 1. This crow is black.
2. That crow is black. 3. Every crow I've ever seen is black. 4. I've traveled around the world examining crows and only found black ones. 5. I've asked everyone I've met, and they've all reported that all the crows they've seen are black. 6. I've read every book ever published about crows, and they all say crows are always black. 7. So, all crows are black. If these premises are true, the conclusion is very likely true. So this is a strong inductive argument. An inductive argument is
strong when
its premises show its conclusion is likely (or
probably) true.
But still the conclusion is not absolutely guaranteed to be true. We must admit that even if all the premises are true it's still possible that somewhere there was a white crow, or a yellow one, that I never heard about. The conclusion here is at best probably true. There is a common misconception about inductive arguments which I would like you to avoid. Notice that the inductive arguments given above both argue "from specific to general," that is, they derive a general claim (that all crows are black) from specific examples (this crow is black, that one is black, etc.). Since many inductive arguments work like this, people are apt to think that this is a defining feature of inductive arguments. However, this is not true. Here is an example of an inductive argument that does not go from specific to general: 1. It has snowed in Massachusetts every
December in recorded history.
2. Therefore, it will snow in Massachusetts this coming December. This is still an inductive argument because, given the premise, the conclusion is still at best only probably true. [2] 3. Evaluating inductive arguments Since they don't even try to guarantee that their conclusions are true, it's pointless to criticize an inductive argument by saying, "That conclusion's not necessarily true!" That's something we just take for granted in inductive reasoning. Rather, we need to consider two things: First, we need to ask whether the premises are true. If I was lying about having traveled around the world, for example, our confidence in the conclusion may be undermined. Second, we need to consider how strongly the premises support the conclusion even if they're all true. There's often no absolutely certain way to figure this out, but we can make some rough judgments; for example, the second version of the crow argument is much stronger than the first because if premises 1-6 are all true there is less chance the conclusion is false than if just premises 1-3 are. There is a large literature on inductive arguments, and deservedly so: most of the judgments we make in our ordinary lives can be characterized as judgments based on induction. When you leave your umbrella at home because it is sunny when you go out, you are reasoning that rain is improbable, not impossible. Because the conclusions of inductions are never completely certain, philosophers very often avoid using inductive arguments and instead try to make deductive arguments to persuade us of things. 4. Deductive arguments While inductive arguments merely try to show that something is probably true, deductive arguments, at best, show their conclusions are true, not just likely true. This is a much higher standard of persuasion, and difficult to meet. But it's something many philosophers aspire to, and understandably so: no matter how strong an inductive argument you make, you must always admit that there is some reason to doubt its conclusion. But if you can make a strong (that is, "sound") deductive argument, you can set aside your doubts. The conclusion is true, period. Here is a very simple deductive argument: 1. All philosophers are nerds.
2. Jeremy is a philosopher. 3. Therefore, Jeremy is a nerd. We can see that the premises don't just make the conclusion probably true; they make it true. Since the point of presenting an argument is to persuade someone that something is true, deductive arguments can be very helpful. That's why many philosophers (and non-philosophers) try to give deductive arguments to try to persuade you of things. Just as it is often said, wrongly, of inductive arguments that they go from specific to general, it is often said--wrongly--of deductive arguments that they go "from general to specific," that is, that they all assert some general principle (like "All humans are mortal") and then apply it to some specific case (like "Jeremy is a human"), as the above example does. Even an introductory textbook I used to use, Philosophy Made Simple, makes these claims.[3] Many deductive arguments do argue from general to specific, but not all. Consider the following example: 1. Minnie is here.
2. Mickey is here. 3. Minnie is a mouse. 4. Mickey is another mouse. 5. Therefore, two mice are here. Even though it only contains specific claims, this is still a deductive argument because it tries to establish its conclusion as true, not just probably true. For that matter, deductive arguments can go "from general to general," like this one: 1. All cats are felines.
2. All felines are mammals. 3. All mammals are animals. 4. So, all cats are animals. The point is that specificity or generality has nothing to do with whether an argument is inductive or deductive. If an argument only tries to establish that its conclusion is probably true, it is inductive. If it tries to prove that its conclusion is true, it is deductive. 5. Evaluating deductive arguments Many arguments are faulty. Some arguments are so obviously bad that you reject them at first sight. But other faulty arguments may look quite appealing, and you may be fooled by them if you're not careful. So it's good to have some tools with which to evaluate arguments. To evaluate deductive arguments it's very handy to understand two concepts philosophers use: validity and soundness. First, let's explain validity. Just as the word "argument" has a technical meaning in philosophy which is different from its meaning in ordinary conversation, in philosophy we use the term "valid" in a special way which you must learn and keep in mind. In ordinary conversation, we tend to say that something is valid when we think it's true, or right, or reasonable; it's a vague term of approval. But in philosophy, "valid" means something very different, and very precise. Look again at the "Jeremy is mortal" argument: 1. All philosophers are nerds.
2. Jeremy is a philosopher. 3. Therefore, Jeremy is a nerd. It has a certain structure or pattern to it. We can begin to see that pattern by looking at similar arguments. For example:
1. All A's are B.
2. X is an A. 2. Therefore, X is B. We can see that no matter what we substitute for "A," "B," and "X," the conclusion will still be logically entailed by the premises. This makes the argument's form valid. Another way to express validity is this: An argument is valid if its form is such that its
conclusion would have to be true if the premises
were true. (Or: its conclusion could not be false if its
premises were true.)
Note the word "if" in the previous sentence. It means that a valid argument does not necessarily have true premises or a true conclusion. In philosophy, saying "That's a valid argument" doesn't tell you anything about whether its premises or conclusion are true. It only tells you that if the premises were true, the conclusion would be true, too. So keep in mind that an argument can be valid even if its premises and conclusion are false. The following argument is perfectly valid:
Even though the premises and conclusion are all false (I hope), the conclusion is still logically supported by the premises, such that if the premises were true, the conclusion would also be true. Thus, this argument is valid even though every part of it is false. It will remain valid no matter what statements are substituted for A, B, and C. Try this: think of three ridiculous claims and substitute them for A, B, and C in the argument above. Write the resulting argument down. Now suppose for a moment that the premises in the argument are in fact true. Can you see that the conclusion would then have to be true? If so, you're getting a sense of what validity is. Given the definition of validity, we can easily figure out what invalidity is: An argument is invalid when even
if the premises are true, the conclusion could be false.
For example, look at this argument:
It may appear that, given the premises, the conclusion must be true—until you realize there are many different places for somebody to get vanilla ice cream. I could have gotten it at the store, at a friend's house, or made it at home. Notice that the same sort of problem will persist no matter what we subsitute for "P" and "Q" here: even if the premises are both true, the conclusion might not be. Arguments like this one are invalid. OK, so now you have some idea what an argument's form is, and you know that validity has to do with an argument's form. And you've noticed that validity—good form—isn't enough, by itself, for a deductive argument to prove its conclusion is true. Just to emphasize that point, let's consider one last example: 1. Jeremy's brother-in-law has bright purple
hair.
2. President Bush is Jeremy's only brother-in-law. 3. So, President Bush has bright purple hair. This argument is valid; we can see that if the premises were true the conclusion would also be true. But we know that President Bush does not have bright purple hair, so something must be wrong: one or more of the premises must be false. In this example, both premises happen to be false: I have no brother-in-law at all, let alone President Bush. On the other hand: An argument is sound when it is
valid and its
premises are all true.
An argument is unsound when it is invalid or at least one of its premises are false, or both. (However, since we already have the term "invalid" for when an argument is invalid, we generally use "unsound" to mean it has at least one false premise.) Just to keep things clear, let's see how deduction, validity, and soundness are related to each other.
1. Is
the argument valid?
2. Are the premises true? If the answer to both questions is "Yes," then the argument is sound and you have very strong reason to believe the conclusion is true. In fact, if the argument is sound it would be irrational for you to deny the conclusion. But if the answer is "No" to either question, the argument is unsound and you have reason to be skeptical about whether the conclusion is true. Note that I said "you have reason to be skeptical" (that is, you may reserve judgment) about the conclusion--not that you should reject it as false. Why? Consider the following example: 1. Circles are round.
2. The moon is made of green cheese. 3. Therefore, the earth is round. This argument's form is invalid; its premises have no logical connection to the conclusion. And premise 2 is false: the moon isn't made of green cheese; we all know it's made of feta cheese, which is why it's white. Yet even so, the conclusion is true. So some caution is in order: even if an argument is unsound (that is, even if its premises don't give you good reason to believe its conclusion), the conclusion might still be true. Even if the reasons given for a conclusion are bad, there may be good reasons for that conclusion lurking out there somewhere. 6. Further reading There are lots of books on logic available via the library on topics ranging from the very elementary to highly technical explanations of its set-theoretical foundations. If you just want some more explanation of basic matters, I recommend two articles in the Internet Encyclopedia of Philosophy: "Argument" and "Deductive and Inductive Arguments." One very good way to get your brain in gear for critical thinking is to look at examples of bad arguments. The Internet Encyclopedia of Philosophy’s discussion, “Fallacies,” has a scholarly discussion of logical fallacy which you may or may not find useful but also a nice bunch of examples of fallacies. A more accessible and fun, though less complete, discussion of fallacies is here at YourLogicalFallacyIs.com. More examples may be found at these sources, as well as many others that are easy to find:
____________________________ Notes 1. This definition is paraphrased from Paul Teller's A Modern Formal Logic Primer, Volume 1 (Sentence Logic), Englewood Cliffs, NJ: Prentice Hall, 1989, pp. 1-2. The complete text is available free online here on Teller's website. 2. This example--as well as the general point made here about inductive arguments--comes from the article "Deductive and Inductive Arguments" in the Internet Encyclopedia of Philosophy. 3. The authors of Philosophy Made Simple, Richard Popkin and Avrum Stroll, say that "while deductive logic is concerned with inferences from the general to the particular...inductive logic is concerned with inferences from the particular to the general" (Philosophy Made Simple, 2nd ed., NY: Doubleday, 1993, p. 239). I hope the above makes clear why I disagree with them. |
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