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Matthew J. This is an introductory textbook in logic and critical thinking. Both logic and critical thinking centrally involve the analysis and assessment of arguments. In one sense of the word, an argument is a heated exchange of differing views as in the following: Sally: Abortion is morally wrong and those who think otherwise are seeking to justify murder! Bob: Abortion is not morally wrong and those who think so are right-wing bigots who are seeking to impose their narrow-minded views on all the rest of us!

Sally and Bob are having an argument in this exchange. That is, they are each expressing conflicting views in a heated manner. For example: Sally: Abortion is morally wrong because it is wrong to take the life of an innocent human being, and a fetus is an innocent human being. In this example Sally has given an argument against the moral permissibility of abortion. That is, she has given us a reason for thinking that abortion is morally wrong.

We can and should be more precise about our definition of an argument. But before we can do that, we need to introduce some further terminology that we will use in our definition. But the reason for thinking the conclusion is true is what we call the premise.

So we have two parts of an argument: the premise and the conclusion. Typically, a conclusion will be supported by two or more premises. Both premises and conclusions are statements. Because it makes sense to inquire whether it is true or false.

In this case, it happens to be true. But a sentence is still a statement even if it is false. For example, the sentence, The Yangtze is a river in Japan is still a statement; it is just a false statement the Yangtze River is in China. So, to reiterate: all arguments are composed of premises and conclusions, which are both types of statements.

The premises of the argument provide a reason for thinking that the conclusion is true. And arguments typically involve more than one premise. A standard way of capturing the structure of an argument is by numbering the premises and conclusion. We could capture the structure of that argument like this: 1. It is morally wrong to take the life of an innocent human being 2. A fetus is an innocent human being 3. This is what we will call standard argument form. We can now give a more precise definition of an argument.

An argument is a set of statements, some of which the premises attempt to provide a reason for thinking that some other statement the conclusion is true. For example, I have just given you this argument not in an attempt to convince you that abortion is morally wrong, but as an illustration of what an argument is. Later on in this chapter and in this book we will learn some techniques of evaluating arguments, but for now the goal is to learn to identify an argument, including its premises and conclusion s.

It is important to be able to identify arguments and understand their structure, whether or not you agree with conclusion of the argument. In the next section I will provide some techniques for being able to identify arguments.

Exercise 1: Which of the following sentences are statements and which are not? No one understands me but you. Alligators are on average larger than crocodiles. Is an alligator a reptile or a mammal? An alligator is either a reptile or a mammal.

You may kill any reptile you see in the house. East Africans are not the best distance runners. Obama is not a Democrat. Some humans have wings. Some things with wings cannot fly. Was Obama born in Kenya or Hawaii? Oh no! A grizzly bear! Meet me in St. We met in St. Louis yesterday. I do not want to meet a grizzly bear in the wild. If so, then there is an argument present. Another thing that can help in identifying arguments is knowing certain key words or phrases that are premise indicators or conclusion indicators.

Here is another example: I know that the student plagiarized since I found the exact same sentences on a website and the website was published more than a year before the student wrote the paper. In addition to premise indicators, there are also conclusion indicators. Conclusion indicators mark that what follows is the conclusion of an argument. Here is another example of a conclusion indicator: A poll administered by Gallup a respected polling company showed candidate x to be substantially behind candidate y with only a week left before the vote, therefore candidate y will probably not win the election.

Table 1 contains a list of some common premise and conclusion indicators: Premise indicators Conclusion indicators since therefore because so for hence as thus given that implies that seeing that consequently for the reason that it follows that is shown by the fact that we may conclude that Although these words and phrases can be used to identify the premises and conclusions of arguments, they are not failsafe methods of doing so.

Just because a sentence contains them does not mean that you are dealing with an argument. This can easily be shown by examples like these: I have been running competitively since I am so happy to have finally finished that class. Rather, we have to rely on our understanding of the English sentence in order to determine whether an argument is being made or not.

Thus, the best way to determine whether an argument is present is by asking the question: Is there a statement that someone is trying to establish as true or explain why it is true by basing it on some other statement? But arguments always require at least two separate statements—one premise and one conclusion, so it cannot possibly be an argument.

A grammatical conjunction is a word that connects two separate statements. So, if a word or term is truly being used as a premise or conclusion indicator, it must connect two separate statements.

Simply substitute another word or phrase from the list of premise indicators or conclusion indicators and see if the resulting sentence still makes sense.

If it does, then you are probably dealing with an argument. Exercise 2: Which of the following are arguments? If it is an argument, identify the conclusion of the argument. I have been wrangling cattle since before you were old enough to tie your own shoes. First I washed the dishes and then I dried them. Are you seeing that rhinoceros over there? It is huge! The fact that obesity has become a problem in the U. What Bob told you is not the real reason that he missed his plane to Denver.

No one who has ever gotten frostbite while climbing K2 has survived to tell about it, therefore no one ever will. Many times the goal of giving an argument is simply to establish that the conclusion is true. For example, when I am trying to convince someone that obesity rates are rising in the U. The studies I cite would function as premises for the conclusion that obesity rates are rising. For example: We know that obesity is on the rise in the U.

We could put this simple argument into standard form like this: 1. Therefore, obesity is on the rise in the U. The standard form argument clearly distinguishes the premise from the conclusion and shows how the conclusion is supposed to be supported by the evidence offered in the premise. Again, the goal of this simple argument would be to convince someone that the conclusion is true.

However, sometimes we already know that a statement or claim is true and we are trying to establish why it is true rather than that it is true. An argument that attempts to show why its conclusion is true is an explanation. Contrast the previous example with the following: The reason that the rate of obesity is on the rise in the U.

Since eating foods high in sugar and low in fiber triggers the insulin system to start storing those calories as fat, it follows that people who consume foods high in sugar and low in fiber will tend to store more of the calories consumed as fat.

Unlike the earlier example, here it is taken for granted that obesity is on the rise in the U. That is the claim whose truth we are trying to explain. We can put the obesity explanation into standard form just like any other argument. In order to do this, I will make some paraphrases of the premises and conclusion of the argument for more on how to do this, see section 1. Over the past four decades, Americans have increasingly consumed foods high in sugar and low in fiber.

Consuming foods high in sugar and low in fat triggers the insulin system to start storing those calories as fat. When people store more calories as fat, they tend to become obese. Therefore, the rate of obesity is on the rise in the U. Notice that in this explanation the premises attempt to give a reason for why the conclusion is true, rather than a reason for thinking that the conclusion is true. That is, in an explanation we assume that what we are trying to explain i.

In this case, the premises are supposed to show why we should expect or predict that the conclusion is true. Explanations often give us an understanding of why the conclusion is true.

We can think of explanations as a type of argument, we just have to distinguish two different types of argument: those that attempt to establish that their conclusion is true arguments , and those that attempt to establish why their conclusion is true explanations.

Exercise 3: Which of the following is an explanation and which is an argument? Identify the main conclusion of each argument or explanation. Remember if the premise s seems to be establishing that the conclusion is true, it is an argument, but if the premise s seems to be establishing why the conclusion is true, it is an explanation.

Wanda rode the bus today because her car was in the shop. Either Bob or Henry rode the bus to work today. Therefore, it was Bob. The reason some people with schizophrenia hear voices in their head is that the cognitive mechanism that monitors their own self-talk is malfunctioning and they attribute their own self-talk to some external source.

Fracking should be allowed because, although it does involve some environmental risk, it reduces our dependence on foreign oil and there is much greater harm to the environment due to foreign oil drilling than there is due to fracking. Wanda could not have ridden the bus today because today is a city- wide holiday and the bus service is not operating. The Tigers lost their star pitcher due to injury over the weekend, therefore the Tigers will not win their game against the Pirates.

No one living in Pompeii could have escaped before the lava from Mt. Vesuvius hit. The reason is simple: the lava was flowing too fast and there was nowhere to go to escape it in time. However, very often arguments and explanations have a more complex structure than just a few premises that directly support the conclusion.

For example, consider the following argument: No one living in Pompeii could have survived the eruption of Mt. Therefore, this account of the eruption, which claims to have been written by an eyewitness living in Pompeii, was not actually written by an eyewitness. This account of the eruption of Mt. Vesuvius was not actually written by an eyewitness.

Rather, some statement provides evidence directly for the main conclusion, but that statement itself is supported by another statement. To determine the structure of an argument, we must determine which statements support which.

We can use our premise and conclusion indicators to help with this. The next question we must answer is: which statement most directly supports A? What most directly supports A is: B. No one living in Pompeii could have survived the eruption of Mt. However, there is also a reason offered in support of B. That reason is that: C. The lava from Mt. Vesuvius was flowing too fast and there was nowhere for someone living in Pompeii to go in order to escape it in time. So the main conclusion A is directly supported by B, and B is supported by C.

Since B acts as a premise for the main conclusion but is also itself the conclusion of further premises, we refer to B as an intermediate conclusion. The important thing to recognize here is that one and the same statement can act as both a premise and a conclusion.

Statement B is a premise that supports the main conclusion A , but it is also itself a conclusion that follows from C. Here is how we would put this complex argument into standard form using numbers this time, as we always do when putting an argument into standard form : 1. Therefore, no one living in Pompeii could have survived the eruption of Mt.

Therefore, this account of the eruption of Mt. It may also help to think about the structure of an argument spatially, as figure 1 shows: The main argument here from 2 to 3 contains a subargument, in this case the argument from 1 to 2. In general, the main argument is simply the argument whose premises directly support the main conclusion, whereas a subargument is an argument that provides indirect support for the main conclusion by supporting one of the premises of the main argument.

You can always add further subarguments to the overall structure of an argument by providing evidence that supports one of the unsupported premises. Another type of structure that arguments can have is when two or more premises provide direct but independent support for the conclusion. Moreover, our coworker, Bob, who works in accounting, saw her riding towards work at am. Here is the argument in standard form: 1. Wanda arrived at work with her right pant leg rolled up.

Cyclists often roll up their right pant leg. Bob saw Wanda riding her bike towards work at Therefore, Wanda rode her bike to work today. In this case, in order to avoid any ambiguity, I have noted that the support for the conclusion comes independently from statements 1 and 2, on the one hand, and from statement 3, on the other hand.

It is important to point out that an argument or subargument can be supported by one or more premises. We see this in the present argument since the conclusion 4 is supported jointly by 1 and 2, and singly by 3.

As before, we can represent the structure of this argument spatially, as figure 2 shows: There are endless different argument structures that can be generated from these few simple patterns. At this point, it is important to understand that arguments can have these different structures and that some arguments will be longer and more complex than others.

Even so, it may help to remember that any argument structure ultimately traces back to some combination of these. Exercise 4: Write the following arguments in standard form and show how the argument is structured using a diagram like the ones I have used in this section. There is nothing wrong with prostitution because there is nothing wrong with consensual sexual and economic interactions between adults.

Prostitution is wrong because it involves women who have typically been sexually abused as children. We know that most of these women have been abused from multiple surveys done with women who have worked in prostitution and that show a high percentage of self-reported sexual abuse as children. There was someone in this cabin recently because there was warm water in the tea kettle and because there was wood still smoldering in the fireplace.

Therefore, there must be someone else in these woods. The train was late because it had to take a longer, alternate route since the bridge was out. Israel is not safe if Iran gets nuclear missiles since Iran has threatened multiple times to destroy Israel and if Iran had nuclear missiles it would be able to carry out this threat. Moreover, since Iran has been developing enriched uranium, they have the key component needed for nuclear weapons—every other part of the process of building a nuclear weapon is simple compared to that.

Therefore, Israel is not safe. Since all professional hockey players are missing front teeth and Martin is a professional hockey player, it follows that Martin is missing front teeth. And since almost all professional athletes who are missing their front teeth have false teeth, it follows that Martin probably has false teeth. Anyone who eats the crab rangoon at China Food restaurant will probably have stomach troubles afterward.

It has happened to me every time, which is why it will probably happen to other people as well. Since Bob ate the crab rangoon at China Food restaurant, he will probably have stomach troubles afterward.

Albert and Caroline like to go for runs in the afternoon in Hyde Park. Since Albert never runs alone, we know that any time Albert is running, Caroline is running too. But since Albert looks like he has just run since he is panting hard , it follows that Caroline must have ran too. Paraphrases of premises or conclusions are sometimes needed in order to make the standard form argument as clear as possible.

A paraphrase is the use of different words to capture the same idea in a clearer way. There will always be multiple ways of paraphrasing premises and conclusions and this means that there will never be just one way of putting an argument into standard form. In order to paraphrase well, you will have to rely on your understanding of English to come up with what you think is the best way of capturing the essence of the argument.

Again, typically there is no single right way to do this, although there are certainly better and worse ways of doing it. What is the conclusion of this argument? Think about it before reading on. This statement seems to capture the essence of the main conclusion in the above argument. The premises of the argument would be: 1. So here is the reconstructed argument in standard form: 1. To illustrate this, I will give a second way that one could accurately capture this argument in standard form.

Here is another way of expressing the conclusion: We do not know that Jeremy killed Tim. That is clearly what the above argument is trying to ultimately establish and it is a much simpler in some ways conclusion than my first way of paraphrasing the conclusion. However, it also takes more liberties in interpreting the argument than my original paraphrase.

So how shall I paraphrase the premises that support this conclusion? Here is another way of paraphrasing the premises and putting the argument into standard form: 1. Therefore, we do not know that Jeremy killed Tim.

I have taken quite a few liberties in interpreting and paraphrasing this argument, but what I have tried to do is to get down to the most essential logic of the original argument. The paraphrases of the premises I have used are quite different from the wording that occurs in the original paragraph. Nonetheless, this reconstruction seems to get at the essence of the logic of the original argument.

As long as your paraphrases help you to do that, they are good paraphrases. Being able to reconstruct arguments like this takes many years of practice in order to do it well, and much of the material that we will learn later in the text will help you to better understand how to capture an argument in standard form, but for now it is important to recognize that there is never only one way of correctly capturing the standard form of an argument. And the reason for this is that there are multiple, equally good, ways of paraphrasing the premises and conclusion of an argument.

Unfortunately, there is no simple way to answer this question. The only answer is that you must rely on your mastery and understanding of English in order to determine for yourself whether the paraphrase is a good one or not.

Validity So far we have discussed what arguments are and how to determine their structure, including how to reconstruct arguments in standard form. But we have not yet discussed what makes an argument good or bad.