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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. The central concept that you will learn in logic is the concept of validity. Validity relates to how well the premises support the conclusion, and it is the golden standard that every argument should aim for.
A valid argument is an argument whose conclusion cannot possibly be false, assuming that the premises are true. Another way of putting this is as a conditional statement: A valid argument is an argument in which if the premises are true, the conclusion must be true. Here is an example of a valid argument: 1. Violet is a dog 2. All that matters for validity is whether the conclusion follows from the premise.
And we can see that the conclusion, Violet is a mammal, does seem to follow from the premise, Violet is a dog. That is, given the truth of the premise, the conclusion has to be true. We can illustrate this with another example, where the premises are clearly false: 1.
Everyone born in France can speak French 2. Barack Obama was born in France 3. Therefore, Barack Obama can speak French from This is a valid argument. Because when we assume the truth of the premises everyone born in France can speak French, Barack Obama was born in France the conclusion Barack Obama can speak French must be true. Notice that this is so even though none of these statements is actually true. So we have a valid argument even though neither the premises nor the conclusion is actually true.
That may sound strange, but if you understand the concept of validity, it is not strange at all. Remember: validity describes the relationship between the premises and conclusion, and it means that the premises imply the conclusion, whether or not that conclusion is true. George was President of the United States 2. Therefore, George was elected President of the United States from 1 This argument is invalid because it is possible for the premise to be true and yet the conclusion false.
Here is a counterexample to the argument. In other words, it is possible for the premise of the argument to be true and yet the conclusion false. And this means that the argument is invalid. If an argument is invalid it will always be possible to construct a counterexample to show that it is invalid as I have done with the Gerald Ford scenario. A counterexample is simply a description of a scenario in which the premises of the argument are all true while the conclusion of the argument is false.
If you can construct a counterexample to an argument, the argument is invalid. To apply the informal test of validity ask yourself whether you can imagine a world in which all the premises are true and yet the conclusion is false. If you can imagine such a world, then the argument is invalid. If you cannot imagine such a world, then the argument is valid. It will help to better understand the concept of validity by applying the informal test of validity to some sample arguments.
Joan jumped out of an airplane without a parachute 2. Therefore, Joan fell to her death from 1 To apply the informal test of validity we have to ask whether it is possible to imagine a scenario in which the premise is true and yet the conclusion is false if so, the argument is invalid.
So, can we imagine a world in which someone jumped out of an airplane without a parachute and yet did not fall to her death? Think about it carefully before reading on. As we will see, applying the informal test of validity takes some creativity, but it seems clearly possible that Joan could jump out of an airplane without a parachute and not die—she could be perfectly fine, in fact.
All we have to imagine is that the airplane was not operating and in fact was on the ground when Joan jumped out of it. If that were the case, it would be a true that Joan jumped out of an airplane without a parachute and yet b false that Joan fell to her death. Thus, since it is possible to imagine a scenario in which the premise is true and yet the conclusion is false, the argument is invalid. Joan jumped out of an airplane traveling mph at a height of 10, ft without a parachute 2.
Joan fell to her death from 1 Is this argument valid? You might think so since you might think that anyone who did such a thing would surely die. But is it possible to not die in the scenario described by the premise? For example, maybe someone else who was wearing a parachute jumped out of the plane after them, caught them and attached the parachute-less person to them, and then pulled the ripcord and they both landed on the ground safe and sound.
Or maybe Joan was performing a stunt and landed in a giant net that had been set up for that purpose. Or maybe she was just one of those people who, although they did fall to the ground, happened to survive it has happened before. All of these scenarios are consistent with the information in the first premise being true and also consistent with the conclusion being false. Thus, again, any of these counterexamples show that this argument is invalid. Notice that it is also possible that the scenario described in the premises ends with Joan falling to her death.
And that means that the argument is not valid i. Obama is President of the United States. Kenya is not in the United States. Therefore, Obama was not born in Kenya from In order to apply the informal test of validity, we have to ask whether we can imagine a scenario in which the premises are both true and yet the conclusion is false. Can you imagine such a scenario? You cannot. The reason is that if you are imagining that it is a true that a person can be President of the United States only if they were born in the United States, b true that Obama is president and c true that Kenya is not in the U.
Thus we know that on the assumption of the truth of the premises, the conclusion must be true. And that means the argument is valid. In this example, however, premises 1, 2, and 3 are not only assumed to be true but are actually true. However, as we have already seen, the validity of an argument does not depend on its premises actually being true. Here is another example of a valid argument to illustrate that point. A person can be President of the United States only if they were born in Kenya 2.
Obama is President of the United States 3. Therefore, Obama was born in Kenya from Clearly, the first premise of this argument is false. And this means that the argument is valid. We cannot imagine a scenario in which the premises of the argument are true and yet the conclusion is false.
Rather, validity depends only on the logical relationship between the premises and the conclusion. In the next section we will address this topic. Exercise 5: Determine whether or not the following arguments are valid by using the informal test of validity. If the argument is invalid, provide a counterexample. Katie is a human being. Therefore, Katie is smarter than a chimpanzee. Bob is a fireman. Therefore, Bob has put out fires. Gerald is a mathematics professor. Therefore, Gerald knows how to teach mathematics.
Monica is a French teacher. Therefore, Monica knows how to teach French. Bob is taller than Susan. Susan is taller than Frankie. Therefore, Bob is taller than Frankie. Craig loves Linda. Linda loves Monique. Therefore, Craig loves Monique. Orel Hershizer is a Christian. Therefore, Orel Hershizer communicates with God. All Muslims pray to Allah. Muhammad is a Muslim. Therefore, Muhammad prays to Allah. Some protozoa are predators. No protozoa are animals. Therefore, some predators are not animals.
Charlie only barks when he hears a burglar outside. Charlie is barking. Therefore, there must be a burglar outside. Soundness is defined in terms of validity, so since we have already defined validity, we can now rely on it to define soundness. A sound argument is a valid argument that has all true premises. That means that the conclusion of a sound argument will always be true.
But if the premises are actually true, as they are in a sound argument, then since all sound arguments are valid, we know that the conclusion of a sound argument is true. Compare the last two Obama examples from the previous section. While the first argument was sound, the second argument was not sound, although it was valid. The relationship between soundness and validity is easy to specify: all sound arguments are valid arguments, but not all valid arguments are sound arguments.
Although soundness is what any argument should aim for, we will not be talking much about soundness in this book. The reason for this is that the only difference between a valid argument and a sound argument is that a sound argument has all true premises. But how do we determine whether the premises of an argument are actually true? Well, there are lots of ways to do that, including using Google to look up an answer, studying the relevant subjects in school, consulting experts on the relevant topics, and so on.
But none of these activities have anything to do with logic, per se. The relevant disciplines to consult if you want to know whether a particular statement is true is almost never logic! Since this is a logic textbook, however, it is best to leave the question of what is empirically true or false to the relevant disciplines that study those topics.
And that is why the issue of soundness, while crucial for any good argument, is outside the purview of logic. For a deductive argument to fail to do this is for it to fail as a deductive argument. Tweets is a healthy, normally functioning bird 2. Most healthy, normally functioning birds fly 3. Therefore, Tweets probably flies Given the information provided by the premises, the conclusion does seem to be well supported. That is, the premises do give us a strong reason for accepting the conclusion.
This is true even though we can imagine a scenario in which the premises are true and yet the conclusion is false. For example, suppose that we added the following premise: Tweets is 6 ft tall and can run 30 mph.
Were we to add that premise, the conclusion would no longer be supported by the premises, since any bird that is 6 ft tall and can run 30 mph, is not a kind of bird that can fly. That information leads us to believe that Tweets is an ostrich or emu, which are not kinds of birds that can fly. As this example shows, inductive arguments are defeasible arguments since by adding further information or premises to the argument, we can overturn defeat the verdict that the conclusion is well-supported by the premises.
Inductive arguments whose premises give us a strong, even if defeasible, reason for accepting the conclusion are called, unsurprisingly, strong inductive arguments. In contrast, an inductive argument that does not provide a strong reason for accepting the conclusion are called weak inductive arguments. Suppose that instead of saying that most birds fly, premise 2 said that all birds fly. Tweets is a healthy, normally function bird. All healthy, normally functioning birds can fly.
Therefore, Tweets can fly. This is true even if we add that Tweets is 6 ft tall because then what we have to imagine in applying our informal test of validity is a world in which all birds, including those that are 6 ft tall and can run 30 mph, can fly.
Although inductive arguments are an important class of argument that are commonly used every day in many contexts, logic texts tend not to spend as much time with them since we have no agreed upon standard of evaluating them.
In contrast, there is an agreed upon standard of evaluation of deductive arguments. We have already seen what that is; it is the concept of validity. In chapter 2 we will learn some precise, formal methods of evaluating deductive arguments. There are no such agreed upon formal methods of evaluation for inductive arguments.
This is an area of ongoing research in philosophy. In chapter 3 we will revisit inductive arguments and consider some ways to evaluate inductive arguments. In such a case, we can supply the premise s needed in order so make the argument valid. Making missing premises explicit is a central part of reconstructing arguments in standard form. We have already dealt in part with this in the section on paraphrasing, but now that we have introduced the concept of validity, we have a useful tool for knowing when to supply missing premises in our reconstruction of an argument.
In some cases, the missing premise will be fairly obvious, as in the following: Gary is a convicted sex-offender, so Gary is not allowed to work with children. Gary is a convicted sex-offender 2. Therefore, Gary is not allowed to work with children from 1 However, as stated, the argument is invalid.
Before reading on, see if you can provide a counterexample for this argument.
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