# A Short Course in Logic Example 8

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1 A Short ourse in Logic xample 8 I) Recognizing Arguments III) valuating Arguments II) Analyzing Arguments valuating Arguments with More than one Line of Reasoning valuating If then Premises Independent Reasons IV) What the valuation Means Independent Lines of Reasoning V) Summary Identifying the Parts of the Argument Diagramming the Argument I) Recognizing Arguments Here s one last passage for us to consider. This passage contains an argument because it s trying to convince us that an idea is true by citing other ideas as evidence. II) Analyzing Arguments The ultimate conclusion is the claim that Ann should major in business. 8) [Ann should major in business.] (Ultimate onclusion) For one thing, capitalism has triumphed over communism so it must be the will of God. learly, though, business majors foster capitalism, which shows that business majors foster the will of God. For another thing, if Ann gets her MBA then she s sure to be happy. After all, MBA s make a lot of money and if someone makes a lot of money then that person is sure to be happy. Before we identify the other parts of this argument, however, we should pause to note something that sets this argument apart from the others we ve seen.

2 Stop and Think: This argument is importantly different from any argument we ve examined so far. an you see how? Independent Reasons In xample 4, we were introduced to dependent reasons, two or more ideas that need to be believed simultaneously in order to stand as evidence for the truth of another idea. We saw that depended reasons need to be added together. When two or more ideas don t need to be believed simultaneously in order to stand as evidence for the truth of another idea, we call them independent reasons. Independent reasons aren t added together; each idea gets its own arrow to the conclusion because each idea stands on its own as a reason to believe that conclusion. To get a better handle on this, consider the following two arguments: Dogs make good pets. After all, dogs tend to be very affectionate, and affectionate animals make good pets.. Dogs make good pets.. Dogs tend to be very affectionate. 3. Affectionate animals make good pets. + 3 A ats make good pets. For one thing, they re clean. For another thing, you don t have to take them on walks.. ats make good pets.. ats are clean. 3. You don t have to take cats on walks. 3 A B

3 3 See the difference? Independent Lines of Reasoning Independent reasons generate independent lines of reasoning. In the cat argument, for example, we have the they re clean line of reasoning to believe that cats are good pets, and the you don t need to walk them line reasoning for the same conclusion. Unlike any of the arguments in examples through 7, the argument that we re considering now gives us more than one line of reasoning. First, there s the will of God sort of reason, which I ll color red. Then there s the being happy sort of reason, which I ll color blue. 8) [Ann should major in business.] (Ultimate onclusion) For one thing, capitalism has triumphed over communism so it must be the will of God. learly, though, business majors foster capitalism, which shows that business majors foster the will of God. For another thing, if Ann gets her MBA then she s sure to be happy. After all, MBA s make a lot of money and if someone makes a lot of money then that person is sure to be happy. You might have noticed that these lines of reasoning are indicated by the expressions for one thing, and for another thing. It s not unusual for lines of reasoning to be signaled in this, or some similar way, but it won t happen all the time. As you might have guessed, when an argument has more than one line of reasoning, each line of reasoning in the argument s diagram has its own approach to the ultimate conclusion sort of like this: For one thing, capitalism has triumphed over communism so it must be the will of God. learly, though, business majors foster capitalism, which shows that business majors foster the will of God. For another thing, if Ann gets her MBA, she s sure to be happy. After all, MBA s make a lot of money and if someone makes a lot of money then that person is sure to be happy. Ann should major in business. If an argument has more than one line of reasoning, it s often good to recognize that as soon as possible because it serves to simplify the rest of the process. In this case, for example, we can think of the passage as presenting us with two fairly short arguments instead of one very long argument.

4 4 Identifying the Parts of the Argument Now that we ve seen that this argument has two lines of reasoning, let s figure out how each line of reasoning works. Stop and Think: Determine whether each of the bracketed sentences is a premise or a subconclusion in the argument. Remember, if the argument does give us reason to believe an idea, it s a subconclusion. If the argument doesn t give us reason to believe an idea, but instead just takes the idea for granted, it s a premise. Remember too that looking for conclusion indicator expressions and reason indicator expressions can be very helpful. 8) [Ann should major in business.] (Ultimate onclusion) For one thing, [capitalism has triumphed over communism] so [it must be the will of God]. learly, though, [business majors foster capitalism], which shows that [business majors foster the will of God]. For another thing, [if Ann gets her MBA then she s sure to be happy]. After all, [MBA s make a lot of money] and [if someone makes a lot of money then that person is sure to be happy]. apitalism has triumphed over communism is being taken for granted by this argument, so it s a premise. It must be the will of God, however, is a subconclusion because the argument is giving us reason to believe it. The conclusion indicator expression so can help us to see that. Business majors foster capitalism, is another premise in the argument, a claim that the argument is asserting without support, business majors foster the will of God is another subconclusion. The conclusion indicator expression which shows that, can help us to see that the argument is giving us reason to believe this claim. 8) [Ann should major in business.] (Ultimate onclusion) For one thing, [capitalism has triumphed over communism] (premise) so [it must be the will of God] (subconclusion). learly, though, [business majors foster capitalism] (premise), which shows that [business majors foster the will of God] (subconclusion). For another thing, [if Ann gets her MBA then she s sure to be happy]. After all, [MBA s make a lot of money] and [if someone makes a lot of money then that person is sure to be happy]. Turning to the other line of reasoning, if Ann gets her MBA then she s sure to be happy is a subconclusion because the argument is giving us reason to believe it, reasons signaled by the reason indicator expression after all. MBA s make a lot of money and if someone makes a lot of money then that person is sure to be happy are both premises in the argument, claims that the author is asserting without providing us with reason to believe that the claims are true.

5 5 8) [Ann should major in business.] (Ultimate onclusion) For one thing, [capitalism has triumphed over communism] (premise) so [it must be the will of God] (subconclusion). learly, though, [business majors foster capitalism] (premise), which shows that [business majors foster the will of God] (subconclusion). For another thing, [if Ann gets her MBA then she s sure to be happy] (subconclusion). After all, [MBA s make a lot of money] (premise) and [if someone makes a lot of money then that person is sure to be happy] (premise). Diagramming the Argument Here s how this argument is diagrammed: 8) [Ann should major in business.] (Ultimate onclusion) For one thing, [capitalism has triumphed over communism] (premise) so [it must be the will of God] (subconclusion). learly, though, [business majors foster capitalism] (premise), which shows that [business majors foster the will of God] (subconclusion). For another thing, [if Ann gets her MBA then she s sure to be happy] (subconclusion). After all, [MBA s make a lot of money] (premise) and [if someone makes a lot of money then that person is sure to be happy] (premise).. Ann should major in business.. apitalism has triumphed over communism. A B D Again, observe how there is really very little new here. It s a friendly diagram. Notice how the will of God line of reasoning (ideas, 3, 4, and 5) is on the left and the being happy line of reasoning (ideas 6, 7, and 8) is on the right. Looking at the will of God line, the conclusion indicator expression so tells us that idea is being given as a reason to believe idea 3. It corresponds to inference A. learly, though is sort of like an and. It s an inference eraser that tells us that there probably isn t an inference between 3 and 4. The conclusion indicator expression which

6 6 shows that tells us that 5 follows from something that came before. It corresponds to inference B. Looking at the being happy line, the reason indicator expression after all tells us that 7 is a reason to believe 6. It corresponds to inference D. The inference eraser expression and tells us that there probably isn t an inference between 7 and 8. There aren t any words in the passage that correspond to inferences and. (Remember, sometimes inferences will be signaled with conclusion indicator expressions and reason indicator expressions, but sometimes they won t be.) Finally, notice in the diagram how the premises (ideas, 4, 7 and 8) have arrows going from them but no arrows going to them. The ultimate conclusion (idea ) has arrows going to it but no arrow going from it. The subconclusions (ideas 3, 5 and 6) have arrows going to them and from them. III) valuating Arguments Now that we understand how this argument works, can evaluate it. Stop and Think: Is this argument good or bad?. Ann should major in business.. apitalism has triumphed over communism. A B D

7 7 Let s begin with left hand line of reasoning. The first thing I notice is that I don t like idea 3, the claim that capitalism is the will of God.. Ann should major in business.. apitalism has triumphed over communism. I don t like this. A B D But this idea is a subconclusion, so I ll need to find something wrong with the line of reasoning in support of 3. I ll need to look up. Idea might be debatable but it pales in comparison to the horror that is inference A. Surely someone could believe that capitalism has triumphed over communism without believing that capitalism is the will of God! Atheists could believe idea without thereby believing that God exists.

8 8. Ann should major in business.. apitalism has triumphed over communism. A B D valuating Arguments with More than one Line of Reasoning Is this enough to show that the entire argument is bad? Actually, it isn t. The fact that inference A is bad is not enough to ruin this argument, because an argument with more than one of reasoning is like a man hanging from more than one rope from more than one beam. Just like the man is safe if even one rope / beam combination is secure, an argument is good if it has even one good line of reasoning. In order to discount an argument with more than one line of reasoning, we need to find something wrong with each of those lines. The fact that inference A is bad means only that the left hand line of reasoning is bad. If the other line of reasoning holds, the argument is good.

9 9 valuating If then Premises So, what about the right hand line of reasoning? Let s stop for a moment to look at premise 8, If someone makes a lot of money then that person is sure to be happy. If then sentences like this can be tricky to evaluate if we don t know the secret. But happily, the secret is pretty simple. A sentence of the form If P then Q is false if the front part, P, can be true and the back part, Q, can be false at the same time. Any other consideration, like the back part being true and the front part being false at the same time, is irrelevant to the truth of the if then sentence. For example, when evaluating If someone makes a lot of money then that person is sure to be happy, we need to ask ourselves an someone make a lot of money (front part true) and still not be happy (back part false)? And when I ask myself that question, I think the answer is Yes. Making a lot of money is no guarantee of happiness. This means that premise 8 is false.. Ann should major in business.. apitalism has triumphed over communism. A B D (Be careful to notice the following: The observation that someone can be happy even though he doesn t make a lot of money, although true, is irrelevant to the truth or falsity of premise 8. Premise 8 talks about what happens if someone does make a lot of money. It doesn t say anything about what happens if someone doesn t make a lot of money.)

10 0 Now we know that the entire argument is bad because there is no line of reasoning left to support the conclusion.. Ann should major in business.. apitalism has triumphed over communism. A B D (By the way, just for practice, can you see that inference D is good? Remember to use the Bob Method. If Bob believes 7 and 8, he d be compelled to believe 6. This makes inference D strong even though premise 8 is bad. Premises and inferences are different things.) IV) What the valuation Means Because this is a bad argument, it tells us nothing interesting about the ultimate conclusion. Maybe Ann should major in business. Maybe she shouldn t. We just don t know. If we were faced with a good argument for the conclusion that Ann should major in business then we should be inclined to think that Ann should major in business. But this is not that argument.

11 V) Summary and people who make a lot of money are sure to be happy.. Ann should major in business.. apitalism has triumphed over communism. 8. People who make a lot of money are sure to be happy. A B D Analyzing Arguments Independent reasons are two or more ideas each of which stands on its own as a reason to believe another idea. Independent reason gets its own arrow to the conclusion, generating independent lines of reasoning. valuating Arguments An argument is good if it has even one good line of reasoning. In order to discount an argument with more than one line of reasoning, we need to find something wrong with all of those lines. To evaluate a sentence of the form If P then Q, we need to ask ourselves if the front part, P, can be true and the back part, Q, can be false at the same time. If so, then the If P then Q sentence is false.

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