A Short Course in Logic Answers to Practice Logic is a skill and, like any skill, it s improved with practice. I) Analyzing Arguments Sometimes it can be difficult to identify the ultimate conclusion of an argument, or to distinguish between premises and subconclusions. It s well worth learning how to do this, though, because this skill sharpens comprehension and makes it much easier to follow the complex readings. After all, arguments are all about presenting some ideas as reasons to believe other ides. If you have difficulty seeing when some ideas are being as reasons to believe other ideas, you ll find arguments very difficult to follow; they re liable seem like jumbled up lists of unrelated bits of information. But if you can see when some ideas are being given as reasons to believe other ideas, then you ll see how it all hangs together; you ll see the argument and you ll understand how it works. So, let s practice doing that. For each of the following arguments, determine whether each of the bracketed ideas is the ultimate conclusion, a premise, or a subconclusion. Just for fun, you might want to try to diagram the arguments, too. ) [Learning how to distinguish between premises and subconclusions is important] (ultimate conclusion) because [it helps you to follow complex chains of reasoning] (premise).. Learning how to distinguish between premises and subconclusions is important.. Learning how to distinguish between premises and subconclusion helps you to follow complex chains of reasoning. ) [Being able to follow complex chains of reasoning allows you to understand interesting and sophisticated material] (premise). Therefore [it s worthwhile spend some time on logic exercises] (ultimate conclusion).. It s worthwhile spend some time on logic exercises. Being able to follow complex chains of reasoning allows you to understand interesting and sophisticated material.
3) [Unless ideas are communicated to others, they re worthless] (premise). Thus, [communication is the most important subject] (ultimate conclusion).. Communication is the most important subject.. Unless ideas are communicated to others, they re worthless. 4) [Unless ideas are communicated to others, they re worthless] (premise). Thus, [communication is the most important subject] (subconclusion). And therefore [Ann should major in communication] (ultimate conclusion).. Ann should major in communication.. Unless ideas are communicated to others, they re worthless. 3. Communication is the most important subject. 3
3 5) [Sam should major in computer science] (ultimate conclusion) because [computer science majors stand the best chance of getting a job] (premise).. Sam should major in computer science.. Computer science majors stand the best chance of getting a job. 6) [Computer science majors stand the best chance of getting a job] (ultimate conclusion), since [every company needs people to maintain its computer system] (premise).. Computer science majors stand the best chance of getting a job.. Every company needs people to maintain its computer system. 7) [Sam should major in computer science] (ultimate conclusion) because [computer science majors stand the best chance of getting a job] (subconclusion), since [every company needs people to maintain its computer system] (premise).. Sam should major in computer science.. Computer science majors stand the best chance of getting a job. 3. Every company needs people to maintain its computer system. 3
4 8) [Ellen should go to a university that has a journalism department] (ultimate conclusion) because [she should major in journalism] (premise).. Ellen should go to a university that has a journalism department. She should major in journalism. 9) [Ellen has always been unusually interested in current events] (premise). Thus, [Ellen should major in journalism] (ultimate conclusion).. Ellen should major in journalism.. Ellen has always been unusually interested in current events. 0) [Ellen should major in journalism] (subconclusion) because [she s always been unusually interested in current events] (premise). And since she should major in journalism, [she should go to a university that has a journalism department] (ultimate conclusion).. Ellen should go to a university that has a journalism department.. Ellen should major in journalism. 3. Ellen s always been unusually interested in current events. 3
5 ) [Frank is good with animals] (premise) so [he should become a veterinarian] (subconclusion). Because Frank should become a veterinarian, [he needs a good science background] (subconclusion). And since Frank needs a good science background, [he should take biology next semester] (ultimate conclusion).. Frank should take biology next semester.. Frank is good with animals. 3. Frank should become a veterinarian. 4. Frank needs a good science background. 3 4 C ) [Beth should ensure that she has a good math background] (ultimate conclusion) because [she wants to major in chemistry] (premise) and because [chemistry majors need to know a lot of math] (premise).. Beth should ensure that she has a good math background.. She wants to major in chemistry. 3. Chemistry majors need to know a lot of math. + 3 3) [George wants to major in English] (premise) and [English majors need a good dictionary] (premise). Therefore, [a good dictionary would be perfect gift for George] (ultimate conclusion).. A good dictionary would be perfect gift for George.. George wants to major in English. 3. English majors need a good dictionary. + 3
6 4) [Peter should major in psychology] (ultimate conclusion). This is because [he d probably make a good counselor] (subconclusion) since [he s always been a good listener] (premise) and [good listeners usually make good counselors] (premise).. Peter should major in psychology.. He d probably make a good counselor. 3. He s always been a good listener. 4. Good listeners usually make good counselors. 3 + 4 5) [The only reason Wendy s majoring is business is that her parents want her to] (premise). But [she shouldn t major in something just because her parents want her to] (subconclusion), since [she will be the one taking the classes and getting the job, not her parents] (premise). That s why [Wendy should drop her business major] (ultimate conclusion).. Wendy should drop her business major. The only reason Wendy s majoring is business is that her parents want her to. 3. She shouldn t major in something just because her parents want her to. 4. She will be the one taking the classes and getting the job, not her parents. 4 + 3 6) [Wendy should keep her business major] (ultimate conclusion) because [her parents want her major in business] (premise) and since [they have more experience than she does] (premise), [they know what s best for her] (subconclusion).. Wendy should keep her business major.. Her parents want her major in business. 3. They have more experience than she does. 4. They know what s best for her. 3 + 4
7 7) [You never see want-ads for philosophers] (premise), so [philosophy majors won t be able to get jobs] (subconclusion). Besides, [philosophy is a painful waste of time] (subconclusion) because [philosophy classes ask people to think hard about questions to which they ll never get any answers] (premise). Therefore, [nobody should major in philosophy] (ultimate conclusion).. Nobody should major in philosophy.. You never see want-ads for philosophers. 3. Philosophy majors won t be able to get jobs. 4. Philosophy is a painful waste of time. 5. Philosophy classes ask people to think hard about questions to which they ll never get any answers. 5 C 3 4 B D 8) [Philosophy is a great major] (ultimate conclusion)! For one thing, [philosophy hones people s critical thinking and communication skills] (premise), and [employers really value such skills] (premise). Thus, [philosophy majors are actually very employable] (subconclusion). For another thing, [philosophy classes are fun] (subconclusion), because [philosophy classes deal with interesting questions like Is anything really right or wrong? and Is there a God? ] (premise) and [it s fun to deal with interesting questions] (premise).. Philosophy is a great major.. Philosophy hones people s critical thinking and communication skills 3. Employers really value such skills. 4. Philosophy majors are actually very employable 5. Philosophy classes are fun. 6. Philosophy classes deal with interesting questions like Is anything really right or wrong? and Is there a God? 7. It s fun to deal with interesting questions. + 3 6 + 7 C 4 5 B D
8 II) Evaluating Arguments Evaluate each of the following arguments and decide what attitude we should adopt toward the ultimate conclusion on the basis of each argument. ) Logic has no bearing upon anything else you ll be doing in this class or outside of it. Therefore, studying logic is a waste of time.. Studying logic is a waste of time.. Logic has no bearing upon anything else you ll be doing in this class or outside of it. This argument is bad because the premise is false. Because the argument is bad, it tells us nothing about the ultimate conclusion. We should neither believe nor disbelieve the ultimate conclusion on the basis of this argument. ) Logic is frequently helpful because it s often useful.. Logic is frequently helpful.. Logic is often useful. This argument is bad because the premise is can only be believed by someone who already believes the ultimate conclusion. Because the argument is bad, it tells us nothing about the ultimate conclusion. We should neither believe nor disbelieve the ultimate conclusion on the basis of this argument. 3) Many people find logic a bit difficult at first, so no good professor would require anyone to study it.
9. No good professor would require anyone to study logic.. Many people find logic a bit difficult at first. This argument is bad because the inference is weak. Because the argument is bad, it tells us nothing about the ultimate conclusion. We should neither believe nor disbelieve the ultimate conclusion on the basis of this argument. 4) In order to evaluate an inference, we have to pretend that we believe the idea at the top of the inference arrow, even if we think it s false. Hence, evaluating inferences improves our ability to understand people who think differently than we do.. Evaluating inferences improves our ability to understand people who think differently than we do.. In order to evaluate an inference, we have to pretend that we believe the idea at the top of the inference arrow, even if we think it s false. This argument is good because the premise and inference are both good. Because the argument is good, we should be inclined to believe the ultimate conclusion.
0 III) More Abstract Arguments A) The God Debate: Some Arguments Most of the arguments that we ve considered so far have had a relatively familiar and concrete subject, like the choice of a major. Philosophical arguments, however, usually address more abstract and tricky material, like the existence of God. For example, let s take a look at the following conversation between five people, each of whom is offering an argument to support his or her opinion. As you read each argument, determine whether each of the bracketed ideas is the ultimate conclusion, a premise, or a subconclusion. Just for fun, you might want to try to diagram and evaluate the arguments, too. ) Linda: Sure [God exists] (ultimate conclusion)! After all, [some people have recovered from very serious illnesses after being prayed for] (premise), and [the only way this could happen is if God exists] (premise).. God exists.. Some people have recovered from very serious illnesses after being prayed for. 3. The only way this could happen is if God exists. + 3 Although I think that premise is true and inference A is strong, I think that premise 3 is false. Maybe the recoveries were simply coincidental. This leads me to conclude that the entire argument is bad, but because I know that bad arguments can have true conclusions, I don t decide that the ultimate conclusion is false.
) Bill: You re right, Linda. Besides, [the Bible is the word of God] (premise) and [God always tells the truth] (premise) so [everything the Bible says is true] (subconclusion). And [the Bible says that God exists] (premise), so [God must exist] (ultimate conclusion).. God must exist.. The Bible is the word of God. 3. God always tells the truth. 4. Everything the Bible says is true. 5. The Bible says that God exists. + 3 4 + 5 It seems to me that inferences A and B are both fine and that premise 5 is good. However, premises and 3 are both bad because neither one of them can be believed by someone who doesn t already believe that the ultimate conclusion is true. This leads me to decide that the argument is bad, but because bad arguments can have true conclusions, I don t decide that the ultimate conclusion is false. 3) Susan: As far as I m concerned, [religion is just another kind of superstition] (ultimate conclusion). Think about it! [Some distinguished scientists don t believe in God] (premise). Consequently, [God doesn t exist] (subconclusion).. Religion is just another kind of superstition.. Some distinguished scientists don t believe in God 3. God doesn t exist. 3 Although it s true that some distinguished scientists don t believe in God, I don t see how it follows from this that God doesn t exist. This makes inference A bad, and that, in turn, makes the argument bad. Because bad arguments can have true conclusions and false conclusions, this argument tells me nothing about whether or not God exists.
4) Mike: Furthermore, [when I was 8, I didn t get the bicycle that I prayed for] (premise). [God, if he existed, would have given me the bicycle] (premise). Therefore, [God doesn t exist] (ultimate conclusion).. God doesn t exist.. When I was 8, I didn t get the bicycle that I prayed for. 3. God, if he existed, would have given me the bicycle. + 3 It seems to me that 3 is false and this is enough to make the argument bad. (Although it s not enough to make inference A bad. Inference A is perfect because someone who believes and 3 would be forced to believe.) Since bad arguments can have true conclusions, this argument tells us nothing about whether or not God exists. 5) Leslie: That s right. [God doesn t exist] (ultimate conclusion). [Belief in God is nothing more than a form of mental illness] (subconclusion), since [there are similarities between religious experiences and schizophrenic hallucinations] (premise). Besides, [if God existed then there d be evidence of his existence] (subconclusion) because [if God existed, he d want people to believe in him] (premise). And [there isn t any evidence that God exists] (premise).. God doesn t exist.. Belief in God is nothing more than a form of mental illness. 3. There are similarities between religious experiences and schizophrenic hallucinations. 4. If God existed then there d be evidence of his existence. 5. If God existed, he d want people to believe in him. 6. There isn t any evidence that God exists. 3 5 C 4 + 6 B D I don t know if premise 3 is true, but even if it is true I don t think that subconclusion follows. Consequently, it seems to me that inference A is weak. This is enough to make the first line of reasoning bad, but it isn t enough to undermine the argument as a whole because the second line of reasoning might be good.
3 Turning to that line of reasoning, it seems to me that reasonable people could disagree with inference C and premise 6. Perhaps God would want us to believe in him on the basis of faith, and perhaps there is evidence for God s existence after all. Because I don t think that either line of reasoning holds up, I don t think that this argument establishes the truth of the ultimate conclusion. Of course, whether or not the ultimate conclusion is true is another matter altogether. B) The God Debate: The Bearing of Arguments on Ultimate Conclusions Now that you ve thought about the arguments in the previous conversation, consider the comments of the following listeners and answer the questions below. Mary: I like Linda s point when she says that people recover from serious illnesses after being prayed for and that this could only happen if God existed. I think this is a really good argument for the existence of God! ) Can you conclude from this that Mary believes in God? Yes. Mary thinks that an Linda s argument for the existence of God is good, so she s led to accept the conclusion of that argument the claim that God exists. George: I can t believe that Mike s an atheist just because he didn t the bike he prayed for. What a lousy argument against the existence of God! ) Can you conclude from this that George believes in God? No. Mike is criticizing an argument, which tells us nothing about his attitude toward the conclusion of the argument. C) The God Debate: Pin the Tail on the Donkey It s useful to be able to identify the part of an argument that s targeted by an objection. I think of these as Pin the Tail on the Donkey exercises because you pin the objection on the diagram. I ll present you with two arguments, followed by criticisms of the argument. For each criticism, see if you can identify the part of the argument (the premise or the inference) that it criticizes. You can check you answer by resting the mouse over the name of the person leveling the objection. The Teleological Argument for God s Existence: God must exist. After all, natural objects are very well put together. (The human eye, for example, adjusts to let in the right amount of light for vision.) We know that many objects like watches are very well put together because intelligent beings created them. It s reasonable to conclude, therefore, that natural objects have been created by an intelligent being. Therefore there must be a God.
4. There must be a God.. Natural objects are very well put together. 3. We know that many objects like watches are very well put together because intelligent beings created them. 4. Natural objects have been created by an intelligent being. + 3 4 ) Elliot: I don t think that natural objects are very well put together. Plants and animals are breaking down all the time! Elliot is criticizing premise. ) Francis: Sure, natural objects are put together well. And it s true that objects like watches are very well put together because intelligent beings created them. But those are artifacts. It doesn t follow from this that natural objects were created by an intelligent being. Francis is criticizing inference A. 3) Ann: Mightn t natural objects have been created by an intelligent being other than God, maybe really smart aliens? Ann is criticizing inference B. A Response to the Teleological Argument: Evolution is the right explanation for why natural objects are very well put together. Therefore, the teleological argument for God s existence doesn t work. But the teleological argument is the best argument we have for God s existence and so no argument for God s existence will be very good. Therefore we shouldn t believe in God.. We shouldn t believe in God.. Evolution is the right explanation for why natural objects are very well put together. 3. The teleological argument for God s existence doesn t work. 4. The teleological argument is the best argument we have for God s existence. 5. No argument for God s existence will be very good.. 3 + 4 5
5 C 4) Roberta: I m not so sure that evolution is correct. The fossil record is pretty weak in some areas. Roberta is criticizing premise. 5) Zach: I think that some versions of the teleological argument presuppose the truth of evolution. The point is why are various natural laws the way the are, the way that allows for evolution? Zach is criticizing inference A. 6) Chris: Aren t other arguments for God s existence better than the teleological argument? Chris is questioning premise 4. 7) Sally: I think we should believe in God on the basis of faith, not argument. Sally is criticizing inference C.