A Short Course in Logic Example 3 I) Recognizing Arguments III) Evaluating Arguments II) Analyzing Arguments Bad Argument: Bad Inference Identifying the Parts of the Argument Premises Inferences Diagramming the Argument The Bob Method IV) What the Evaluation Means Conclusions of Bad Arguments V) Summary I) Recognizing Arguments Here s another argument. Like the previous examples, this passage is an argument because it s attempting to prove that an idea is true by citing other ideas as evidence. II) Analyzing Arguments Identifying the Parts of the Argument As usual, we ll tackle this argument by identifying its parts. And remember, the ultimate conclusion is what the passage is trying to prove. Premises are taken for granted by the argument without support. And subconclusions are intermediate steps. The argument does give us reason to believe the subconclusions and then goes on to use the subconclusions to prove other ideas. So, in order to identify the parts of an argument, it helps to do two things:. Start out by asking, What is the main idea that this argument is trying to prove? The answer to that question is the ultimate conclusion of the argument. 2. Then, for all other important ideas in the argument (that is to say, for all of the ideas that strike you as relevant to establishing the truth of the ultimate conclusion) ask Does the argument give us reason to believe that this is true, or does the argument just take this for granted? 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.
2 Stop and Think: Determine whether each of the bracketed sentences is the ultimate conclusion, a premise, or a subconclusion in the argument. 3) [Ann s parents enjoy history]. Thus [she should major in it]. In this argument, She should major in it is the ultimate conclusion because it s the main idea that the argument is trying to prove. (The word thus, a conclusion indicator expression like therefore, can help us to see that reasons are being given for this idea.) Ann s parents enjoy history, is a premise in this argument; the argument is just taking it for granted and it s being used as evidence for the ultimate conclusion. 3) [Ann s parents enjoy history] (premise). Thus [she should major in it] (ultimate conclusion). Diagramming the Argument Argument 3 is diagrammed like this.. Ann should major in history. 2 A Does it make sense to you that this should be the diagram for Argument 3? Notice once again how the premise, idea 2, is at the top of the inference arrow and how the ultimate conclusion, idea, is at the bottom of the inference arrow. The inference arrow itself shows that idea 2 is being given as reason to believe idea. Notice, too, how the conclusion indicator expression thus can help us to see that is a conclusion following from 2. III) Evaluating Arguments Now that we have a diagram of the argument, we can proceed to evaluate it.
3 Stop and Think: Is this argument good or bad? Remember, a good argument succeeds in proving to its audience that the ultimate conclusion is true. Does this argument do that? Why or why not?. Ann should major in history. 2 A Bad Argument: Bad Inference We ve seen that we should ask two questions of an argument s premises: ) Do we think that this premise is true? and 2) Could people in the argument s audience, including people who don t already believe the ultimate conclusion, reasonably think that this premise is true? We can assume that Ann s parent s enjoy history, and since someone could believe that Ann s parents enjoy history without already believing that Ann should major in history, it seems to me that the answer to both of these questions is yes, and that the premise is okay.. Ann should major in history. A Nonetheless, I think that this argument is bad because the fact that Ann s parents enjoy history doesn t prove that Ann should major in it. What if Ann, herself, hates the subject, or has no aptitude for it? The connection between 2 and isn t as good as it could be, and since this connection is the inference, inference A is bad. And because a bad inference can prevent an argument from proving that its ultimate conclusion is true, a bad inference can make an entire argument bad, just like a bad premise can.
4. Ann should major in history. A We ve seen that a bad inference can make an argument bad no matter how good the premise is, just like a weak rope can snap and make the man fall, no matter how strong the beam is. Premise Inference Ultimate conclusion Premises Inferences Just like beams and ropes are two different things and one can be good while the other is bad, premises and inferences are two different things and one can be good while the other is bad. An inference is the connection between two ideas. To say that an inference is good is that say that if the claims at the top of the arrow were true (which they may not actually be) then the claim at the bottom would probably be true as well, just like to say that a rope is strong is to say that if the beam is good (which it might not actually be) then the man is in no danger.) Similarly, to say that an inference is bad is to say that even if the claims at the top of the arrow were true, the claim at the bottom of the arrow could easily be false, just like to say that a rope is bad is to say that even if the beam is strong the fellow could fall. This means that evaluating premises and evaluating inferences are two very different things, like evaluating the strength of a beam and evaluating the strength of a rope are two very different things, and that, consequently, it s a mistake to conclude that an inference is bad just because the premise is, or vice versa.
5 This can make evaluating inferences a little tricky because it s easy (although an error) to allow our assessment of the premises to influence our assessment of the inference. In order to avoid this mistake, we ll evaluate inferences using the Bob Method. Here s how it works: The Bob Method for Evaluating Inferences To evaluate an inference, imagine Bob, a perfectly gullible but perfectly rational guy. Because Bob is perfectly gullible, he ll believe anything we tell him, but because Bob is perfectly rational, he ll reason well. We suppose Bob believes the ideas at the top of the arrow and ask ourselves How likely is Bob to believe the idea at the bottom of the arrow? If Bob is compelled to believe the idea at the bottom of the arrow, then the inference is perfect. If Bob is likely, but not compelled, to believe the idea at the bottom of the arrow, then the inference is imperfect but good. If Bob isn t even likely to believe the idea at the bottom of the arrow, then the inference is bad. Using the Bob Method, we can see that the inference in Example 3 is bad because Bob could very easily believe idea 2 and not believe idea.. Ann should major in history. A (By the way, it s important to remember that we should never use the Bob Method to evaluate premises. Can you see why not? Because Bob believes everything we tell him, he ll always believe the premises, no matter how outlandish. If we used the Bob method to evaluate premises, every premise would turn out to be good!) IV) What the Evaluation Means Conclusions of Bad Arguments So, what does this argument tell us about the truth or falsity of its ultimate conclusion? Absolutely nothing. Bad arguments can have true conclusions and they can have false conclusions, so if this argument is all we have to go on, we should suspend judgment about whether or not Ann should major in history.
6 V) Summary. Ann should major in history. A Evaluating Arguments Premises Inferences Premises and inferences are different things. A premise can be good when the inference is bad, and a premise can be bad when the inference is good. The Bob Method for Evaluating Inferences (not Premises) To evaluate an inference, imagine Bob, a perfectly gullible but perfectly rational guy. Because Bob is perfectly gullible, he ll believe anything we tell him, but because Bob is perfectly rational, he ll reason well. We suppose Bob believes the ideas at the top of the arrow and ask ourselves How likely is Bob to believe the idea at the bottom of the arrow? If Bob is compelled to believe the idea at the bottom of the arrow, then the inference is perfect. If Bob is likely, but not compelled, to believe the idea at the bottom of the arrow, then the inference is imperfect but good. If Bob isn t even likely to believe the idea at the bottom of the arrow, then the inference is bad.