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Critical Thinking: Chapter 10 Inductive Arguments Arguments Before we can evaluate an argument, we need to analyze it. We need to be clear what the argument is trying to prove, what evidence it uses, and how it relates this evidence to its conclusion. Inductive Arguments When we extend what we have already observed to things or situations we have not observed, we are reasoning inductively; we are producing inductive arguments. Inductive Arguments Example: The dog has barked at me for the last three mornings, so I think he will bark at me this morning. Inductive Arguments Remember: An inductive argument is an argument the premises of which are intended to provide some degree of probability for the truth of the conclusion. Therefore it is not sound or valid, but weak or strong. Deductive Arguments Remember: A deductive argument sets out to guarantee the truth of its conclusion based on the truth of its premises. Inductive Arguments Remember:an inductive argument attempts to offer a probability that its conclusion is true based on the truth of its premises. Inductive Arguments Inductive arguments give us a way of extending our belief from things we know about to things unknown. Important Definitions Sample: The term sample refers to an item or items we believe something about. Important Definitions Target: The term target refers to an item or group of items to which we wish to extend our belief. Important Definitions Feature: The item we know about in the sample and we extend to the target object is the feature (or property) in question. Example Premise: X has properties a, b, c. Premise: Y has properties a, b, c. Premise: X has further property p. Conclusion: Y also has property p. X is our sample, Y is our target, an p is our feature (or property) in question. Analogical Arguments and Generalizations Inductive arguments can be divided into two categories: Analogical arguments (or argument by analogy) and inductive generalizations. Arguments by Analogy Ordinarily, arguments by analogy have one thing or event for a target. In an analogical argument, the sample and target are distinct-one is not a part of the other. Analogies Analogies are arguments that deal with comparing two similar things, one which is familiar and one which is unfamiliar. The key to analyzing analogies, is to determine what these two things are and how they are similar. Analyzing Analogies So, analyzing an analogy means translating it into standard form. Example: “Three of my friends bought their computers on the internet and they were all unhappy with them. I was thinking about ordering my new computer online but now I think that if I do, I’ll be unhappy with it.” Analyzing Analogies Such translations are made easier since you know from the standard form what parts you need to look for: The sample and the target, the similarities that are known, and the property in question “X.” Remember, the conclusion is always about the target and always asserts that the target has the property in question “X.” Analyzing Analogies p1: Friends’ computers were: (1) bought online p2: My computer will be: (1) bought online p3: Friends’ computers: (2) made them unhappy c: My computer will: (2) make me unhappy Evaluating Analogies There are several things to consider when evaluating an analogy, but they all boil down to this basic rule, “the more similar the sample and the population, the higher the probability that the conclusion is true.” Each of the individual things to consider in your evaluation is concerned in some way with measuring this similarity. Evaluating Analogies 1. The larger the sample, the stronger the argument. If our computer buyer had 10 friends who were unhappy with the computers they purchased on the internet, the argument would be stronger. Evaluating Analogies 2. The greater the percentage of the sample that has the property in question, the greater the chance that the target has the additional attribute. Consider an analogy with a sample of 10 people who bought computers online. Suppose 3 of the 10 were unhappy. Now suppose that 8 of the 10 were unhappy. Which would make our analogy stronger? Evaluating Analogies 1. The greater the number of relevant similarities between the sample and the target, the stronger the conclusion. If all of our friends’ computers were the same brand as the one we are buying, the analogy gets stronger. If they all ordered from the same company that we are going to use, the analogy gets stronger. Evaluating Analogies 2. The fewer know dissimilarities between the sample and the target, the stronger the argument. If all the friends bought one type of computer and you are considering a different type, the analogy gets weaker. If theirs were refurbished and yours will be new, the analogy gets weaker. Evaluating Analogies 1. When considering a feature of the sample that we are unsure of in the target, the greater the diversity in the sample, the better the argument. Consider processor speed. If we don’t know the speed of the processor in the target, we want a large diversity of processors in our sample. This gives a greater likelihood that the sample will be similar to our target population. Evaluating Analogies 2. The more guarded the conclusion is, the stronger the argument is. (Consider the burden of proof!) Consider these two conclusions: (1) I will be terribly unhappy with my computer, (2) I will be less than perfectly pleased with my computer. Evaluating Analogies Conclusion 2 is more guarded, it is much more likely that you’ll be less than pleased than it is that you’ll be terribly unhappy, thus 2 is easier to prove. Evaluating Analogies Unlike determining the validity or invalidity of a deductive argument, evaluating an inductive argument like an analogy is somewhat subjective. The strength or weakness of an analogy will depend, in part, to how relevant and similar the two analogues seem to the reader. Evaluating Analogies Instead of immediately trying to determine in some objective way an analogy’s absolute strength, it is prudent to evaluate it by determining what would make it stronger or by comparing it to other analogies. By comparing the relative strength of an analogy with actual or potential rivals you can get a good sense of its absolute strength. Arguments by Analogy Example: I am scared to let Susan see me in this sweater. A couple of my other friends told me it makes me look like a child, and she’s at least as critical as they are. A weak or strong analogy? Strong. Arguments by Analogy Example: A watch could not assemble itself, because it’s too complex. The universe is at least as complex as a watch. So the universe could not have assembled itself either. A weak or strong analogy? Weak. Inductive Generalization Generalizations always have a class of things or events as a target (rather than one thing or event for a target as in analogies). In all cases, generalizations have their samples drawn from the target class (while this is never true of arguments by analogy). Inductive Generalization Example: How can you say that people act out of self-interest? Didn’t you read the story about the airplane that skidded off the runway into the ocean? One man kept passing the life preservers to other people so they would live instead of him. Analogical Arguments and Generalizations In other words: In an inductive generalization, we generalize from a sample of a class or population to the entire class or population, while in an analogy we generalize from a sample of a class or population to another member of the class or population. Fallacies What is a biased example? It is a sample that does not accurately represent its class. A biased generalization is a fallacy because its sample is not representative of the target population. Fallacies A hasty generalization is a generalization which is made with a sample that is too small. An appeal to anecdotal evidence is a form of the hasty generalization. Fallacies We generally reject anecdotal evidence because, while credible, an anecdote is only one experience and as such is statistically irrelevant. When should a random sample be used? A random sample should be used in an inductive generalization whenever the target class is heterogeneous (unrelated to or unlike each other), otherwise you would have an analogy. When should a random sample be used? For example, if you want to know how Republicans are going to vote, then you have to have a large sample size because people are so different from each other. Margin of Error The larger the sample size size the smaller the margin of error. True or False? It is fair to say the same criteria used to evaluate inductive generalizations can also be used to evaluate analogies. True or False? True! This is because while they differ in how they are set up, the two kinds of arguments both follow the same principles. True or False? An inductive generalization moves from something we know about the target class to a claim about a sample. True or False? An inductive generalization moves from something we know about the target class to a claim about a sample. False! It goes the other way, from a sample to a target. Review When we make an analogical argument or a generalization, we draw a conclusion about a target based on a sample. Review The goal of randomness is to achieve representativeness. A sample is random if every member of the target population has an equal chance at being selected for the sample. Review True or False? No generalization based on an unrepresentative sample is trustworthy. Review True! The sample must be representative to be used appropriately. Review True or False? An inductive generalization cannot establish that some precise percentage of a target population has a given characteristic. Review True! Remember, with inductive arguments we are talking about probabilities rather than certainties.