An Introduction to Inductive Arguments Chapter 9 Lecture Notes An Introduction to Inductive Arguments

Chapter 9 Induction is the basis for our commonsense beliefs about the world. In the most general sense, inductive reasoning, is that in which we extrapolate from experiences to what we have not yet experiences. In this chapter we are going to focus on: inductive generalizations, statistical syllogisms, and common errors or fallacies that are associated with inductive reasoning in general.

Chapter 9 Many logic texts define inductive arguments in contrast with deductive arguments. We aren’t going to do that. For us, inductive arguments have the following characteristics: The premises and the conclusion are all empirical propositions. The conclusion is not deductively entailed by the premises. The reasoning used to infer the conclusion from the premises is based on the underlying assumption that the regularities described in the premises will persist. The inference is either that unexamined cases will resemble examined ones or that evidence makes an explanatory hypothesis probable. See page 255 for a full explanation.

Chapter 9 This means that inductive and deductive are contrary predicates, not contradictory predicates. We will also see that there are arguments that are neither inductive nor deductive and so we will have to have another category for those in future chapters. For inductive arguments, it is always some possibility that the conclusion will turn out to be false even though the premises are true. (256) Following David Hume, this is the problem of induction.

Chapter 9 Inductive Generalizations (IG) In an IG, the premises describe a number of observed objects or events as having some particular feature. From this observed set of objects or events a conclusion asserts a claim about all (or most) of the objects and events of the same type have the feature in question. 85% of polled students at Notre Dame think the football team is great. So, probably: 85% of all Notre Dame students think the the football team is great. The word probably indicates that there is an extrapolation from the polled (observed) group the the entire group.

Chapter 9 Phrases like: probably, in all likelihood, and most likely are often used in inductive arguments. Inductive arguments and inductive reasoning is used in contexts of prediction. Reasoning from the past to the future. Cases where we reason from the present to the past (as in archeology) is called retrodiction. We might make a claim about which dinosaurs went extinct first based on current fossil records. This would be an inductive, retrodictive argument. Induction require a belief in the regularities in the world.

Chapter 9 Some important points about the many types of IGs. We need to take into account: Sample size relative to the size of the target population. Samples need to be random Random for samples is defined as: every member of the population having an equal chance of being chosen for the sample. If this is the case, then the sample is random.

Chapter 9 Problems of Sampling: Size issues: more samples of a population does not necessarily make an IG stronger. What one needs for the sample is for it to be representative. Representativeness will work as a substitute condition for randomness. Sometimes it is more reliable than random depending on the point of the sample. What one needs for a sample sixe depends on the variability of the population. (260)

Chapter 9 Often it is useful (in medical trials and the like) to move to what is called stratified sampling. A stratified sampling occurs when a sample is selected in such a way that significant characteristics within the population are (approximately) proportionately represented within it. The Gallup polling group uses stratified sampling to predict political outcomes with fewer members in the sample population being polled. When done properly, it can be quite useful for predicting outcomes. (263)

Chapter 9 Guidelines for Evaluating Inductive Generalizations Try to determine what the sample is and what the population is. If it is not stated what the population is, make an inference as to what population is intended, relying on the context for cues. Note the size of the sample. If the sample is lower than 50, then, unless the population is extremely uniform or itself very small, the argument is weak. Reflect on the variability of the population with regard to the trait or property, x, that the argument is about. If the population is not known to be reasonably uniform with regard to x, the sample should be large enough to reflect the variety in the population. Reflect on how the sample has been selected. Is there any likely source of bias in the selection process? If so, the argument is inductively weak. For most purposes, samples based on volunteers, college students, or persons of a single gender, race, or social class are not representative. Taking the previous considerations into account, try to evaluate the representativeness of the sample. If you can give good reasons to believe that it is representative of the population, the argument is inductively strong. Otherwise, it is weak.

Chapter 9 Statistical Syllogism (SS) In SS argument we reason from characteristics that are generally present (or absent) within a certain reference lass to a characteristic likely present (or absent) in a member of the reference class. Typically the premise of a SS is derived from the conclusion of some IG or other. 95% of Notre Dame students are football fans. Gordon is a Notre Dame student So, probably, 3. Gordon is a Notre Dame football fan. SS arguments can work in the other direction with low %s.

Chapter 9 Language Problems in the Context of Induction: Pseudoprecision: these are claims that appear to be precise because of the use of numbers, but cannot be precise because of the impossibility of obtaining knowledge to the level of exactness described. Typically there is a problem with an operational definition when this occurs. Examples of pseudoprecision are experation dates on food, calorie content on foods and many studies relating to increases in usage and the like. (see page 270-2)

Chapter 9 Questionable Operational Definitions Sometimes an operational definition used in science or the like is used in a manner that is illicit. So when a term or phrase that is vague or imprecise is used (like: unfocused hyperactivity) and a precise measurement is applied (like 40% reduction), then we have an instance of a term that has been operationalized. The claim or number is misleading because there is no precision, but only pseudoprecision (272).

Chapter 9 Common Errors in Inductive Reasoning The Biased Sample: this occurs with cases of over- or under- emphasized characteristics being sampled. Or it could occur because the sample isn’t random or the question in a poll is presented in such a way to guarantee the outcome desired by the poll taker. A hasty generalization occurs when the sample is hopelessly inadequate based on the size of the sample.

Chapter 9 Anecdotal arguments describe premises from one person’s experiences and try to base a conclusion. Typically the problem with these anacdotal arguments is that they don’t satisfy the G condition from our ARG conditions. There is no good grounds to accept a robust conclusion. Anecdotal arguments are a form of hasty generalization and are thus fallacies. See pages 277-8 for a fuller example of an anecdotal argument.

Chapter 9 The Fallacy of Composition and Division These two fallacies deal with inferences that occur between the part and the whole or members of a group and the group itself. Fallacy of Composition: a conclusion about a whole or group is reached based on premises about its parts or members. Fallacy of Division: a conclusion about a part or member is reached based on premises about the whole or group.

Chapter 9 Examples of the fallacies of composition and division. Composition: Each apartment is small. So the whole apartment building is small. We can see that the building could be quite large. Division: The Florida Marlins baseball team is 16 years old. So, each Florida Marlins baseball player is 16 years old. We know that the professional baseball players are not all 16 years old. These are mistakes in reasoning.

Chapter 9 Terms to review: Anecdotal argument Biased sample Fallacy of composition Fallacy of division Hasty inductive generalization Inductive argument Inductive generalization Inductive reasoning Operationalized Pseudoprecision Random sample Representativeness Retrodiction Sample/Stratified sample Statistical syllogism Target population