PHI 101 Chapter 4 Enumerative and Analogical Induction PDF

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These notes give overviews of chapter content for Dr. Michael Horton's Critical Thinking class, but can be used as a supplement to any other modern philosophy book as well....

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1 Chapter 4: Induction I.

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4.1 Introduction A. Arguments can be divided into two subcategories: deductive arguments and inductive arguments. 1. Valid Deductive Argument: An argument in which, without fail, if the premises are true, the conclusion will also be true. (Validity is all or nothing) a) Exp: All mammals are animals. All humans are mammals. Therefore, all humans are animals. 2. Strong Inductive Argument: An argument in which the premises provide good reasons for believing the conclusion. The premises make the conclusion likely, but the conclusion might be false even if the premises are true. (Arguments have degrees of validity and can be strengthened with additional information.) a) Exp: 75% of 1000 randomly selected students on campus are Chicago Blackhawk Fans. Therefore, 75% of all students are Chicago Blackhawk Fans. (1) This may not actually be true. Inferential statistics tell us that a statistic from a randomly selected sample can be representative of the population, but in this case, the sample from students on campus at harper is not representative of students on all campuses across the nation, meaning the argument is weak. 3. Sound Argument: When it is valid and has all true premises. (Applies to a deductive argument.) 4. Cogent Argument: When it is strong and has all true premises. (Applies to inductive arguments.) Enumerative Induction A. Enumerative Induction: An argument that begins with claims about some observed members of a group and concludes with a generalization about all of the members from that group. 1. Form: x percent of the observed members of Group A has property P. Therefore, X percent of all members of Group A has property P. a) Exp: 53% of 2000 randomly polled people said that they would support the measure. Therefore, 53% of all people will support the measure. b) If sampling is done right (see MTH 165) then we can conclude that probably the entire group has that property in common. 2. Target Group or Target Population: The group as a whole, the whole collection of individuals in questions (population). 3. Sample Members or Sample: The observed members of the population.

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a) Whether an enumerative inductive argument is strong or weak is dependent on the quality of the sample. If the sample is good, the inference works, the conclusion can be believed and the argument is strong. If the sample is bad, the inference is not applicable to the entire population, so the conclusion cannot be believed and it is a weak argument. b) The more homogenous a target group is with respect to the relevant property, the smaller the sample size can reliably be. c) Sampling (1) A sample has to be representative of the target group, resembling it in relevant ways. (a) Exp: Sampling both genders about abortion. (b) Exp: Sampling in urban and rural districts (2) A non-representative sample is BIASED. (3) Self-selecting sample (convenience sample): When potential survey subjects choose themselves to be a part of a survey. 4. Relevant Property: The property we are observing. 5. A strong enumerative induction can have false premises. Analogical Induction A. Analogy: A comparison of two or more things that are alike and which differ in certain respects. (Analogies can be literary or argumentative.) B. Analogical Induction: Argues that because two or more things are similar in some respect, they must be similar still in some further respect 1. Exp: We once invaded a country because we believed it posed an imminent threat. This new country poses an imminent threat. Therefore, we should invade. a) The reasoning is that the two situations share a similarity, and that similarity is grounds for treating the situations in the same way. b) This follows the form of a deductive argument (Modeus Ponems), but it is not deductive because it has degrees of validity. C. Evaluating Strength of Arguments by Analogy 1. Relevant Similarities - the more relevant similarities there are between the subjects of comparison, the more probable the conclusion. 2. Relevant Dissimilarities - the more relevant dissimilarities there are between the things being compared, the less probable the conclusion. 3. Instances Being Compared - the greater number of instances of relevant similarities, the more probable the conclusion. 4. Diversity Among Cases - the greater the diversity among the cases that exhibit relevant similarities, the more probable the conclusion. a) Form: Thing A has properties 1, 2, 3, and 4. Thing B has properties 1, 2, and 3. Therefore, Thing B probably has property 4.

3 (1) If properties 1, 2, and 3 are relevant to the possession of property 4, then the analogy is a strong argument. If there are properties that are relevant but dissimilar between the cases, then the argument is weaker....