Inductive Reasoning

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We may construe the courses which she has so far taken as a subset of all the courses she will take. This argument predictsfuture occurrences on the basis of past occurrences.Example 4None of the IB students interviewed thought that final exams were very well scheduled. Hence, no IB student thinks thatfinal exams are very well scheduled.0% of interviewed S are ETherefore, 0% of all S are ELike the previous, this argument has a conclusion which is a generalization about all the members of a particular class basedon a sample of the class. This is the general feature of all instances of induction by enumeration.We can generalize the above four arguments forms as follows (using “observed” to represent adjectives like ‘sampled’,‘polled’, and ‘interviewed,’):Y% of observed A are BTherefore, Y% of all A are B(where Y is equal to or greater than 0 and equal to or less than 100)The Statistical SyllogismHere we draw conclusions about a particular member of a class, based on information about all members of the class.Example 180% of the chickens on this farm are grade A. Since Gobble Neck is a chicken on this farm, Gobble Neck is grade A.80% of all C are AM is CTherefore, M is AExample 2Most of the remarks made by Sui are insulting. The next remark made will be insulting because Sui will make the remark.*“Most” is understood as ‘more than half’. And so it is more likely than not that the next remark will be insulting.More than half of all S are IN is STherefore, N is IExample 360,000 of the tickets in the drum were purchased by people from Michigan, 15,000 of the tickets were purchased by peoplefrom Canada, and 5000 of the tickets were purchased by people from Ohio. The million-dollar ticket will be drawn from thedrum. Hence, the million-dollar ticket was purchased by someone from Michigan.(T = tickets in the drum; M = tickets by people from Michigan; D = million-dollar ticket)
75% of all T are MD is TTherefore, D is MExample 415% of the people who enter the Ohio lottery win money in the lottery. Hence, Ebenezer will win money in the lottery sincehe entered the Ohio lottery.15% of O are WE is OTherefore, E is WIt is more likely than not that Ebenezer will not win money in the lottery. In a good inductive argument of the form of astatistical syllogism, more than 50% of the class in question must have the property in question.In a good inductive argument of the form of a statistical syllogism, less than 100% and more than 50% of the class inquestion must have the property in question.The argument form of statistical syllogisms:Y% of all A are B (where Y is greater than 50 and less than 100)X is ATherefore, X is BModified Induction by EnumerationIn the argument forms above, we drew inferences about all the members of a class based on the results of sampling some ofthe members of the class (induction by enumeration), and we drew certain inferences about a particular member of a classgiven information about all the members of a class (statistical syllogism). Now we shall examine an argument form whichenables us to draw certain inferences about a particular member of a class given the results of sampling some of themembers of the class. These arguments are instances of modified induction by enumeration.Example 187% of IB students polled were dissatisfied with the scheduling of final exams. Since Shalia is an IB student, she isdissatisfied with the scheduling of final exams.87% of polled IBS are DS is IBSTherefore, S is DTo see why this is a good inductive argument, consider the following:A) (Induction by Enumeration)87% of polled IBS are DTherefore 87% of all IBS are DB) (Statistical Syllogism)87% of all IBS are DS is IBSTherefore, S is D
Page 1: Inductive Arguments (Inferences)Ind
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Inductive Reasoning

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