Inductive Reasoning

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Argument A is a standard case of induction by enumeration. In B we have a standard case of a statistical syllogism. Therelationship between A and B and the example of modified induction by enumeration is that example 1 of Modified Inductionby Enumeration and A have the same first premise (87% of polled IBS are D). As a result, we can conclude that 87% of allIBS are D in both arguments, though we do not do this explicitly in example 1 of Modified Induction by Enumeration.Instead, in example 1 we implicitly use as evidence the statement which occurs as the conclusion of argument A, and thisinformation, along with the premise S is IBS, is used as a statistical syllogism of the form shown in argument B. In short,Modified Induction by Enumeration functions much like a statistical syllogism whose first premise is derived on thebasis of induction by enumeration.Since the conclusion in the argument form of modified induction by enumeration depends, in part, on a statistical syllogism,the percentage of the sample that has the property in question must be greater than 50. For example, consider thefollowing:Example 210% of the voters polled favored proposal B. Johnny is a voter, and therefore Johnny favors proposal B.The form of the above argument is:10% of observed V are FJ is VTherefore, J is FAs with example 1, the above can be understood on the basis of induction by enumeration and a statistical syllogism. Therelevant instances of these argument forms are the following:A)10% of observed V are FTherefore 10% of all V are FB)10% of all V are FJ is VTherefore, J is F.Although A satisfies all the conditions necessary for an acceptable instance of induction by enumeration (correct form andcorrect percentages), argument B is not an acceptable instance of a statistical syllogism since the percentage of V’s whichare F is not greater than 50%. Since the acceptability of example 2 rests on both argument A and B, and since argument Bis unacceptable, example 2 is unacceptable.Finally,Example 3100% of McGivney students polled favored a reduction in classroom interruptions. Anwal favors a reduction in classroominterruptions since Anwal is a McGivney student.100% of observed M are FA is MTherefore, A is F
The two arguments relevant to understanding and assessing example 3 are these:A)100% of observed M are FTherefore 100% of all M are FB)100% of all M are FA is MTherefore, A is FArgument A is clearly an acceptable instance of induction by enumeration, whereas argument B is not an acceptableinstance of a statistical syllogism. In argument B, if the premises are true then the conclusion must also be true; in otherwords, argument B is valid. The issue that confronts us, then, is whether example 3 is an acceptable instance of modifiedinduction by enumeration.The answer here is yes. If the premises of example 3 are true, then the conclusion is probably true. Additionally, since theconclusion rests, in part, on a sample of all M’s, it might be false: Anwal may be a McGivney student who does not favor areduction in classroom interruptions. Understood in terms of arguments A and B, example 3 is acceptable, since induction byenumeration is an acceptable argument form and argument B is an acceptable deductive argument. Consideration of theabove cases gives the following as the argument form of modified induction by enumeration:Y% of observed A are B (where Y is greater than 50% and less than or equal to 100)X is ATherefore, x is BInduction by Enumeration Statistical Syllogism Modified Induction by EnumerationY% of observed A are BTherefore, Y% of all A are B(where Y is equal to or greater than 0 and equal toor less than 100)Y% of all A are B (where Y is greater than 50 andless than 100)X is ATherefore, X is BY% of observed A are B (where Y is greater than50% and less than or equal to 100)X is ATherefore, x is B*The argument form of modified induction by enumeration is weaker than the argument form of the statistical syllogism. This is so because the statisticalsyllogism part of a modified induction by enumeration depends on an argument of the form induction by enumeration. As a result, in the case ofmodified induction by enumeration, the X which is said to be B depends upon the strength of the induction by enumeration argument. That is, modifiedinduction by enumeration, understood in terms of two inductive arguments—statistical syllogism and induction by enumeration—is likely to lead to falseconclusions more often than is statistical syllogism, since the possibility of error is greater when two inductive arguments, rather than one, are considered.Question to think about: Is Induction by Enumeration ultimately reducible to Inference to the Best Explanation?
Page 1 and 2: Inductive Arguments (Inferences)Ind
Page 3: 75% of all T are MD is TTherefore,

Inductive Reasoning

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