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Week 7 – Induction.doc

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University of Toronto Mississauga
Nate Charlow

Week 7 – Induction Induction vs. Deduction Deductive argument is one that aspires to validity. But an argument can be good without aspiring to validity 1. The sun has risen everyday in history of the world 2. The sun will rise everyday Two notes: • Clearly it’s an argument. Premise is offered as reason for conclusion • Logically possible for premise to be true when conclusion is false, since it’s possible that the sun doesn’t rise e.g. tomorrow Arguments can offer two kinds of reasons for conclusions: • Conclusive – given premises are true, conclusions must be true • Defeasible – given premises are true, reasonable to believe conclusion in absence of further considerations against it We have criterion for assessing whether (deductive) argument gives conclusive reasons for its conclusion. Need assessing whether (inductive) argument gives defeasible reason for its conclusion. Refer to this criterion as strength Strength vs. Validity: Defeasible Strength unlike validity is defeasible: inductively strong argument can become weak when you add premises, while valid argument cannot be invalid when add premises 1. All ravens are black 2. If there is a raven on top of Pike Peak, it’s black ->Valid 1. All ravens are black 2. There might be a while raven 3. If there is a raven on top of Pikes Peak, it’s black ->Still valid Strength, unlike validity, is degreed: arguments can be more or less strong, while arguments cannot be more (or less) valid. • This, together with the defeasible character of strength, means that strength is more subtle than validity. o Strong arguments can be made weak o Inductive arguments can provide some reason for their conclusion whose strength can be modulated (ratcheted up or down) in subtle ways Strength vs. Validity: Which is Preferable? Such complexities might seem to make inductive arguments inferior to deductive arguments. That’s an illusion. Uncertainty of conclusion introduced by making an inductive inference is matched by uncertainty about truth about one or more of argument’s premises • Intuitively, arguments provide same amount of justification for believing their conclusions to be true: probable but not 100% • Difference is premise can not be 100% (but reasoning is conclusive, which one argument can be 100% but reasoning is defeasible Uncertainty and Deduction Mistake to equate fact that deductively valid arguments are conclusive reasons for their conclusions (give that premises are true) with the idea that deductively valid arguments make their conclusions certain • Deductive arguments don’t generally make conclusion certain unless we’re certain of their premises • Likelihood of error accumulates as deductive arguments invoke more premises Statistical Generalization Induction used frequently to infer characteristics of group/population (one large enough for observing of its members impracticable) from characteristics of sample of that group 1. Statistical claim: all members of sample of P are F 2. All members of P are F • Is sample large enough? • Is sample biased or representative? Sample Size ~ Worse than large samples • Small samples can be easily affected by runs of luck • Hasty generalization is statistical generalization made on basis of sample size that is too small • Large sample doesn’t guarantee that statistical generalization will be strong, if sample is not representative of intended class of objects or events • Biased sampling will not support the corresponding generalization o Biased often identified, posteriori, through observation o Large sample leads to incorrect prediction ~ look for explanation for discrepancy Statistical Syllogisms Use statistical claims to reason to claims about characteristics of member of the intended group ~ can be relatively strong or relatively weak • No formal way to characterize when statistical syllogisms are strong: x can be extremely high, but corresponding syllogism extremely weak • Using reference class may lead to another conclusion o Need to draw background knowledge to inform us latter syllogisms is better indicator o Note: inductive inferences are defeasible Inference to the Best Explanation Unlock the general features of this sort of reasoning to understand how it works The structure of IBE 1. Observa
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