Induction Handout
1. Opposed to deduction, inductive arguments try to offer probabilistic support for a conclusion. At best, the conclusion follows in a highly likely way, making it irrational to think that the conclusion is unsupported or false, for example. Importantly, it is always possible that the conclusion is false, even for the best inductive argument. Given the premises, however, it is irrational to think that it is. Note the difference between possibility and probability and do not confuse the two.
2. Inductive arguments still need proper form and true premises to be good arguments. When an inductive argument has the form if the premises are true the conclusion is probably true, it is strong; when it fails to have this form, it is weak; when it has both strong form and verified true premises it is cogent. Remember, induction infers by going beyond the evidence in concluding something; it is always a kind of leap between premise and conclusion. The question is if the leap beyond the evidence is supported by the evidence.
3. To identify an inductive argument, look for indicator language that implies probability as the tactic, words and phrases like the following: it is probably the case that, it is most likely true that, there’s more reason to believe that; look for concepts that imply but also limit.
4. In evaluating inductive arguments, ask, as always, what happens if the premises are true. If the premises are true, does the conclusion likely follow? Additionally, since induction is messier than deduction, ask if the premises are sufficient, or if major gaps are present. Many inductive arguments will be strong, but only if the premises aren’t missing anything or misguided. This is always possible with induction because it is always imperfect.
5. The following are short explanations and tools for three common types of induction and a fourth point on inference to the best explanation (theories).
a. Enumerative Induction (Generalization): uses parts/whole relations; “observed portion” i. Form: (P1) X percent of an observed sample group of a target group have a
particular property. (C) The target group probably has Y percent of that property. ii. To analyze, determine what the sample group, target group, and relevant property
are. iii. To evaluate, make sure that the sample is neither too-small/quantity (hasty
generalization) nor unrepresentative/quality (biased sample). If the argument is neither a hasty generalization nor biased sample, it is likely strong.
iv. If the target is more homogeneous in composition, the sample may be smaller. b. Analogical Induction: uses comparisons between the qualities of things; “alike”
i. Form: (P1) Thing A has properties 1, 2, 3, 4, 5. (P2) Thing B has properties 1, 2, 3, 4. (C) Thing B probably has property 5.
ii. To analyze, determine what the compared things are, what shared properties are given, and which property is being extended.
iii. To evaluate, determine whether the argument is a faulty analogy or not: verify that the shared properties are relevant to the extended property, consider the ways in which the things are dissimilar and if this is significant, consider whether number of instances and diversity among cases is relevant to the argument. If
Prof. Eckel, U. Toledo, FA17
there’s no good reason to think the argument presents a faulty analogy, it is likely strong.
c. Causal Induction: uses patterns of causal relations between events in time; “X caused Y” i. Form: (P1; instance 1) Factors A, B, C, and D precede event E. (P2; instance 2)
Factors A and B precede non-E. (P3; instance 3) An increase in C correlates with an increase in E. (P4; instance 4) Factors C and F precede E. (C; inference) C is probably the cause of event E.
ii. To analyze, determine the instances and the range of factors and events present, determine the precise causal claim in the conclusion, determine which methods are employed (agreement, difference, joint, correlation), ask whether relevant factors are missing.
iii. To evaluate, determine whether relevant factors are misidentified, multiple factors are mishandled, coincidence is asserted as causal, correlations are assumed as causal relations, post hoc fallacy is present, cause and effect are confused or not. If not, the argument is likely strong.
d. Inference to the Best Explanation: uses theoretical explanations as accounts of events to argue that a theory is good or worth accepting as an account.
i. Form: (P1) Event E. (P2) Theory 1 is the best explanation for event E. (C) Theory 1 is probably an adequate account.
ii. Opposed to particular causal accounts, theories are general frameworks explaining why or how some class of instances is the case. Theories explain why or how something is the case; arguments assert that something is the case. Theories need to be asserted in the form of inference to the best explanation if they are to be advanced; otherwise, they remain speculative.
iii. The focus should be on theory as actual inference, not theoretical accounts that are procedural (How to do X), interpretive (What X means), functional (How X operates in a productive structure), or teleological (What X is for, its purpose or end).
iv. To analyze look for the event and proposed theory, understanding them as clearly as possible.
v. To evaluate, everything rests on P2, determining whether the theory is actually better than the competitors. First, make sure the theory is internally and externally consistent. Then, make sure the theory is the best because it ranks highest using the criteria for an adequate theory: testability, fruitfulness, scope, simplicity, conservatism. If P2 is justifiably true, the argument is likely strong.
Prof. Eckel, U. Toled
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