Inductive Logic Part II Argument from Authority Argt. from Authority (1) S (some person) is a reliable authority regarding P (some statement). (2) S believes P. ∴ (3) P. Argument from Authority Argt. from Authority (1) S (some person) is a reliable authority regarding P (some statement). (2) S believes P. ∴ (3) P. Example: (1) Ed Smith has a Ph.D in physics, and (2) he believes that objects fall at the same rate regardless of weight, once air resistance is taken into account. (3) Therefore, it’s probably true that objects fall like that. Argument from Analogy Argt. from Analogy (1) Items A and B have property X. (2) A also has property Y. ∴ (3) B also has Y. A = Primary Analogate B = Secondary Analogate X = shared property that is known. Y = shared property that is inferred. Argument from Analogy Argt. from Analogy (1) Items A and B have property X. (2) A also has property Y. ∴ (3) B also has Y. A = Primary Analogate B = Secondary Analogate X = shared property that is known. Y = shared property that is inferred. Example: (1) Jane and Nancy both received National Merit Scholarships, both are math majors, and both like Dr. Rich’s classes. (2) Jane received an A in Dr. Rich’s Calculus II class last semester, so (3) Nancy should do equally well in the same class this coming semester. Six Rules for Strong Analogies Analogy: Six Rules (1) Relevance: Relevance of the known shared property (x) to the inferred shared property (y). [The more relevant, the stronger the analogy.] (2) Disanalogy: Nature and degree of disanalogy, i.e., differences between the primary and secondary analogates. [Usually, the more disanalogies, the weaker the analogy.] (3) Similarities: Number of similarities between primary and secondary analogates. [The more similarities, the stronger the analogy.] (4) Sample size: Number and kind of primary analogates. [The more samples, the stronger the analogy.] (5) Sample diversity: Diversity among the primary analogates; randomized sampling strengthens the likelihood of the secondary analogate sharing the contested property. [Usually, the greater the number, the stronger the analogy.] (6) Specificity: Specificity of the conclusion relative to the premises. [The more specific the conclusion, the weaker the analogy.] Analogy: Applying Applying the the Rules Analogy: Rules Jane and Nancy both received National Merit Scholarships, both are math majors, and both like Dr. Rich’s classes. Jane received an A in Dr. Rich’s Calculus II class last semester, so Nancy should do equally well in the same class this coming semester. (1) Relevance All three stated similarities are relevant. [strengthens] (2) Disanalogy Suppose Jane’s SAT math was 800, while Nancy’s was only 450. [weakens] (3) Similarities Suppose there are more similarities, e.g., Jane and Nancy have always performed equally well in their math classes. [strengthens] (4) Sample size Suppose Al, Betty, and Carl also share these same properties with Jane. [strengthens] (5) Sample diversity Suppose all four differ on many other characteristics, some of which Nancy shares, others she does not. [strengthens] (6) Specificity We change the claim to: Nancy will get at least a B. [strengthens] Hypothetical Induction Hypothetical Induction (abduction) (1) P (some surprising phenomenon). (2) If H (some hypothesis), then P. (3) H is the best available explanation of P. ∴ (4) H. Hypothetical Induction Hypothetical Induction (abduction) (1) P (some surprising phenomenon). (2) If H (some hypothesis), then P. (3) H is the best available explanation of P. ∴ (4) H. Example: (1) The left-over pizza has been eaten. (2) If John stopped by, then he would have eaten it. (3) I can’t think of anyone else who might have eaten my pizza without asking. Therefore, (4) John must have stopped by and eaten my pizza. Explanation to the Best Inference Hypothetical induction (abduction; explanation to the best inference) is the positing of some theoretical entity or structure in order to explain some observed phenomenon (a “surprising fact”). ———————— The hypothesis is meant to explain the observed phenomenon, so that if the explanation were true then the fact would no longer be surprising.