Inductive Argument Forms

Induction vs. deduction Inductive arguments aim to make the conclusion probable, not certain, though sometimes, extremely probable. False conclusion is logically compatible with true premises. A strong inductive argument: one where true premises would render the conclusion highly likely. inductive counterpart of validity

Induction vs. deduction Strength of inductive argument comes in degrees. Additional information can make it rational to retract the conclusion, without retracting the premises.

Statistical Syllogism

universal modus ponens statistical syllogism Most universal modus ponens All As are Bs x is an A x is a B statistical syllogism Still a reasonable inference, but no longer deductive, no longer UMP

How strong is a statistical syllogism? Depends on proportion of As that are premised to be Bs whatever other information you possess rule of total evidence

Rule of Total Evidence Strength of any inductive argument is determined not just by what’s internal to the argument, but by everything else you know.

Defeaters: considerations that tell against accepting a conclusion. Rebutting defeaters: evidence for thinking the conclusion is false. Undercutting defeaters: reasons for rejecting the argument that aren’t reasons for rejecting the conclusion.

Two arguments; one for thinking she can, one for thinking she can’t Sheila can read music. (CONCLUSION) Most musicians can read music. (PREMISE) Sheila is a musician. (PREMISE) Most drummers can’t read music. (PREMISE) Sheila is a drummer. (PREMISE) Solid black indicates positive support Two arguments; one for thinking she can, one for thinking she can’t Dotted blue indicates defeat in this case, rebutting defeat What to conclude?

Statistical syllogism n% of As are Bs. x is an A. x is a B.

Statistical syllogism n% of As are Bs. x is an A. x is a B. reference class

Statistical syllogism n% of As are Bs. x is an A. x is a B. reference class attribute class We’re attributing B to x, by reference to its being A.

Statistical syllogism In the earlier example, Drummer is a narrower reference class than Musician: all drummers are musicians, but not vice versa. Use statistical syllogism only for the narrowest reference class for which you have information. Given our evidence, we should infer that Sheila cannot read music.

Inductive Generalization

Inductive generalization x% of observed As have been Bs. x% of As are Bs.

Inductive generalization x% of observed As have been Bs. x% of As are Bs. sample

Inductive generalization x% of observed As have been Bs. x% of As are Bs. sample population

Sample must be representative of the population. no systematic difference large and random have variety that matches population homogeneous population carefully crafted (stratified) sample

Defeaters for Inductive Generalization

Biased sample serves as undercutting defeater. Most people think dinner should start at 4 P.M. (CONCLUSION) Most of the people we surveyed thought dinner should start at 4 P.M. (PREMISE) The survey was conducted at a retirement home. (PREMISE) Biased sample serves as undercutting defeater. not a reason to deny the conclusion, but a reason not to believe it on the basis of this argument (hence the arrow attacking the other arrow, not the conclusion box)

Fallacies of inductive generalization Hasty generalization small sample Biased statistics unrepresentative sample Misleading vividness relying on anecdotes, rather than inductive generalization

Fallacies of inductive generalization Argument from counterinstances rejecting statistical generalization (“most As are Bs”) on the grounds of one or a few counterinstances (“here’s an A that’s not a B”) note, this is a legitimate defeater for a universal generalization (“all As are Bs”)

Representativeness heuristic (Unreliable) System1 heuristic for making fast judgments about probabilities, relative frequencies Probability that something is a member of a group based on how much it resembles a stereotypical member of that group

Availability heuristic Another unreliable System1 heuristic for making fast judgments about probabilities, relative frequencies Judge how common something is on the basis of how easy it is to think of examples but easiness is affected by vividness, recently, rarity, etc. factors other than how common it really is

a.k.a. Analogical argument Argument From Analogy a.k.a. Analogical argument

Argument from analogy x resembles y in known respects. y has F. x has F. Dolphins and whales breathe air, give live birth, and are warm-blooded. Dolphins lactate. Whales (probably) lactate.

Strength of analogical argument Strength of analogy (degree of similarity) relevance of similarities Fallacy of false analogy otherwise

Inference to the Best Explanation

Inference to the best explanation We have such-and-such data. Hypothesis H would explain the data, sufficiently well and do so better than any rival hypothesis we can think of. Therefore, H.

Best explanation? Genuinely explains Has some independent plausibility Is simple and unified rather than a grab-bag of independent hypotheses Ockham’s Razor: everything else being equal, we should believe the simpler hypothesis over the more complicated one.

Balance of Features

each feature serves as independent evidence It was a great movie. (CONCLUSION) The plot was engaging. (PREMISE) The acting was superb. (PREMISE) The cinematography was fantastic. (PREMISE) The characters were well-developed. (PREMISE) We argue that the movie was great by listing some “greatness-making” features the movie had. The argument has an independent-premise (rather than a linked-premise) structure. each feature serves as independent evidence hence the converging, rather than bracketed, arrows

“Greatness-ruining” features serve as rebutting defeaters. It was a great movie. (CONCLUSION) The plot was engaging. (PREMISE) The acting was superb. (PREMISE) The characters were well-developed. (PREMISE) The cinematography was fantastic. (PREMISE) The special effects were terrible. (PREMISE) It was 6 hours long. (PREMISE) “Greatness-ruining” features serve as rebutting defeaters.