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Generalization and Argument by Example forms of inductive reasoning
argument from generalization Generalizations are one of the most common forms of reasoning. Definition: Generalizing involves attempts to identify general patterns, gauge what is typical or average, or formulate general rules Generalizing is necessary, indispensable – Imagine what life would be like if you couldn’t form generalizations--if all knowledge was particularized and fragmented. Generalizing is also fraught with risks – Think how many false stereotypes people hold about race, gender, age, etc. – What if Jim Abbot had believed people who said you couldn’t pitch in the major leagues with only one arm? – What if Stephen Hawking presumed that a person in a wheelchair couldn’t be a leading theoretical physicist?
Bondes are dumb? Blondes are dumb? – Does the stereotype refer only to natural blondes? Does the stereotype only to female, not male blondes? – Reese Witherspoon attended Stanford and won an oscar. – Hillary Clinton, law degree from Yale – Lisa Kudrow, degree in biology from Vassar – Sharon Stone has a reported IQ of 154 – Kim Campbell, Canada’s first female prime minister, is blonde.
White men can’t jump? – Does the stereotype only apply to basketball? – Andrey Silnov, a Russian, won the gold medal in the high jump in Beijing in – Javier Sotomayor, a Cuban has the current world record in the men’s high jump. – Patrick Sjöberg of Sweden has the 2 nd highest world record in the high jump – Igor Paklin, a Russian, has the 3 rd place world record, – Rudolph Povarnitsyn, another Russian, is 4 th best. Andrey Silnov
Asians are bad drivers? African or Black Anglo or White Asian and Pacific Islande r Hispani c or Latino Native Americ an Percenta ge of deaths from traffic fatalities Does the stereotype apply to all Asians, or only some? Are Taiwanese better than Japanese or Vietnamese or Korean drivers? Does it apply to 2 nd or 3 rd generation Asian- Americans? A study by the NHTSA published in 2006 revealed that Asian drivers were not responsible for a disproportionate share of fatal accidents As a percentage of the population Hispanics and Native Americans accounted for more fatal crashes.
An “Indian” kid always wins the spelling bee? An “Indian” kid (sub-Asian continent) always wins the national spelling bee? 4 of the past 9 winners were of Indian descent National Spelling Bee Winners Since Sameer Mishra 2007 Evan O’Dorney 2006 Katharine “Kerry” Close 2005 Anurag Kashyap 2004 David Scott Pilarski Tidmarsh 2003 Sai R. Gunturi 2002 Pratyush Buddiga 2001 Sean Conley 2000 George Abraham Thampy
Polling and surveys as a form of generalizing Public opinion polls Nielsen ratings for TV shows American Idol voting ratemyprofessor.com call-screening on radio talk shows To be truly valid a sample should be: – random – representative – sufficient in size.
universal and statistical generalizations Universal generalization: Universal generalization: claims that all members of a group have certain attributes or characteristics – Asians are good at math. Feminists hate men. – Republicans favor tax cuts, Democrats oppose tax cuts. Statistical generalization: Statistical generalization: claims that a percentage or a portion of a group has a certain attribute or property. – 76% of felons are recidivists – 1 out of 3 children in the U.S. is born out of wedlock – 19 of the 21 hijackers on Sept. 11 were Saudi Arabians. Contingent generalization: based on conditions or qualifications that must be met for the generalization to hold true. Generalizations are more likely to hold true if they are confined to specific times, places, or situations – Most serial killers are male – The majority of journalists are Democrats
inductive and deductive generalizations Two types of generalizations: inductive and deductive Inductive Generalization: Inductive Generalization: bases a larger inference on an example, sample, or particular instance – example: Babbs bought a Saturn and it runs well. Biff bought a Saturn and it runs well. I guess Saturns are reliable cars. (the generalization is based on a nonrandom sample of 3 cars) – example: Of the 19 hijackers on Sept. 11, 15 were Saudis. I think we can safely conclude that Saudi Arabia is a breeding ground for terrorists.
inductive and deductive generalizations Deductive Generalization: Deductive Generalization: proceeds from a general rule or general principle to a specific case – example: Brazilians love soccer. Hector is from Brazil, so he probably loves soccer too. – example: Don’t give money to that vagrant. They are all winos and drug addicts. – example: Biff is a Republican, so of course he’ll be opposed to gun control.
tests of generalizations How valid or reliable is the “general rule”? Is the sample from which the generalization is drawn random, and representative? Is the sample from which the generalization is drawn sufficient? (sample size) Are there any exceptions to the rule? Even if the general rule is true, does it apply in this particular case?
Reasoning by Example A sub-set of inductive generalizations (a sample of one, or a few) Offers a generalization based on one or more cases to other cases which are presumed to share the same features as the example. Examples may be based on personal experience, hearsay, anecdotes, or case studies – example: testimonials on infomercials, “The X47 Super mop worked so well I threw away all my other mops!” – example: deciding whether to take a class, see a movie, or eat at a particular restaurant based on a friend’s say so.
reasoning by example: Beware of testimonials! These testimonials serve as examples of how effective diets, supplements, or exercise equipment is He is a real person, but was he selected at random?
Reasoning by example: Beware of testimonials! “Before” and “After” pictures for miracle diets, or testimonials for various products are based on examples.
tests of examples Is the example relevant or germane? How typical or representative is the example? – Watch out for hand-picked examples Do the examples cover a critical period of time? Are there enough examples to prove the case? Are there any negative or contradictory examples?