Generalization andArgument 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 2008.

– Javier Sotomayor, a Cuban has the current world record in the men’s high jump.

– Patrick Sjöberg of Sweden has the 2nd highest world record in the high jump

– Igor Paklin, a Russian, has the 3rd place world record,

– Rudolph Povarnitsyn, another Russian, is 4th best. Andrey Silnov

Asians are bad drivers?

African or Black

Anglo or White

Asian and Pacific Islander

Hispanic or Latino

Native American

Percentage of deaths from traffic fatalities

1.8 1.6 2.5 4.7 6.8

Does the stereotype apply to all Asians, or only some?

Are Taiwanese better than Japanese or Vietnamese or Korean drivers? Does it apply to 2nd or 3rd 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 2000

2008 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 GeneralizationInductive 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 GeneralizationDeductive 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?