IF YOU HAVE TAKEN A COURSE IN LOGIC, YOU ARE PROBABLY FAMILIAR WITH THESE FO

RMULAS. THEIR VALIDITY IS INTUITIVELY CLEAR: THE CONJUNCTION A&B IS FALSE WH

EN EITHER, OR BOTH, OF ITS PARTS ARE FALSE. THIS IS PRECISELY WHAT ~A OR ~B

SAYS. AND THE DISJUNCTION A OR B IS FALSE ONLY WHEN BOTH A AND B ARE FALSE,

WHICH IS PRECISELY WHAT ~A AND ~B SAYS.

YOU WILL RARELY GET AN ARGUMENT WHOSE MAIN STRUCTURE IS BASED ON THESE RULES

--THEY ARE TOO MECHANICAL. NEVERTHELESS, DEMORGAN’S LAWS OFTEN HELP SIMPLIFY

, CLARIFY, OR TRANSFORM PARTS OF AN ARGUMENT. THEY ARE ALSO USEFUL WITH GAME

S.

EXAMPLE: (DEMORGAN’S LAW)

IT IS NOT THE CASE THAT EITHER BILL OR JANE IS GOING TO THE PARTY.

THIS ARGUMENT CAN BE DIAGRAMMED AS ~(B OR J), WHICH BY THE SECOND OF DEMORGA

N’S LAWS SIMPLIFIES TO (~B AND ~J). THIS DIAGRAM TELLS US THAT NEITHER OF TH

EM IS GOING TO THE PARTY.

A UNLESS B

~B-->A

"A UNLESS B" IS A RATHER COMPLEX STRUCTURE. THOUGH SURPRISINGLY WE USE IT WI

TH LITTLE THOUGHT OR CONFUSION IN OUR DAY-TO-DAY SPEECH.

TO SEE THAT "A UNLESS B" IS EQUIVALENT TO "~B-->A," CONSIDER THE FOLLOWING S

ITUATION:

BIFF IS AT THE BEACH UNLESS IT IS RAINING.

GIVEN THIS STATEMENT, WE KNOW THAT IF IT IS NOT RAINING, THEN BIFF IS AT THE

BEACH. NOW IF WE SYMBOLIZE "BIFF IS AT THE BEACH" AS B, AND "IT IS RAINING"

AS R, THEN THE STATEMENT CAN BE DIAGRAMMED AS ~R-->B.

CLASSIFICATION

IN LOGIC II, WE STUDIED DEDUCTIVE ARGUMENTS. HOWEVER, THE BULK OF ARGUMENTS

ON THE GMAT ARE INDUCTIVE. IN THIS SECTION WE WILL CLASSIFY AND STUDY THE MA

JOR TYPES OF INDUCTIVE ARGUMENTS.

AN ARGUMENT IS DEDUCTIVE IF ITS CONCLUSION NECESSARILY FOLLOWS FROM ITS PREM

ISES--OTHERWISE IT IS INDUCTIVE. IN AN INDUCTIVE ARGUMENT, THE AUTHOR PRESEN

TS THE PREMISES AS EVIDENCE OR REASONS FOR THE CONCLUSION. THE VALIDITY OF T

HE CONCLUSION DEPENDS ON HOW COMPELLING THE PREMISES ARE. UNLIKE DEDUCTIVE A

RGUMENTS, THE CONCLUSION OF AN INDUCTIVE ARGUMENT IS NEVER CERTAIN. THE TRUT

H OF THE CONCLUSION CAN RANGE FROM HIGHLY LIKELY TO HIGHLY UNLIKELY. IN REAS

ONABLE ARGUMENTS, THE CONCLUSION IS LIKELY. IN FALLACIOUS ARGUMENTS, IT IS I

MPROBABLE. WE WILL STUDY BOTH REASONABLE AND FALLACIOUS ARGUMENTS.

WE WILL CLASSIFY THE THREE MAJOR TYPES OF INDUCTIVE REASONING--GENERALIZATIO

N, ANALOGY, AND CAUSAL--AND THEIR ASSOCIATED FALLACIES.

GENERALIZATION

GENERALIZATION AND ANALOGY, WHICH WE CONSIDER IN THE NEXT SECTION, ARE THE M

AIN TOOLS BY WHICH WE ACCUMULATE KNOWLEDGE AND ANALYZE OUR WORLD. MANY PEOPL

E DEFINE GENERALIZATION AS "INDUCTIVE REASONING." IN COLLOQUIAL SPEECH, THE

PHRASE "TO GENERALIZE" CARRIES A NEGATIVE CONNOTATION. TO ARGUE BY GENERALIZ

ATION, HOWEVER, IS NEITHER INHERENTLY GOOD NOR BAD. THE RELATIVE VALIDITY OF

A GENERALIZATION DEPENDS ON BOTH THE CONTEXT OF THE ARGUMENT AND THE LIKELI

HOOD THAT ITS CONCLUSION IS TRUE. POLLING ORGANIZATIONS MAKE PREDICTIONS BY

GENERALIZING INFORMATION FROM A SMALL SAMPLE OF THE POPULATION, WHICH HOPEFU

LLY REPRESENTS THE GENERAL POPULATION. THE SOUNDNESS OF THEIR PREDICTIONS (A

RGUMENTS) DEPENDS ON HOW REPRESENTATIVE THE SAMPLE IS AND ON ITS SIZE. CLEAR

LY, THE LESS COMPREHENSIVE A CONCLUSION IS THE MORE LIKELY IT IS TO BE TRUE.

EXAMPLE:

DURING THE LATE SEVENTIES WHEN JAPAN WAS RAPIDLY EXPANDING ITS SHARE OF THE

AMERICAN AUTO MARKET, GM SURVEYED OWNERS OF GM CARS AND ASKED THEM WHETHER T

HEY WOULD BE MORE WILLING TO BUY A LARGE, POWERFUL CAR OR A SMALL, ECONOMICA

L CAR. SEVENTY PERCENT OF THOSE WHO RESPONDED SAID THAT THEY WOULD PREFER A

LARGE CAR. ON THE BASIS OF THIS SURVEY, GM DECIDED TO CONTINUE BUILDING LARG

E CARS. YET DURING THE’80S, GM LOST EVEN MORE OF THE MARKET TO THE JAPANESE

..

WHICH ONE OF THE FOLLOWING, IF IT WERE DETERMINED TO BE TRUE, WOULD BEST EXP

LAIN THIS DISCREPANCY.

(A) ONLY 10 PERCENT OF THOSE WHO WERE POLLED REPLIED.

(B) FORD WHICH CONDUCTED A SIMILAR SURVEY WITH SIMILAR RESULTS CONTINUED TO

BUILD LARGE CARS AND ALSO LOST MORE OF THEIR MARKET TO THE JAPANESE.

(C) THE SURVEYED OWNERS WHO PREFERRED BIG CARS ALSO PREFERRED BIG HOMES.

(D) GM DETERMINED THAT IT WOULD BE MORE PROFITABLE TO MAKE BIG CARS.

(E) EIGHTY PERCENT OF THE OWNERS WHO WANTED BIG CARS AND ONLY 40 PERCENT OF

THE OWNERS WHO WANTED SMALL CARS REPLIED TO THE SURVEY.

THE ARGUMENT GENERALIZES FROM THE SURVEY TO THE GENERAL CAR-BUYING POPULATIO

N, SO THE RELIABILITY OF THE PROJECTION DEPENDS ON HOW REPRESENTATIVE THE SA

MPLE IS. AT FIRST GLANCE, CHOICE (A) SEEMS RATHER GOOD, BECAUSE 10 PERCENT D

OES NOT SEEM LARGE ENOUGH. HOWEVER, POLITICAL OPINION POLLS ARE TYPICALLY BA

SED ON ONLY .001 PERCENT OF THE POPULATION. MORE IMPORTANTLY, WE DON’T KNOW

WHAT PERCENTAGE OF GM CAR OWNERS RECEIVED THE SURVEY. CHOICE (B) SIMPLY STAT

ES THAT FORD MADE THE SAME MISTAKE THAT GM DID. CHOICE (C) IS IRRELEVANT. CH

OICE (D), RATHER THAN EXPLAINING THE DISCREPANCY, GIVES EVEN MORE REASON FOR

GM TO CONTINUE MAKING LARGE CARS. FINALLY, CHOICE (E) POINTS OUT THAT PART

OF THE SURVEY DID NOT REPRESENT THE ENTIRE PUBLIC, SO (E) IS THE ANSWER.

ANALOGY

TO ARGUE BY ANALOGY IS TO CLAIM THAT BECAUSE TWO THINGS ARE SIMILAR IN SOME

RESPECTS, THEY WILL BE SIMILAR IN OTHERS. MEDICAL EXPERIMENTATION ON ANIMALS

IS PREDICATED ON SUCH REASONING. THE ARGUMENT GOES LIKE THIS: THE METABOLIS

M OF PIGS, FOR EXAMPLE, IS SIMILAR TO THAT OF HUMANS, AND HIGH DOSES OF SACC

HARINE CAUSE CANCER IN PIGS. THEREFORE, HIGH DOSES OF SACCHARINE PROBABLY CA

USE CANCER IN HUMANS.

CLEARLY, THE GREATER THE SIMILARITY BETWEEN THE TWO THINGS BEING COMPARED TH

E STRONGER THE ARGUMENT WILL BE. ALSO THE LESS AMBITIOUS THE CONCLUSION THE

STRONGER THE ARGUMENT WILL BE. THE ARGUMENT ABOVE WOULD BE STRENGTHENED BY C

HANGING "PROBABLY" TO "MAY." IT CAN BE WEAKENED BY POINTING OUT THE DISSIMIL

ARITIES BETWEEN PIGS AND PEOPLE.

EXAMPLE:

JUST AS THE FISHING LINE BECOMES TOO TAUT, SO TOO THE TRIALS AND TRIBULATION

S OF LIFE IN THE CITY CAN BECOME SO STRESSFUL THAT ONE’S MIND CAN SNAP.

WHICH ONE OF THE FOLLOWING MOST CLOSELY PARALLELS THE REASONING USED IN THE

ARGUMENT ABOVE?

(A) JUST AS THE BOW MAY BE DRAWN TOO TAUT, SO TOO MAY ONE’S LIFE BE WASTED P

URSUING SELF-GRATIFICATION.

(B) JUST AS A GAMBLER’S FORTUNES CHANGE UNPREDICTABLY, SO TOO DO ONE’S CAREE

R OPPORTUNITIES COME UNEXPECTEDLY.

(C) JUST AS A PLANT CAN BE KILLED BY OVER WATERING IT, SO TOO CAN DRINKING T

OO MUCH WATER LEAD TO LETHARGY.

(D) JUST AS THE ENGINE MAY RACE TOO QUICKLY, SO TOO MAY LIFE IN THE FAST LAN

E LEAD TO AN EARLY DEATH.

(E) JUST AS AN ACTOR MAY BECOME STRESSED BEFORE A PERFORMANCE, SO TOO MAY DW

ELLING ON THE NEGATIVE CAUSE DEPRESSION.

THE ARGUMENT COMPARES THE TAUTNESS IN A FISHING LINE TO THE STRESS OF CITY L

IFE; IT THEN CONCLUDES THAT THE MIND CAN SNAP JUST AS THE FISHING LINE CAN.

SO WE ARE LOOKING FOR AN ANSWER-CHOICE THAT COMPARES TWO THINGS AND DRAWS A

CONCLUSION BASED ON THEIR SIMILARITY. NOTICE THAT WE ARE LOOKING FOR AN ARGU

MENT THAT USES SIMILAR REASONING, BUT NOT NECESSARILY SIMILAR CONCEPTS. IN F

ACT, AN ANSWER-CHOICE THAT MENTIONS EITHER TAUTNESS OR STRESS WILL PROBABLY

BE A SAME-LANGUAGE TRAP.

CHOICE (A) USES THE SAME-LANGUAGE TRAP--NOTICE "TOO TAUT." THE ANALOGY BETWE

EN A TAUT BOW AND SELF-GRATIFICATION IS WEAK, IF EXISTENT. CHOICE (B) OFFERS

A GOOD ANALOGY BUT NO CONCLUSION. CHOICE (C) OFFERS BOTH A GOOD ANALOGY AND

A CONCLUSION; HOWEVER, THE CONCLUSION, "LEADS TO LETHARGY," UNDERSTATES THE

SCOPE OF WHAT THE ANALOGY IMPLIES. CHOICE (D) OFFERS A STRONG ANALOGY AND A

CONCLUSION WITH THE SAME SCOPE FOUND IN THE ORIGINAL: "THE ENGINE BLOWS, TH

E PERSON DIES"; "THE LINE SNAPS, THE MIND SNAPS." THIS IS PROBABLY THE BEST

ANSWER, BUT STILL WE SHOULD CHECK EVERY CHOICE. THE LAST CHOICE, (E), USES L

ANGUAGE FROM THE ORIGINAL, "STRESSFUL," TO MAKE ITS WEAK ANALOGY MORE TEMPTI

NG. THE BEST ANSWER, THEREFORE, IS (D).

CAUSAL REASONING

OF THE THREE TYPES OF INDUCTIVE REASONING WE WILL DISCUSS, CAUSAL REASONING

IS BOTH THE WEAKEST AND THE MOST PRONE TO FALLACY. NEVERTHELESS, IT IS A US

EFUL AND COMMON METHOD OF THOUGHT.

TO ARGUE BY CAUSATION IS TO CLAIM THAT ONE THING CAUSES ANOTHER. A CAUSAL AR

GUMENT CAN BE EITHER WEAK OR STRONG DEPENDING ON THE CONTEXT. FOR EXAMPLE, T

O CLAIM THAT YOU WON THE LOTTERY BECAUSE YOU SAW A SHOOTING STAR THE NIGHT B

EFORE IS CLEARLY FALLACIOUS. HOWEVER, MOST PEOPLE BELIEVE THAT SMOKING CAUSE

S CANCER BECAUSE CANCER OFTEN STRIKES THOSE WITH A HISTORY OF CIGARETTE USE.

ALTHOUGH THE CONNECTION BETWEEN SMOKING AND CANCER IS VIRTUALLY CERTAIN, AS

WITH ALL INDUCTIVE ARGUMENTS IT CAN NEVER BE 100 PERCENT CERTAIN. CIGARETTE

COMPANIES HAVE CLAIMED THAT THERE MAY BE A GENETIC PREDISPOSITION IN SOME P

EOPLE TO BOTH DEVELOP CANCER AND CRAVE NICOTINE. ALTHOUGH THIS CLAIM IS HIGH

LY IMPROBABLE, IT IS CONCEIVABLE.

THERE ARE TWO COMMON FALLACIES ASSOCIATED WITH CAUSAL REASONING:

1. CONFUSING CORRELATION WITH CAUSATION.

TO CLAIM THAT A CAUSED B MERELY BECAUSE A OCCURRED IMMEDIATELY BEFORE B IS C

LEARLY QUESTIONABLE. IT MAY BE ONLY COINCIDENTAL THAT THEY OCCURRED TOGETHER

, OR SOMETHING ELSE MAY HAVE CAUSED THEM TO OCCUR TOGETHER. FOR EXAMPLE, THE

FACT THAT INSOMNIA AND LACK OF APPETITE OFTEN OCCUR TOGETHER DOES NOT MEAN

THAT ONE NECESSARILY CAUSES THE OTHER. THEY MAY BOTH BE SYMPTOMS OF AN UNDER

LYING CONDITION.

2. CONFUSING NECESSARY CONDITIONS WITH SUFFICIENT CONDITIONS.

A IS NECESSARY FOR B MEANS "B CANNOT OCCUR WITHOUT A." A IS SUFFICIENT FOR B

MEANS "A CAUSES B TO OCCUR, BUT B CAN STILL OCCUR WITHOUT A." FOR EXAMPLE,

A SMALL TAX BASE IS SUFFICIENT TO CAUSE A BUDGET DEFICIT, BUT EXCESSIVE SPEN

DING CAN CAUSE A DEFICIT EVEN WITH A LARGE TAX BASE. A COMMON FALLACY IS TO

ASSUME THAT A NECESSARY CONDITION IS SUFFICIENT TO CAUSE A SITUATION. FOR EX

AMPLE, TO WIN A MODERN WAR IT IS NECESSARY TO HAVE MODERN, HIGH-TECH EQUIPME

NT, BUT IT IS NOT SUFFICIENT, AS IRAQ DISCOVERED IN THE PERSIAN GULF WAR.

SEVEN COMMON FALLACIES

CONTRADICTION

A CONTRADICTION IS COMMITTED WHEN TWO OPPOSING STATEMENTS ARE SIMULTANEOUSLY

ASSERTED. FOR EXAMPLE, SAYING "IT IS RAINING AND IT IS NOT RAINING" IS A CO

NTRADICTION. TYPICALLY, HOWEVER, THE ARGUER OBSCURES THE CONTRADICTION TO TH

E POINT THAT THE ARGUMENT CAN BE QUITE COMPELLING. TAKE, FOR INSTANCE, THE F

OLLOWING ARGUMENT:

"WE CANNOT KNOW ANYTHING, BECAUSE WE INTUITIVELY REALIZE THAT OUR THOUGHTS A

RE UNRELIABLE."

THIS ARGUMENT HAS AN AIR OF REASONABLENESS TO IT. BUT "INTUITIVELY REALIZE"

MEANS "TO KNOW." THUS THE ARGUER IS IN ESSENCE SAYING THAT WE KNOW THAT WE D

ON’T KNOW ANYTHING. THIS IS SELF-CONTRADICTORY.

EQUIVOCATION

EQUIVOCATION IS THE USE OF A WORD IN MORE THAN ONE SENSE DURING AN ARGUMENT.

THIS TECHNIQUE IS OFTEN USED BY POLITICIANS TO LEAVE THEMSELVES AN "OUT." I

F SOMEONE OBJECTS TO A PARTICULAR STATEMENT, THE POLITICIAN CAN SIMPLY CLAIM

THE OTHER MEANING.

EXAMPLE:

INDIVIDUAL RIGHTS MUST BE CHAMPIONED BY THE GOVERNMENT. IT IS RIGHT FOR ONE

TO BELIEVE IN GOD. SO GOVERNMENT SHOULD PROMOTE THE BELIEF IN GOD.

IN THIS ARGUMENT, RIGHT IS USED AMBIGUOUSLY. IN THE PHRASE "INDIVIDUAL RIGHT

S" IT IS USED IN THE SENSE OF A PRIVILEGE, WHEREAS IN THE SECOND SENTENCE RI

GHT IS USED TO MEAN PROPER OR MORAL. THE QUESTIONABLE CONCLUSION IS POSSIBLE

ONLY IF THE ARGUER IS ALLOWED TO PLAY WITH THE MEANING OF THE CRITICAL WORD

RIGHT