GMT考试--Testprep数学精解(4)

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

　　EN EITHER, OR BOTH, OF ITS PARTS ARE FALSE. THIS IS PRECISELY² 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 SYMBOLIZE³ "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 PREMISES⁴ 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.

　　GENERALIZATION⁵

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

　　AIN TOOLS BY WHICH WE ACCUMULATE KNOWLEDGE AND ANALYZE⁶ OUR WORLD. MANY PEOPL

　　E DEFINE GENERALIZATION AS "INDUCTIVE REASONING." IN COLLOQUIAL⁷ 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

　　HOOD⁸ 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 AUTO⁹ 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 DECIDED¹⁰ 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 DETERMINED¹¹ TO BE TRUE, WOULD BEST EXP

　　LAIN THIS DISCREPANCY¹².

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

　　(B) FORD¹³ 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 RELIABILITY¹⁴ OF THE PROJECTION¹⁵ 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 IRRELEVANT¹⁶. 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 EXPERIMENTATION¹⁷ 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 SACCHARINE¹⁸ 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 TAUT¹⁹, SO TOO THE TRIALS AND TRIBULATION²⁰

　　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 DRAWN²¹ 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 TAUTNESS²² 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 PRONE²³ 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 LOTTERY²⁴ 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 GENETIC²⁵ PREDISPOSITION IN SOME P

　　EOPLE TO BOTH DEVELOP CANCER AND CRAVE²⁶ NICOTINE²⁷. ALTHOUGH THIS CLAIM IS HIGH

　　LY IMPROBABLE, IT IS CONCEIVABLE.

　　THERE ARE TWO COMMON FALLACIES ASSOCIATED WITH CAUSAL REASONING:

　　1. CONFUSING CORRELATION²⁸ WITH CAUSATION.

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

　　LEARLY QUESTIONABLE²⁹. IT MAY BE ONLY COINCIDENTAL THAT THEY OCCURRED TOGETHER

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

　　FACT THAT INSOMNIA³⁰ 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 DEFICIT³¹, 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-TECH³² EQUIPME

　　NT, BUT IT IS NOT SUFFICIENT, AS IRAQ DISCOVERED IN THE PERSIAN GULF³³ WAR.

　　SEVEN COMMON FALLACIES

　　CONTRADICTION

　　A CONTRADICTION IS COMMITTED WHEN TWO OPPOSING STATEMENTS ARE SIMULTANEOUSLY³⁴

　　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.

　　EQUIVOCATION³⁵

　　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