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
责任编辑：sealion1986
