Testprep数学精解

OSBANKRUPTCY.

THE CONCLUSION, "THE STRIKERS SHOULD ACCEPT THE MANAGEMENT’S OFFER," IS STAT

ED IN THE FIRST SENTENCE. THEN "ADMITTEDLY" INTRODUCES A CONCESSION; NAMELY,

THAT THE OFFER WAS LESS THAN WHAT WAS DEMANDED. THIS WEAKENS THE SPEAKER’S

CASE, BUT IT ADDRESSES A POTENTIAL CRITICISM OF HIS POSITION BEFORE IT CAN B

E MADE. THE LAST TWO SENTENCES OF THE ARGUMENT PRESENT MORE COMPELLING REASO

NS TO ACCEPT THE OFFER AND FORM THE GIST OF THE ARGUMENT.

FOLLOWING ARE SOME OF THE MOST COMMON COUNTER-PREMISE INDICATORS:

COUNTER-PREMISE INDICATORS

BUT DESPITE

ADMITTEDLY EXCEPT

EVEN THOUGH NONETHELESS

NEVERTHELESS ALTHOUGH

HOWEVER IN SPITE OF THE FACT

AS YOU MAY HAVE ANTICIPATED, THE GMAT WRITERS SOMETIMES USE COUNTER-PREMISES

TO BAIT WRONG ANSWER-CHOICES. ANSWER-CHOICES THAT REFER TO COUNTER-PREMISES

ARE VERY TEMPTING BECAUSE THEY REFER DIRECTLY TO THE PASSAGE AND THEY ARE I

N PART TRUE. BUT YOU MUST ASK YOURSELF "IS THIS THE MAIN POINT THAT THE AUTH

OR IS TRYING TO MAKE?" IT MAY MERELY BE A MINOR CONCESSION.

LOGIC II (DIAGRAMMING)

MOST ARGUMENTS ARE BASED ON SOME VARIATION OF AN IF-THEN STATEMENT. HOWEVER,

THE IF-THEN STATEMENT IS OFTEN EMBEDDED IN OTHER EQUIVALENT STRUCTURES. DIA

GRAMMING BRINGS OUT THE SUPERSTRUCTURE AND THE UNDERLYING SIMPLICITY OF ARGU

MENTS.

IF-THEN

A-->B

BY NOW YOU SHOULD BE WELL AWARE THAT IF THE PREMISE OF AN IF-THEN STATEMENT

IS TRUE THEN THE CONCLUSION MUST BE TRUE AS WELL. THIS IS THE DEFINING CHARA

CTERISTIC OF A CONDITIONAL STATEMENT; IT CAN BE ILLUSTRATED AS FOLLOWS:

A-->B

A

THEREFORE, B

THIS DIAGRAM DISPLAYS THE IF-THEN STATEMENT "A-->B," THE AFFIRMED PREMISE "A

," AND THE NECESSARY CONCLUSION "B." SUCH A DIAGRAM CAN BE VERY HELPFUL IN S

HOWING THE LOGICAL STRUCTURE OF AN ARGUMENT.

EXAMPLE: (IF-THEN)

IF JANE DOES NOT STUDY FOR THE GMAT, THEN SHE WILL NOT SCORE WELL. JANE, IN

FACT, DID NOT STUDY FOR THE GMAT; THEREFORE SHE SCORED POORLY ON THE TEST.

WHEN SYMBOLIZING GAMES, WE LET A LETTER STAND FOR AN ELEMENT. WHEN SYMBOLIZI

NG ARGUMENTS, HOWEVER, WE MAY LET A LETTER STAND FOR AN ELEMENT, A PHRASE, A

CLAUSE, OR EVEN AN ENTIRE SENTENCE. THE CLAUSE "JANE DOES NOT STUDY FOR THE

GMAT" CAN BE SYMBOLIZED AS ~S, AND THE CLAUSE "SHE WILL NOT SCORE WELL" CAN

BE SYMBOLIZED AS ~W. SUBSTITUTING THESE SYMBOLSSINTOSTHE ARGUMENT YIELDS TH

E FOLLOWING DIAGRAM:

~S-->~W

~S

THEREFORE, ~W

THIS DIAGRAM SHOWS THAT THE ARGUMENT HAS A VALID IF-THEN STRUCTURE. A CONDIT

IONAL STATEMENT IS PRESENTED, ~S-->~W; ITS PREMISE AFFIRMED, ~S; AND THEN TH

E CONCLUSION THAT NECESSARILY FOLLOWS, ~W, IS STATED.

EMBEDDED IF-THEN STATEMENTS

USUALLY, ARGUMENTS INVOLVE AN IF-THEN STATEMENT. UNFORTUNATELY, THE IF-THEN

THOUGHT IS OFTEN EMBEDDED IN OTHER EQUIVALENT STRUCTURES. IN THIS SECTION, W

E STUDY HOW TO SPOT THESE STRUCTURES.

EXAMPLE: (EMBEDDED IF-THEN)

JOHN AND KEN CANNOT BOTH GO TO THE PARTY.

AT FIRST GLANCE, THIS SENTENCE DOES NOT APPEAR TO CONTAIN AN IF-THEN STATEME

NT. BUT IT ESSENTIALLY SAYS: "IF JOHN GOES TO THE PARTY, THEN KEN DOES NOT."

EXAMPLE: (EMBEDDED IF-THEN)

DANIELLE WILL BE ACCEPTED TO GRADUATE SCHOOL ONLY IF SHE DOES WELL ON THE GR

E.

GIVEN THIS STATEMENT, WE KNOW THAT IF DANIELLE IS ACCEPTED TO GRADUATE SCHOO

L, THEN SHE MUST HAVE DONE WELL ON THE GRE. NOTE: STUDENTS OFTEN WRONGLY INT

ERPRET THIS STATEMENT TO MEAN:

"IF DANIELLE DOES WELL ON THE GRE, THEN SHE WILL BE ACCEPTED TO GRADUATE SCH

OOL."

THERE IS NO SUCH GUARANTEE. THE ONLY GUARANTEE IS THAT IF SHE DOES NOT DO WE

LL ON THE GRE, THEN SHE WILL NOT BE ACCEPTED TO GRADUATE SCHOOL.

"A ONLY IF B" IS LOGICALLY EQUIVALENT TO "IF A, THEN B."

AFFIRMING THE CONCLUSION FALLACY

A-->B

B

THEREFORE, A

REMEMBER THAT AN IF-THEN STATEMENT, A-->B, TELLS US ONLY TWO THINGS: (1) IF

A IS TRUE, THEN B IS TRUE AS WELL. (2) IF B IS FALSE, THEN A IS FALSE AS WEL

L (CONTRAPOSITIVE). IF, HOWEVER, WE KNOW THE CONCLUSION IS TRUE, THE IF-THEN

STATEMENT TELLS US NOTHING ABOUT THE PREMISE. AND IF WE KNOW THAT THE PREMI

SE IS FALSE (WE WILL CONSIDER THIS NEXT), THEN THE IF-THEN STATEMENT TELLS U

S NOTHING ABOUT THE CONCLUSION.

EXAMPLE: (AFFIRMING THE CONCLUSION FALLACY)

IF HE IS INNOCENT, THEN WHEN WE HOLD HIM UNDER WATER FOR SIXTY SECONDS HE WI

LL NOT DROWN. SINCE HE DID NOT DIE WHEN WE DUNKED HIM IN THE WATER, HE MUST

BE INNOCENT.

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