¡¡¡¡A¡ª¡ª>B
¡¡¡¡A
¡¡¡¡Therefore£¬ B
¡¡¡¡This diagram displays the if-then statement ¡°A¡ª¡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£º £¨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£º
¡¡¡¡~S¡ª¡ª>~W
¡¡¡¡~S
¡¡¡¡Therefore£¬ ~W
¡¡¡¡This diagram shows that the argument has a valid if-then structure. A condit
¡¡¡¡ional statement is presented£¬ ~S¡ª¡ª>~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£º £¨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£º ¡°if John goes to the party£¬ then Ken does not.¡±
¡¡¡¡Example£º £¨Embedded If-then£©
¡¡¡¡Danielle will be accepted to graduate school only if she does well on the GR
¡¡¡¡E.
