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.