Self-study
Support The trees always blossom in May if April rainfall exceeds 5 centimeters. ██ █████ ████████ ███████ █ ████████████ ████ ███ ██████████ ███ ██████ ████ ██ ███ ██ ███ ██████████ ████ ███ ████ ████ ███ █ ███ ████ ███ █████ ████ ███ ███████ ████ ████
Method of Reasoning
As shown below, this argument starts with two conditional premises that share a sufficient condition:
If it rains more than 5cm in April, the trees blossom in May.
If it rains more than 5cm in April, the reservoirs are full on May 1.
The argument adds that one of the necessary conditions has not been met this year: The reservoirs weren’t full on May 1. Because that necessary condition wasn’t met, the author concludes that the other necessary condition fails, as well: the trees won’t blossom this May.
Identify and Describe Flaw
This is a cookie-cutter invalid argument form. A necessary condition of “more than 5cm of rain fell in April” isn’t met, but that doesn’t guarantee that no necessary condition of “more than 5cm of rain fell in April” can be met!
21.
Which one of the following ████████ █ ██████ ███████ ██ █████████ ████ ███████ ██ ███ ██████ ███████ ██ █████████ ██ ███ ████████ ██████
a
If the garlic ██ ██ ███ ███████ ████ ██ ██ █████ ██████ ███ ███ ████████ ███ ██ ███ ████████ ██████ ██ ███ ██████ ██ ██ ███ ███████ ███ ████████ ███ ███ ██ ███ ████████ ███████ ██ ███ ██████ ██ ███ █████ ██████
As shown below, this argument starts with two conditional premises that share a sufficient condition:
If the garlic is in the pantry, it’s fresh.
If the garlic is in the pantry, the potatoes are on the basement stairs.
The argument adds that one of the necessary conditions isn’t met: The potatoes aren’t on the stairs. Like the stimulus, (A) takes the fact that one necessary condition has failed to guarantee that the other necessary condition—the garlic is fresh—isn’t met, either. But that’s not a valid conclusion!
b
The jar reaches ███████ ███████████ ██ ██ ██ ████ ████ ███ ██████ ███ █ ████████ ███ ████████ ██ ███ ███ ███████ ███████████ ██ ███ ███ ██ ██ ███████ ████████████ ███ ███ ███ ████ ████ ███ ██████ ███ █ ████████ ██ ███ ████████ ██ ███ ███ ████ ████ █████████ ████████████
No flaw. This is a valid argument! If the jar is held over the burner for 2 minutes, it reaches optimal temperature; at optimal temperature, the contents of the jar liquefy immediately. The har was held over the burner for 2 minutes, so we can follow the chain of conditional claims to conclude that the contents liquefied immediately!
c
A book is ██████████ █████████ ██ ██ ██ ████ ████ ███ █████ ████ ██ █ ████ ███ ███ ████ ██████ █████ ████ ██ ██ ████ ████ ███ █████ ████ ████ ████ ██ ███ ██████████ ██████████ ██ ██ ██ ███ ███████ ████ ██████ █████
No flaw. This is a valid argument! If a book was set with wooden type, then it’s over 200 years old; if it’s over 200 years old, it’s classified “special.” This book wasn’t classified “special,” so we can take the contrapositives back through the chain of conditional claims to validly conclude that the book wasn’t printed with wooden type.
d
The mower will ███████ ████ ██ ███ ██████ ██ ███ ████████ ███ ██████ ██ ███████ ██ ███ ████ █████ ██ ██████████ ███ ████ █████ ██ ███ ██████████ ██ ███ █████ ████ ████████
Wrong flaw. (D) reaches its conclusion via a mistaken belief that a negated sufficient condition guarantees a negated necessary condition: “won’t operate” is a necessary condition of “foot pedal depressed,” so when (D) says the foot pedal isn’t depressed, it’s negating the sufficient condition to erroneously conclude that the necessary condition must also be negated. Unlike the stimulus, (D) is structured as a chain of conditional claims, rather than two conditional claims that share a sufficient condition.
e
If the kiln ██ ███ ████ ████ ███ ██████ ████ ██████ ██ ███ ██████ ██████ ████ ███ ███████ ████ ████ ███ ██████ ███ ███████ ████ ███ ████ ███ ██████ █████ ███ ████ ███ ███ ███ ████
No flaw. This is a valid argument! If the kiln is too hot, then the plates will crack; if the plates crack, the artisan must redo the order. The artisan doesn’t have to redo the order, so we can take the contrapositives back through the chain of conditional claims to validly conclude that the kiln wasn’t too hot.