Self-study
A poor farmer was fond of telling his children: “In this world, Support you are either rich or poor, and Support you are either honest or dishonest. ███ ████ ███████ ███ ███████ ██████████ ███ ████ ███████ ███ ██████████
Identify a Sufficient Assumption: Conditional Reasoning
The farmer concludes that all rich farmers are dishonest. This is supported by three conditional claims: (1) everyone is either rich or poor, (2) everyone is either honest or dishonest, and (3) all poor farmers are honest. Our job is to identify a sufficient assumption to make these premises logically guarantee the conclusion.
Conditional arguments are often easier to understand by diagramming the claims. We can start with the universal principles the farmer sets out:
1. /rich → poor
2. /honest → dishonest
But then the farmer shifts to a third premise and a conclusion that concern farmers specifically:
3. farmerpoor → farmerhonest
______
C. farmerrich → farmerdishonest
Taking the contrapositive of premise 3, we get:
farmer/honest → farmerSo we can infer that all dishonest farmers are rich, but not that all rich farmers are dishonest, as the farmer concludes. To guarantee the farmer's conclusion, we need to assume that honest farmers must be poor. Otherwise, the argument leaves open the possibility that some rich farmers could also be honest. The correct answer will express this condition, the contrapositive of the conclusion:
farmerhonest → farmerpoor
23.
The farmer’s conclusion is properly █████ ██ ███ ████████ ███████ ████
a
every honest farmer ██ ████
We can diagram this as farmerhonest → farmerpoor, which is the contrapositive of the conclusion and therefore the sufficient assumption we need.
b
every honest person ██ █ ██████
We can diagram this as honest → farmer, which isn't what we need. The correct answer needs to tell us that honest farmers must be poor.
c
everyone who is █████████ ██ █ ████ ██████
We can diagram this as dishonest → farmerrich, which isn't what we need. By taking the contrapositive of premise (3) of the argument, we can already infer that all dishonest farmers must be rich. There's no need to generalize that to anyone dishonest being a rich farmer.
d
everyone who is ████ ██ ██████
We can diagram this as poor → honest, which isn't what we need. Premise (3) of the argument already affirms this for farmers, and generalizing it to be true for everyone doesn't improve the argument. The conclusion we're trying to guarantee is still about farmers, so (D) effectively repeats premise (3).
e
every poor person ██ █ ██████
We can diagram this as poor → farmer, which isn't what we need. We're trying to guarantee the conclusion that rich farmers are dishonest; knowing that all poor people are farmers doesn't get us any closer to that, because it doesn't constrain the honesty of rich farmers at all.