Lessons 23-25
If the premises are true, then the conclusion has to be true
valid
some chanting story-tellers are rap singers
I
some fruits are bananas. No bananas are apples. T, some apples are not fruit.
4
all cherries are fruit. all maraschinos are cherries. t, all maraschinos are fruit.
valid
AAA-1
When the premises are true but the conclusion is false
invalid
No mid-management secretaries are secret agents
E
all gorillas are mammal. some apes are gorillas. t, some apes are not mammals
1
all apples are fruit. all bananas are fruit. t, all apples are bananas.
invalid
AAA-2
undistributed middle
a syllogism that is valid AND the premises are true
sound syllogism
all chanting story tellers are bards
A
all oats are grain. some grains are rice. t, some rice is oats.
4
no cherries are meat. all hot dogs are meat. t, no hot dogs are cherries.
valid
EAE-2
a way to test if a syllogism is valid by using a syllogism of the same form BUT with true premises and a false conclusion
Counterexample
some graduates of medical school are professional nurses
I
some harps are not pianos. no harps are grand pianos. t. some grand pianos are not pianos
3
no meat is fruit. all meat is an edible thing. t, no edible things are fruit.
invalid
eae-3
a term that refers to all members of its category. Universal statements distribute the subject. Negative statements distribute the predicate
Distributed terms
some robots are not programmed humanoids
O
no reptiles are mammals. are apes are mammals. t, some apes are reptiles.
2
some cherries are not sweet tasting things. all cherries are fruits. t, some fruits are not sweet tasting things.
valid
OAO-3