Syllogisms that violate this rule are said to commit the fallacy of
the particular premises:
Rule: No syllogism with a particular conclusion can have two universal
All people who write about flowers are inhabited by fairies.
All poets are people that write about flowers
Therefore, some poets are inhabited by fairies.
(Note: Neither UNIVERSAL premise of this AAI-1 syllogism establishes the existence
of a single, individual poet, the MINOR term. Yet the conclusion asserts that "There
exists at least one poet, such that, this poet is inhabited by ferries". Hence, this syllogism
commits the EXISTENTIAL FALLACY.)
Although it is possible to identify additional features shared by all valid categorical
syllogisms (none of them, for example, have two particular premises), these six rules are
individually NECESSARY and jointly SUFFICIENT to distinguish between all
valid and invalid syllogisms in the complete set of 256 permutations and combinations of
MOOD and FIGURE for standard form categorical syllogisms.
From two particular premises, nothing follows.
Some men are old;
Some old people are women
Some women are men.
Some cows are animals;
Some dogs are not cows
Some dogs are not animals.
Some delegates are not foreigners
Some Americans are delegates
Some Americans are not foreigners.
Fallacy of Particular Premises
The conclusion follows the weaker premise.
All roses are flowers
Some roses are fragrant
All fragrant things are flowers
All rebels are deviants
Some students are not deviants
Some students are rebels
Fallacy of Universal Conclusion drawn from a Particular Premise
Fallacy of Affirmative Conclusion drawn from a Negative Premise.
Rule: If both premises are universal, the conclusion cannot be particular.
Fallacy: Existential fallacy
All mammals are animals
All tigers are mammals
Some tigers are animals
Justification: On the Boolean model, Universal statements make no claims about existence
while particular ones do. Thus, if the syllogism has universal premises, they necessarily say
nothing about existence. Yet if the conclusion is particular, then it does say something
about existence. In which case, the conclusion contains more information than the premises
do, thereby making it invalid.
The quantity of propositions
Rule: at least one premise must be universal.
Example: Every animal is mortal;
But every dog is an animal;
Therefore every dog is mortal.
Rule: If the premise is particular, the conclusion must be particular.