revised 9/6/00

The refutation by logical analogy or counter-example method for testing syllogisms has four steps:

1. Test a syllogism with true premises and true conclusion.
2. Assume that the syllogism is valid.
3. Attempt to discover an analogous syllogism (one with an identical mood and figure) with true premises and a false conclusion.
4. If none can be found, treat the syllogism as valid; if one can be found, then declare the syllogism invalid.

Here are some categorical syllogisms that have true premises and a true conclusion:

	No rabbits are cats.
	No turtles are rabbits.
	Thus no turtles are cats.


	All dogs are canines.
	No dogs are felines.
	Thus no felines are canines.


	Some students are not lazy.
	Some teachers are not lazy.
	Thus some teachers are not students.


	Some professors are not married.
	All husbands are married.
	Thus some husbands are not professors.


	Some races are not marathons.
	Some races are not 10Ks.
	Thus some 10Ks are not marathons.


	Some cars are expensive.
	Some cars are fast.
	Thust some fast things are expensive.


	Some primates are small animals.
	Some mammals are primates.
	Thus some mammals are small animals.


	Some students are not happy.
	No greedy persons are happy.         [Assume this premise is true.]
	Thus some greedy persons are students.


	No books are conscious.
	No spoons are books.
	Hence no spoons are conscious.


	Some busses are not diesel-powered.
	Some busses are city-operated.
	Thus some city-operated vehicles are not diesel-powered.

	
	No lethal things are toys.
	Some guns are lethal.
	Thus some guns are toys.


	All cedar chests are aromatic.
	No aromatic thing is fragrance-free.
	Hence some fragrance-free things are not cedar chests.

	

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Copyright © 1999, Michael Eldridge