I took an excellent course in Formal Logic in college, taught by Dr. Leonard Peikoff, a close associate of Ayn Rand. The syllogism was the lynchpin of the syllabus. The format is Major Premise, Minor Premise, Conclusion. If the two premises are true, the conclusion must be true, as in:
Everyone connected to the Obama administration is a liar.
Jay Carney is connected to the Obama administration.
Therefore, Jay Carney is a liar.
I recall that the NEGATIVE may or may not be true:
(Here’s a case where it’s not true:)
Everyone connected to the Obama administration is a liar.
Bill Clinton is not connected to the Obama administration.
Therefore, Bill Clinton is not a liar.
(Here’s a case where it is true:)
Everyone connected to the Obama administration is a liar.
Mother Theresa is not connected to the Obama administration.
Therefore, Mother Theresa is not a liar.
The CONVERSE also may or may not be true:
(Here, it is true)
Everyone connected to the Obama administration is a liar.
Jay Carney is a liar.
Therefore, Jay Carney is connected to the Obama administration.
(Here, it is false)
Everyone connected to the Obama administration is a liar.
Bill Clinton is a liar.
Therefore, Bill Clinton is connected to the Obama administration.
One thing I recall fairly well is that the CONTRAPOSITIVE is always true (assuming the original syllogism is true.)
Thus:
Everyone connected to the Obama administration is a liar.
George Washington is not a liar.
Therefore, George Washington is not connected to the Obama administration
Correct. People often want the converse to be true, but that is not logically so.
A deductive argument can be valid or invalid. If it is valid and both premises are true, then the conclusion is true and the argument is sound. If it is invalid, it is unsound. If it is valid, but has a false premise, it is unsound.
An example of a valid hypothetical argument would be:
If A, then B
A
Therefore, B
Another would be:
If A, then B
Not B
Therefore, not A
Many people have a hard time with the second example, which is “modus tollens” meaning “denying the consequent”