*Introductory Logic* Lesson 23 introduces the concepts of validity and soundness. The lesson says that a syllogism is valid if and only if the premises imply the conclusion. If a syllogism can have true premises and a false conclusion, the argument is invalid. A sound argument is a valid argument with all true statements.

The *only *purpose of Lesson 23 is to *introduce *the concepts of validity and soundness. This lesson does *not* explain *how* to determine validity. So if after studying this lesson you have trouble knowing whether a given syllogism is valid or invalid, don’t worry about it. You will learn how to do that in the next three lessons. Lessons 24-26 are dedicated to teaching the methods for determining the validity of a syllogism.

Appreciate! Because I’m there now! With that said, I’m sweating a little over this question: In the example on p. 164, the form is EOI-2. If we go back to relationships between affirmatives and particulars, I and E are contradictory…how does this work into validity? Can we automatically make a statement about validity based on this relationship?

It appears that you are asking this question: If a premise of a syllogism is a contradictory form of the conclusion, can the syllogism be valid? The EOI-1 on page 164 has an E premise and an I conclusion, which are contradictory, and it is invalid. Is this the case generally?

The answer is no. First, the E and I are contradictory only when the subject and predicate are the same (remember how the Square of Opposition is produced). But the subject and predicate are different for a premise and conclusion in a given syllogism. Second, there are valid forms of mood and figure with an A premise and an O conclusion, such as AOO-2.

On the other hand, it is not possible to have a valid syllogism with an E premise and I conclusion, or an O premise and A conclusion, because they would make the negative premise and affirmative conclusion fallacy. It is also not possible to have a valid syllogism with an I premise and E conclusion, because a valid syllogism cannot have a particular premise and a universal conclusion.

I hope I have answered your question!