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!