Reflections: In this chapter we study syllogisms. Knowing how to work with syllogisms help prepare us for longer, more complex arguments and help build analytical skills in a more general way. The value of learning to work with syllogisms goes far beyond argumentation, helping us learn to think in a more systematic way and approach problem solving with more confidence.

Goals: In this chapter, we will learn how to examine syllogisms in order to determine if they are valid or invalid. We will also cover techniques for assessing validity of syllogisms, so you'll be able to check them out quickly and easily. My goals are to help you acquire the skills to break down a syllogism, learn the rules of the syllogism that allow us to assess validity, and put them to work.

Why bother? This system of analyzing syllogisms is not only a time saver; it lessens the chance of error. If you were like the Tom Hanks character in Castaway, you might prefer taking a very long time to puzzle through the problems you face. On the other hand, you may prefer the jet propulsion model of reasoning, where speed and accuracy is of the essence. It helps to know how to organize the material to quickly determine whether or not the reasoning is worth paying attention to. Plus, you may not have time to linger.

Think about it: What if your house is on fire, you've just hit an ice slick on the road, or you're on a TV show like Weakest Link or Survivor and stand to make your fortune if you can think quickly on your feet? The ability to dismantle and evaluate syllogistic arguments quickly and correctly is more valuable than you may realize.

Syllogisms

A syllogism is a three-line argument with two premises and one conclusion in which there are only three terms. With the techniques of this chapter, we can break down syllogisms and quickly test them for validity with the tools and rules here put to work.

1. Validity and Soundness
Validity: The argument is structurally correct (so that if the premises were true, the conclusion could not be false). You may remember that this means the argument is valid. It does not mean that the premises are necessarily true.

Soundness: You may also remember the two criteria for sound arguments--first, the argument is valid and, second, the premises are actually true. If an argument has both these characteristics, it is called sound. Since you need to look at the particular circumstances to determine the truth of the premises, our focus in this section will be on validity.

Validity
It is generally held that only deductive arguments can be considered valid or invalid. Validity, therefore, is an issue about the relationship between the premises and the conclusion--not about whether any statements are actually true or not. The question here is: Do the premises, if they were assumed to be true, fully support the conclusion? This means the conclusion could not be false if the premises were true in a valid argument. Valid argument example: "Either there's a burglar in the house or that's the plumber. There's no burglar in the house. Therefore, that's the plumber."

Universal vs. Particular Propositions
Universal propositions: Basically, propositions fall into one of two categories, as we saw in the last chapter. They could be universal, which means something is being predicated about all members of the subject class (i.e., that they do or do not have some characteristic). The "all" here may refer to the collective or to "each and every one" or "any" of the subject. This includes propositions in which something is being affirmed or denied about some proper noun in the subject (e.g., the name of a person, a city, a title of a song, etc.). Universal claims are all-or-nothing claims. E.g., "All race cars are vehicles" and "No SUV is a bicycle."

Particular propositions: In the case of a particular proposition, some trait is being predicated about some (but not all or none) of the subject class. Some of the subject class are claimed to have or lack the characteristic in question. This means that it predicates something of an indefinite part of that class, but never all of it. This includes statistical propositions of the form x% of A is B, where x¹ 100 and x¹ 0. E.g., "Some birds are ducks" and "Many ducks are mallards."

Categorical Propositions
In analyzing a syllogism, it's generally easiest to do so by rewriting the premises and the conclusion in the form of categorical propositions. The Four Categorical Propositions

Variations of the Categorical Propositions

1. Proper Nouns as Subject: Remember, if you use specific individuals or proper names, like Andrea, Chicago, or the Statue of Liberty, then the claim is universal and will be either an A or an E claim, depending on whether the sentence is positive or negative. (For example, Lisa is a wild woman is an A claim, whereas Kareem is not a short man is an E claim).
2. Statistical Claims: If you have statistical claims x% of A is B, (where x¹ 100 or 0), then that claim is treated as an I or O claim (depending upon whether it's positive or negative). So 82% of donuts are greasy is an I claim and 19% of chocolate is not addictive is an O claim.

Categorical Syllogisms
A categorical syllogism is a syllogism in which the premises and the conclusion are categorical claims. The standard form of a categorical syllogism is what we have when we set out the syllogism in a particular order: major premise, minor premise, and then the conclusion. The standard form of the syllogism always starts with the major premise. This is the premise that contains the predicate term of the conclusion. The next premise is called the minor premise and it contains the subject term of the conclusion. This means the premise nearest to the conclusion should contain the minor term (the subject of the conclusion). Both premises have a linking term (called the "middle term") that does not appear in the conclusion.

The Three Terms of the Syllogism
Once we have the premises and conclusion expressed in standard form, we can take the next step. This is to locate the three terms. The major term is the predicate of the conclusion. The minor term is the subject of the conclusion. And the middle term is the term that is only found in the two premises.

Major and Minor Premises
Order is everything in the world of syllogisms. If we are testing a syllogism, we must first set out the argument. Our first step is to locate the conclusion. Our next step is to examine the conclusion to determine which term is the major term and which is the minor term. The predicate is the major term and, once you know this, you also know the major premise. The major premise is the premise containing the major term. The subject of the conclusion is the minor term and, once you know this, you also know the minor premise. The minor premise is the premise containing the minor term. To express the syllogism in standard form, set it out this way:

Major Premise → Contains the major and middle terms
Minor Premise → Contains the minor and middle terms
Conclusion → Contains the minor and major terms

Remember: Minor term = Subject of the conclusion. Major term = Predicate of the conclusion

Once we have the argument in standard form, we can see its structure. The first premise should have the major term and the middle term in it. The second premise should have the minor term and the middle term in it. The conclusion contains the major and minor terms. The argument must be exactly in this order to be in standard form. Once the argument is set out in this order we can proceed to the next step. Be sure to express each proposition in categorical form:

1.The Mood and Figure of a Syllogism
After you get a syllogism in standard form, you are in a position to name the mood and the figure. These are very useful for quickly evaluating an argument for validity.

Mood of the Syllogism: The mood of a syllogism is the list of the types of claims (A, E, I, and O) of the major premise, minor premise, and conclusion (in that order). Because there are the two premises and one conclusion, you will have three letters indicating the categorical propositions that constitute the syllogism.

Abbreviations for Speedy Reference

P =	Predicate of the conclusion	→	Major term
S =	Subject of the conclusion	→	Minor term
M =	Linking term in both premises	→	Middle term

Figure of the Syllogism

Checking for Validity: Before we can test the syllogism for validity, we need to know how to tell if a term is distributed. Distribution involves the question of how much. If someone asked you to distribute all of a stack leaflets, you'd know that what was wanted was that you pass them all out. Distribution of a term is similar, in the sense that a distributed term includes all its members.

Distribution: When we talk distribution, we are talking about number of members of the class in question. If the term is meant to apply to all members of the class it defines, then it is called distributed. If it applies to only an indefinite part of those members, it's called undistributed. For any given proposition there are only two terms to examine to determine distribution--the subject and the predicate. The subject is distributed in any universal claim, the predicate in any negative claim.

Distribution of Terms: Checking distribution of terms involves two steps. Step 1: Check the location of the term (Is it the subject or the predicate of the proposition?). Step 2: According to the location, check either quality or quantity of the proposition. If the term is in the subject place, then check the quantity (universal proposition = subject is distributed). If the term is in the predicate place, check the quality (negative proposition = predicate is distributed).

Subject Distributed. If the claim is universal, the subject is then distributed, because you are saying that all of the members of the subject class either have or don't have some characteristic. To determine if the subject is distributed: Check the quantity of the proposition.

→ See if the claim is universal.
→ The subject is distributed in A and E claims.

Predicate Distributed. If the claim is negative, the predicate is distributed. This is because a negative is excluding the subject class (some or all of it) from having the characteristic set out in the predicate. To determine if the predicate is distributed. Check the quality of the proposition.

→ See if the claim is negative.
→ The predicate is distributed in E and O claims.

Summary of Distribution

Rules of the Syllogism
Any syllogism that satisfies each of the rules is valid. So you can test for validity simply by running through each rule and seeing if the syllogism checks out on each one.

Rules of the Syllogism

Rule 1: The middle term must be distributed at least once.

Rule 2: If a term is distributed in the conclusion, it must also be distributed in its corresponding premise.

Illicit major: When the major term is distributed in the conclusion, but is not distributed in the major premise.
Illicit minor: When the minor term is distributed in the conclusion, but is not distributed in the minor premise.
Note: This rule is not saying that a valid syllogism requires the conclusion to have its terms distributed. But if a term is distributed in the conclusion, it is crucial that it also be distributed in its corresponding premise.

Rule 3: At least one premise must be positive. (If both premises are negative, the syllogism is invalid.)

Rule 4: If the syllogism has a negative premise, there must be a negative conclusion, and vice versa.

Rule 5: If both of the premises are universal, the conclusion must also be universal, and vice versa.