PHILOSOPHY OF THE HUMAN PERSON

LOGIC #3

THE VALIDITY OF CATEGORICAL SYLLOGISMS

Although there are many ways to explain the concept of VALIDITY as it applies to Categorical Syllogisms, one of the easiest is to think of it as the "plumbing" of an argument. Technically, VALIDITY is the structural feature of an argument concerned with whether the PREMISES logically lead to or support the CONCLUSION. In short, an argument's VALIDITY is determined by the form/structure of the syllogism. As such, the VALIDITY of an argument can be determined independent of the truth of the PREMISES and CONCLUSION of the argument. In other words, an INVALID argument contains PREMISES that do not logically support the CONCLUSION.

Another way of capturing the concept of VALIDITY is to say that a VALID argument is one in which you CANNOT accept the PREMISES as true and deny the CONCLUSION without contradicting yourself. In other words, a VALID syllogism cannot have true premises and a false conclusion. However, be aware that VALID syllogisms may have false premises and/or a false conclusion, and an argument whose premises and conclusion are all true may nevertheless be INVALID.

Recall that CATEGORICAL SYLLOGISMS have a STANDARD FORM:

P1--ALL M IS P.

P2--ALL S IS M.

C-- ALL S IS P.

The SUBJECT of the CONCLUSION is called the Minor Term. The PREDICATE of the CONCLUSION is called the Major Term. P1 is called the Major Premise (because it contains the Major Term), and P2 is called the Minor Premise (because it contains the Minor Term). M is the Middle or Linking Term. The RULES of VALIDITY are based on the form of the syllogism and the terms in it.

The shortest and perhaps easiest set of RULES for testing the VALIDITY of a CATEGORICAL SYLLOGISM is as follows:

1. The MIDDLE TERM (M) must be DISTRIBUTED in at least one premise. If not, the argument is INVALID.

2. IF a term is DISTRIBUTED in the CONCLUSION, then it must be DISTRIBUTED in the PREMISE in which it occurs.

3. The PREMISES cannot both be NEGATIVE (i.e., E or O Propositions).

4. IF one PREMISE is NEGATIVE, then the CONCLUSION must be NEGATIVE.

5. IF the CONCLUSION is NEGATIVE, one PREMISE must be NEGATIVE.

One last thing--DISTRIBUTION is a feature of the SUBJECT and PREDICATE TERMS in a CATEGORICAL SYLLOGISM. The SUBJECT or PREDICATE TERM is said to be DISTRIBUTED when it refers to ALL the members of the class of things for which it stands. If the term does NOT refer to ALL the members of the class for which it stands, then the term is NOT DISTRIBUTED or UNDISTRIBUTED.

The DISTRIBUTION of terms in standard form categorical syllogisms is as follows:

1. All S is P. (A)-S is DISTRIBUTED and P is NOT DISTRIBUTED--(Obviously ALL the S's are being referred to, but it DOES NOT refer to all the P's)

2. No S is P. (E)-S is DISTRIBUTED and P is DISTRIBUTED--(ALL the S's are unrelated to ALL the P's)

3. Some S is P. (I)-NEITHER S nor P is DISTRIBUTED--(Obviously SOME S is not ALL S and P DOES NOT refer to all the P's)

4. Some S is not P. (O)-S is NOT DISTRIBUTED and P is DISTRIBUTED--(At least one S has nothing to do with ALL the P's)