Testing Syllogisms with the Six Rules for validity
The Six Necessary Conditions For Valid Categorical Syllogisms:
With the purely formal nature of logical validity now understood, and with the precise technology of Venn idagramming readily at hand in both Essentials of Logic and Reason, Argue, Refute texts, we can formulate yet another way to check the validity of any standard form categorical syllogism. This is done by making valid inferences after Venn diagramming each of the 15 known valid syllogistic forms. By looking at the Venn diagrams of the 15 valid forms and comparing them to the Venn diagrams of the remaining 241 INVALID forms of syllogisms a set of six necessary conditions (The Six Rules) for all the 15 valid forms is easily inferred.
For writing argumentative essays and term papers in this course and for your life of ideas mastery of the 15 valid forms of standard form categorical syllogisms is indispensable. As already demonstrated, the Venn diagram technique gives you a handy tool to quickly check ANY syllogism across the academic disciplines. But what if you don't have paper and pen at the ready to evaluate any given syllogism? By formulating the six rules for validity in any standard form syllogism both texts give you a purely mental process to demonstrate either validity or invalidity for any categorical syllogism you may encounter. It all starts with establishing the list of necessary conditions under which ANY standard form categorical syllogism is valid.
In our list of 20 distinctions for Critical Thinkers it will be recalled: "Any list of required elements for something to take place is known as a list of its necessary conditions."
As a direct result of finding the necessary conditions for all valid syllogistic forms, it can also be inferred that any use of a syllogistic form outside the 15 valid forms, will constitute a formal fallacy That is, quite literally, a breech of the proper form of reasoning syllogistically.
The most common of these formal fallacies are:
1. Fallacy of Four Terms (Quaeternio Terminorum)
2. Fallacy of the Undistributed Middle Term
3. Fallacy of the Illicit Major Term or Fallacy of the Illicit Minor Term
4. Fallacy of Exclusive Premises ( Two negative premises)
5. Fallacy of Affirming a positive conclusion from a negative premise
6. Fallacy of a Particular conclusion inferred from two Universal premises ( Existential Fallacy)
For each of these formal fallacies there is corresponding necessary condition for validity that has been violated. Copi, Cohen stipulate the six rules. ANY standard form categorical syllogism that meets these necessary conditions is VALID, and ANY that violate any one of these necessary conditions is INVALID. Knowing the six rules means that you can demonstrate validity or invalidity in your head without drawing any Venn Diagram.
Here are the six rules and examples of arguments that commit a FORMAL FALLACY by violating a given rule:
Rule 1: A syllogism must contain exactly three terms, each of which is used in the same sense.
Example that violates Rule 1: All rare things are expensive things. All great novels are rare things / Therefore, all great novels are expensive things.
(Note: This syllogism SEEMS to be a valid AAA-1, Barbara, but because the middle term is used in the major premise in one meaning and then the meaning of the middle term is shifted in the minor premise, you actually have FOUR terms and not THREE as required by the very definition of any standard form categorical syllogism. THIS IS A COMMON MISTAKE FOR BEGINNING STUDENTS IN LOGIC AND CRITICAL THINKING WHEN FORMULATING ESSAY AND TERM PAPER ARGUMENTS.)
Rule 2: The middle term must be distributed in at least one premise.
Example that violates Rule 2: All Popes are Catholics. Some Catholics are not pious people / Therefore, some pious people are not Popes.
(Note: This AOO-4 syllogism is not one of the 15 valid forms, The reason it is invalid is that the MIDDLE TERM, Catholics is not distributed in EITHER premise. And since nothing is claimed about ALL members this category, Catholics, then no NECESSARY inference can be related to the other two terms, Popes and pious people.)
Rule 3: If MAJOR or MINOR term is distributed in the conclusion, then it must be distributed in the premises.
Example that violates Rule 3 (ILLICIT MINOR): All conservatives are mean-spirited people. All mean-spirited people are Republicans / Therefore, all Republicans are conservatives.
(Note: In this AAA-4 syllogism the MINOR term, Republicans, IS distributed in the CONCLUSION, yet it is not distributed in the MINOR PREMISE. And since the premise does not tell us something about ALL Republicans, then the conclusion cannot tell us something about ALL Republicans either. This violation of Rule 3 is called the ILLICIT MINOR. For similar reasons the following IAO-3 syllogism is an example of the ILLICIT MAJOR violation of Rule 3, since it applies to the MAJOR term and premise.)
Rule 4: No syllogism can have two negative premises.
Example that violates Rule 4: No citizens are people that need to own a hand gun. Some women are not people that need to own a hand gun / Therefore, some women are not citizens.
(Note: From the two negative premises of this EOO-2 syllogism, no NECESSARY conclusion can be inferred about 'some women' not being people that need to own a hand gun. If you try to Venn Diagram this argument, then you will see that there is no clear UNAMBIGUOUS area to put the 'x' for the MINOR premise.)
Rule 5: If either premise is negative, the conclusion must be negative.
Example that violates Rule 5 (and violates Rule 4 as well): No pornographers are decent people. Some film producers are not pornographers / Therefore, some film producers are decent people.
(Note: This EOI-1 violates Rule 5 in that it improperly infers a AFFIRMATIVE conclusion from two NEGATIVE premises, and it violates Rule 4 that stipulates that no valid syllogism can have two negative premises.)
Rule 6: No syllogism with a particular conclusion can have two universal premises.
Example that violates Rule 6: All people who write about flowers are inhabited by fairies. All poets are people that write about flowers / Therefore, some poets are inhabited by fairies.
(Note: Neither UNIVERSAL premise of this AAI-1 syllogism establishes the existence of a single, individual poet, the MINOR term. Yet the conclusion asserts that "There exists at least one poet, such that, this poet is inhabited by ferries". Hence, this syllogism commits the EXISTENTIAL FALLACY.)
Although it is possible to identify additional features shared by all valid categorical syllogisms (none of them, for example, have two particular premises), these six rules are individually NECESSARY and jointly SUFFICIENT to distinguish between all valid and invalid syllogisms in the complete set of 256 permutations and combinations of MOOD and FIGURE for standard form categorical syllogisms.
Link to Power of Logic Site for Testing Venn Diagrams
The Power of Logic Web Tutor is a free tutorial to accompany C. Stephen Layman's text, The Power of Logic. This internet-based study guide provides you with numerous ways to check your understanding of logic and to independently check your work and receive feedback.
Link to Syllogism Evaluator
Master the skills of using both Venn diagrams and the Six Rules to test the validity of Categorical Syllogisms by using poweroflogic.com Syllogism Evaluator.