9.1 Enthymemes - My Notes on "The Reasonable Person" by Mark Grannis

Advanced Deductive Arguments

Enthymemes

"...an argument that is logically equivalent to a categorical syllogism but in which one of the three propositions goes unstated."

NOTE - Valid syllogisms require TWO premises and ONE conclusion, so it must be supplied. 

First Order Enthymeme - "an enthymeme that omits its major premise." 

Example:

[Minors can't buy beer]; 

Teenagers are minors; 

Therefore, teenagers can't buy beer. 

Second Order Enthymeme - "An enthymeme that omits its minor premise." 

Example:

No great thing is easy;

[Truth is a great thing];

Therefore Truth is not easy. 

Third Order Enthymeme - "An enthymeme that omits its conclusion."

Example: 

The homework was due Monday;

Today is Monday;

[Therefore, homework is due today.]

Detecting the Missing Premise 

First, Find the Conclusion 

- If there's not a conclusion, then you clearly have a third order enthymeme. 

- If you see "reason-signaler" words like: because, since, inasmuch, by reason of ... then the conclusion probably is stated first. 

- If you see "conclusion-signaler" words like: so, therefore, thus, consequently, ergo, etc ...then the conclusion probably comes second. 

Second, Find the Major, Minor, and Middle Terms 

- Once the conclusion is identified, look to the predicate for the major term, the subject for the minor term, and the term not in the conclusion for the middle term. 

Third, Place the Included Premise in its Proper Place as the Major or Minor Premise 

- The one premise that is given will now clearly be either the major or minor premise depending whether it includes the major or minor term. Arrange that premise and the conclusion. 

Fourth, Identify the Two Terms that Remain to be Related to Each Other 

- Identify which combination of a term and middle term that need to be related to create the missing premise. 

Fifth, Decide how the Two Terms of the Missing Premise Must Relate to Each Other 

- Then you need to figure out how to arrange the subject and predicate and into the correct A, E, I or O premise. Either use Barbara, Celerant or the seven rules of validity to make sure things are correct. 

"... it is crucial to remember that what we have been calling the 'omitted' premise is not really absent for purposes of logical analysis; it must be there fore the deductive inference to be valid."