Conclusion of Deductive Logic - Salmon

(Originally written September 7, 2005 in Book 1)

Logic
Wesley Salmon

Chapter 2

The Dilemma

Form of Dilemma

Either P or Q
If P, then R
If Q, then S
Therefore, either R or S

There are four forms of categorical statements, each form is represented by a vowel:

A) All F are G (F is the subject term, G is the predicate term) [Universal Affirmative]
E) No F are G [Universal Negative]
I) Some F are G [Particular Affirmative]
O) Some F are not-G [Particular Negative]

There are variations to all forms

The Universal affirmative is better stated as "If anything is F, then it is G" so as not to assume the existence of F

In the Particular Affirmative and the Particular Negative it is better stated as either, "at least one F is G" or "at least one F is not G".

Categorical Syllogisms are arguments composed entirely of categorical statements. For example:

All dogs are mammals
All mammals are animals
Therefore, all dogs are animals

In this case, dogs are the end term, mammals are the middle term and animals are the end term. The form of the argument is thus:

X=Y
Y=Z
Therefore, X=Z

A term is distributed in a categorical statement if that statement says something about each and every member of the class that the term designates. Example: All horses are mammals. In this statement the subject term (horses) is distributed because the statement says something about horses, but the predicate term (mammals) is undistributed because the statements makes no claim about mammals.

The fallacy of conclusion is an illogical syllogism that concludes (collectively) that a class has a property because (distributively) every member of that class has that property. For example, Each man on the team is an excellent player, therefore the team is an excellent one.

The fallacy of division is an illogical syllogism that concludes (distributively) that every member of a class has a certain property from the premise that the class (collectively) has that property. For example, Congress is a distinguished organization, therefore each congress man is a distinguished one.

Categorical Syllogisms:

A) Universal Affirmative
-Subject distributed
-Predicate undistributed

E) Universal Negative
-Subject distributed
-Predicate distributed

I) Particular Affirmative
-Subject undistributed
-Predicate undistributed

O) Particular Negative
-Subject undistributed
-Predicate Distributed

Three rules for testing the validity of the syllogism:

1. The middle term must be distributed exactly once.
2. No end term can only be distributed once.
3. The number of negative premises must equal the number of negative conclusions.

All three rules must be met for a syllogism to be valid.

The fallacy of every and all is the confusion of the two terms. It occurs when the premise states that for every 'F' there is some 'G' to which it has the relation 'R' but the conclusion finds that every 'F' has a relation 'R' to a specific 'G'. For example:

Premise: Every family here has a minivan
Conclusion: All the families here own a Dodge Caravan

The premise states that all the families in the neighborhood own a minivan, but the conclusion finds that all the families own the same type of minivan. You could check the garages and see if this was true or not, but that is immaterial. The truthfulness of the conclusion is not at question here. It is simply the fact that argument is illogical as constituted.

This was an over simplification of Deductive Logic. Deductive logic has much more complex arguments and proofs of arguments. But complex arguments can be separated into small arguments to test validity. They can be assigned symbols to make the testing quicker and more effective.