Discover your intellectual strengths
These rules confirm the validity of an argument. On the flip side, they may also be said to negate the possibility of a valid argument (in the case of fallacies). Use these rules in tandem with the Euler case diagrams. Keep in mind that any one of these rules can render an argument invalid.
When both premises are positive, then the conclusion must be positive.
Exactly one of the premises of the argument must be negative in order to reach a negative conclusion. Two negative premises results in an invalid argument (rule 6).
For example, all conclusions of All A is B, and All B is C, are true. If both the statements are positive, then the conclusion must be true.
Related: 'Negative conclusion from affirmative premises' is a fallacy that occurs whenever an argument has two affirmative premises, and a negative conclusion.
When 'No' appears in a statement, 'Some-not' should follow as a valid possible conclusion.
For example, if A is not B, then some A is not B also follows.
The middle term must be distributed in at least one of the two premises. (Fallacy of the undistributed middle).
The middle term is the common term between two given premises.
When the major term is distributed in the conclusion, it should also be distributed in the major premise. (Fallacy of the illicit major).
The major premise contains the middle term and the major term (predicate).
When the minor term is distributed in the conclusion, it should also be distributed in the minor premise. (Fallacy of the illicit minor).
The minor premise contains the middle term and the minor term (subject).
When both statements are negative, no conclusion is possible. (Fallacy of exclusive premises.)
Negative premises are independent statements with no direct connection; the excusivity of the terms implies means that no valid conclusion can be derived.
If one statement is negative, the conclusion must be negative. (Affirmative conclusion from negative premise fallacy).
If both statements start with 'some', no conclusion is possible.
If a statement begins with 'some', the conclusion must begin with 'some'.
If both premises are universal, and the conclusion requires a class to have at least one member, then it's important for a specific class in the premises to be non-empty.
If the above conditions hold true therefore, particular conclusions (some/some not) may be invalidated depending on which classes are empty/non-empty.
This 'existential rule' derives from the fact that in everyday language, 'some' means at least one. All Panthers are Malaysian would be a valid statement, even if all Panthers were extinct. 'Some' panthers however, would require information that at least one panther is in existence for the argument to be valid.
It is usually taken for granted that classes are non-empty. Keep in mind that in the strictest sense, if an argument is to satisfy the existential rule, then information about non-empty classes should be displayed with the question.