The Traditional Square of Opposition
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Original Question
I noticed that, although Dr Bennett has entries for (illicit) conversion and contraposition , there aren't any for the other four logical operations that are prone to being performed incorrectly, like contradiction , contrary , subcontrary and subalternation . There also isn't one for obversion (though this is understandable). Is it because these are rare, or because they're not intuitive to most people?
For the uninitiated, I'll save you the struggle of looking it up yourself:
Statement types
A - "All/Every"
E - "No/None"
I - "Some"
O - "Some (is/are/will) not"
Logical operations
Contradictory - in other words, proof by contradiction, which shows the first statement to be false. This is valid for all the types. O contradicts A, and I contradicts E. This applies in reverse, too.
E.g. "All X are Y" is contradicted by "Some X are not Y." If some X are not Y, then "All X are Y" is a false statement.
Contrary - the opposite of the first statement. Paired together, at least one is false (but the other can also be false). If one is true, the other cannot be. A and E are contrary to one another.
E.g. "No X are Y" and "Every X are Y" cannot co-exist.
Subcontrary - similar to the contrary, except at least one statement must be true (the other may also be true). If one is false, the other cannot be. I and O are subcontrary to one another.
E.g. "Some S are P" and "Some S are not P" cannot both be non-existent.
Subalternation - stepping 'up' or 'down' a claim based on previous information. A and I are subalternates, as are E and O. If A is true, then I is also true. Likewise, if I is false, A is false. The same applies for the other side - if E is true, O is true. If O is false, E is false.
Where A is false or I is true, the other has an undetermined truth value. The same applies if E is false or O is true.
E.g. just because some S are P doesn't mean all S are P (illicit subalternation) but it also doesn't imply some S are not P (unwarranted contrast).
TL;DR - does Dr Bennett consider the other illicit operations fallacies that deserve to be classified in future works?
Answers
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