Square of Opposition Contradictory Pair Mapper (A-O, E-I)
Map a categorical proposition to its contradictory form for the same subject and predicate.
Description
Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative.
Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative. Contradictories have opposite truth values for the same subject and predicate, including when the subject class is empty.1
The tool returns contradictory. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Square of Opposition Contradictory Pair Mapper (A-O, E-I)
Use this for the following task: Map a categorical proposition to its contradictory form for the same subject and predicate. Prepare the specified logical encoding before running the check or transformation.
How to use Square of Opposition Contradictory Pair Mapper (A-O, E-I) and understand its results
- Prepare the requested Boolean values, complete truth-table rows, or identifier atoms. An atom is a name such as p or premise_1, not a natural-language sentence.
- Enter kind according to the field table, then run the tool.
- Read contradictory. Use the matching rule, assignment order or nonempty-class assumptions below to interpret the result.
- For a false check, inspect the supplied encoding and matching rule. A well-formed false result is different from an input error.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| kind | Categorical proposition kind | string; choices "A", "E", "I", "O" | Required |
Select an A/E/I/O kind. Return the fixed contradictory partner while implicitly retaining the original subject and predicate.
A ↔ O; E ↔ I The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| contradictory | Contradictory proposition kind | string |
{
"input": {
"kind": "A"
},
"output": {
"contradictory": "O"
}
}Limitations and assumptions
The result is a form label; no proposition text, truth value or nonempty-class assumption is supplied or inferred.
The supplied encodings must represent the intended propositions or classes. No natural-language parsing or assessment of empirical premise truth is performed. Malformed input gives a tool error rather than a logical false result.
Alternative or Complementary methods
Choose Square of Opposition Subcontrary Pair Mapper (I-O) when you need its operation: Map an I or O proposition to its subcontrary and state whether a nonempty subject guarantees the relation. Choose Square of Opposition Contrary Pair Mapper (A-E) for the complementary operation: Map an A or E proposition to its contrary and state whether a nonempty subject guarantees the relation.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- Square of Opposition Subcontrary Pair Mapper (I-O)
Map an I or O proposition to its subcontrary and state whether a nonempty subject guarantees the relation.
- Square of Opposition Contrary Pair Mapper (A-E)
Map an A or E proposition to its contrary and state whether a nonempty subject guarantees the relation.