Undistributed Middle Fallacy Detector
Detect an undistributed middle term in the two premises of a standard categorical syllogism.
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. A syllogism must distribute its middle term in at least one premise to connect the two other terms.1
The tool returns undistributedMiddle. Interpret the result under the rule and assumptions below; an encoded premise’s truth is not independently established.
When to use Undistributed Middle Fallacy Detector
Use this for the following task: Detect an undistributed middle term in the two premises of a standard categorical syllogism. Prepare the specified logical encoding before running the check or transformation.
How to use Undistributed Middle Fallacy Detector 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 majorKind, minorKind, figure according to the field table, then run the tool.
- Read undistributedMiddle. 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 |
|---|---|---|---|
| majorKind | Major proposition kind | string; choices "A", "E", "I", "O" | Required |
| minorKind | Minor proposition kind | string; choices "A", "E", "I", "O" | Required |
| figure | Syllogism figure | integer; minimum 1; maximum 4 | Required |
Choose the two premise kinds and figure. Locate M in each premise using that figure and apply the distribution rules: A distributes its subject, E both terms, I neither, O its predicate.
undistributed middle ⇔ neither premise distributes M The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| undistributedMiddle | Undistributed Middle | boolean |
{
"input": {
"majorKind": "A",
"minorKind": "A",
"figure": 2
},
"output": {
"undistributedMiddle": true
}
}Limitations and assumptions
A false flag does not establish validity: other fallacies and existential assumptions still matter.
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 Illicit Minor Fallacy Detector when you need its operation: Detect a minor term distributed in a categorical conclusion but undistributed in its minor premise. Choose Illicit Major Fallacy Detector for the complementary operation: Detect a major term distributed in a categorical conclusion but undistributed in its major premise.
Background reference: Categorical Logic.
References
-
Categorical Logic — Philip B. Stark, University of California Berkeley
Similar or alternative tools
- Illicit Minor Fallacy Detector
Detect a minor term distributed in a categorical conclusion but undistributed in its minor premise.
- Illicit Major Fallacy Detector
Detect a major term distributed in a categorical conclusion but undistributed in its major premise.