Unit 3: Immediate Inference & The Square of Opposition
How the truth or falsity of one proposition necessitates the truth or falsity of another.
Table of Contents
1. Immediate vs. Mediate Inference
In logic, Inference is the process by which a conclusion is derived from one or more premises.
- Immediate Inference: The conclusion is drawn from one single premise (e.g., Square of Opposition, Conversion).
- Mediate Inference: The conclusion is drawn from two or more premises (e.g., Syllogisms).
2. The Aristotelian Square of Opposition
The Square of Opposition maps the logical relationship between A, E, I, and O propositions when they have the same subject and predicate.
(Diagram representing Contradictories, Contraries, Subcontraries, and Subalternation)
3. The Four Logical Relations
| Relation | Propositions | Logical Rule |
|---|---|---|
| Contradictories | A-O and E-I | They have opposite truth values. If one is true, the other must be false. They cannot both be true and cannot both be false. |
| Contraries | A-E | They cannot both be true, but they can both be false. If one is true, the other is false. If one is false, the other is undetermined. |
| Subcontraries | I-O | They cannot both be false, but they can both be true. If one is false, the other is true. If one is true, the other is undetermined. |
| Subalternation | A-I and E-O | If the Universal (A/E) is true, the Particular (I/O) is true. If the Particular is false, the Universal is false. |