Immediate Inference
Immediate inference is the process of drawing a logical conclusion from a single categorical statement — without combining it with any other premises. Unlike syllogisms (which need two premises), immediate inference derives new claims by formally manipulating one statement’s structure.
How It Appears Per Course
PHIL 252
Unit 5, as part of the categorical logic framework. Immediate inference extends the power of categorical statements: knowing one statement lets you derive logically equivalent or logically opposed statements.
The Six Relations
Equivalences (the inferred statement is logically equivalent to the original)
| Operation | How | Valid For | Example |
|---|---|---|---|
| Conversion | Switch subject and predicate | E and I only | ”No S are P” ↔ “No P are S” |
| Contraposition | Switch S and P, then replace both with their complements | A and O only | ”All S are P” ↔ “All non-P are non-S” |
| Obversion | Change quality (aff↔neg) + replace predicate with its complement | All four types | ”All S are P” ↔ “No S are non-P” |
Opposition Relations (logical opposition, not equivalence)
| Relation | Pair | Property |
|---|---|---|
| Contradiction | A↔O, E↔I | Cannot both be true; cannot both be false |
| Contrariety | A vs. E | Cannot both be true; can both be false |
| Subcontrariety | I vs. O | Cannot both be false; can both be true |
| Subalternation | A→I, E→O | If A is true, I must be true (if class is non-empty) |
The Square of Opposition
A visual diagram showing all six relations among the four statement types simultaneously:
- A (top-left) and E (top-right) are contraries
- I (bottom-left) and O (bottom-right) are subcontraries
- A and O are contradictories; E and I are contradictories
- A and I are subalternation; E and O are subalternation
Worked Example
Original: “All poets are imaginative people.” (A statement)
- Obverse: No poets are non-imaginative people. (equivalent — always works)
- Contrapositive: All non-imaginative people are non-poets. (equivalent — works for A)
- Converse: All imaginative people are poets. (NOT equivalent — conversion invalid for A)
- Contradictory: Some poets are not imaginative people. (A and O contradict)
Common Errors
- Attempting conversion on A or O statements (invalid)
- Attempting contraposition on E or I statements (invalid)
- Confusing contrariety (cannot both be TRUE) with contradiction (cannot be same truth value)
- Forgetting that obversion always works — it’s the universal operation
Cross-Course Connections
CategoricalStatements — immediate inference operates on the A/E/I/O forms
Syllogism — immediate inference feeds into and supports syllogistic reasoning
Validity — equivalences preserve truth; oppositions define boundaries
Key Points for Exam/Study
- Obversion: always valid, change quality + complement predicate
- Conversion: E and I only (the “symmetric” ones)
- Contraposition: A and O only
- Contradiction: A/O and E/I pairs — always opposite truth values
- Contrariety (A,E): cannot both be true — but can both be false (the world might be mixed)
- Subcontrariety (I,O): cannot both be false — at least one must hold