# Logic & Propositions Mediate & Immediate Inference YouTube Lecture Handouts

## Logic & Propositions Mediate & Immediate Inference

Subject and predicate in propositions

### Immediate Inference

• Implication - If a given proposition is A - type, then it also implies that the I - type conclusion must be true
• E - Type proposition also implies an O - type conclusion.
• Conversion - The first step is to change the subject as the predicate and the predicate as the subject. The second step is to change the type of the given proposition to the pattern given in the following table. Type of the given proposition Type of the proposition after conversion
• A I
• E E
• I I
• O Cannot be converted
• All cats are dogs ⇾ All dogs are cats ⇾ Some dogs are cats
• Conversion is the inference in which the subject and predicate are interchanged. In modern logic, it is only valid for the E and I propositions. The valid converse is logically equivalent to the original proposition. In traditional logic, the A proposition has a converse by limitation which is the subaltern of the invalid A-converse; i.e.. , the corresponding I proposition. The converse by limitation is implied by the original but is not (usually) equivalent to it.

Original converse valid? By Limitation

• All S are P All P are S no Some P are S
• No S are P No P are S yes
• Some S are P Some P are S yes
• Some S are not P Some P are not S no

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