Logic / Unit 3 Logic 087 worked example, 60 to 90 seconds
Applying Immediate Inferences
The idea
Applying immediate inferences means starting from one statement known to be true and chaining conversion, obversion, and contraposition, checking at each link whether that operation is legal for that form.
In practice
Start from a true A statement: all sparrows are birds. Obvert it — change the quality and replace the predicate with its complement: no sparrows are non-birds. Obversion is legal on all four forms, so that link holds. Go back to the original and contrapose instead: swap subject and predicate, then negate both. All non-birds are non-sparrows. Contraposition is legal on A, so that link holds too. Now insert the bad one. Convert the original: all birds are sparrows. Conversion swaps subject and predicate and touches nothing else, and it is legal only on E and I statements. On an A statement it fails, and the output is false although the starting point was true. The chain still reads in orderly steps while the meaning has quietly reversed.
Where people slip
The operations are easy to perform and equally easy to perform on a form that does not permit them, because nothing in the mechanics resists. Conversion on an A statement yields a grammatical sentence that sounds reasonable. Check which forms allow the operation before applying it — the result carries no mark of having come from an illegal move.
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