1. Universal affirmative: “All parrots are birds.”
Valid converse: “Some birds are parrots.”
Reason: the bird class contains other species too.
2. Universal negative: “No triangle is a circle.”
Valid converse: “No circle is a triangle.”
Reason: complete disjointness.
3. Particular affirmative: “Some teachers are authors.”
Valid converse: “Some authors are teachers.”
Reason: shared individuals.
4. Particular negative: “Some birds are not pigeons.”
No guaranteed converse: “Some pigeons are not birds” is false.
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Four worked conversions
Simple Conversion: Definition, Categorical Rules and Reductio
1. Universal affirmative: “All parrots are birds.”
Valid converse: “Some birds are parrots.”
Reason: the bird class contains other species too.
2. Universal negative: “No triangle is a circle.”
Valid converse: “No circle is a triangle.”
Reason: complete disjointness.
3. Particular affirmative: “Some teachers are authors.”
Valid converse: “Some authors are teachers.”
Reason: shared individuals.
4. Particular negative: “Some birds are not pigeons.”
No guaranteed converse: “Some pigeons are not birds” is false.