Premise 1: All birds are living beings.
Premise 2: All cows are living beings.
Invalid conclusion: All cows are birds.
Both classes belong to a broader class, but this does not make them identical or make one a subset of the other. A repeated middle term alone does not ensure a valid link.
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An invalid argument with a shared attribute
Ḥujjah: Deriving a Conclusion from Known Judgments
Premise 1: All birds are living beings.
Premise 2: All cows are living beings.
Invalid conclusion: All cows are birds.
Both classes belong to a broader class, but this does not make them identical or make one a subset of the other. A repeated middle term alone does not ensure a valid link.