Represent the first example abstractly:
Premise 1: If A, then B.
Premise 2: If B, then C.
Conclusion: If A, then C.
B is the shared intermediate component. The consequent of the first premise matches the antecedent of the second, producing one directed chain.
The reverse “If C, then A” does not follow. Reversing a conditional needs a separate justification and cannot be smuggled into the conclusion.
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Conjunctive Syllogisms with Conditional Propositions
Represent the first example abstractly:
Premise 1: If A, then B.
Premise 2: If B, then C.
Conclusion: If A, then C.
B is the shared intermediate component. The consequent of the first premise matches the antecedent of the second, producing one directed chain.
The reverse “If C, then A” does not follow. Reversing a conditional needs a separate justification and cannot be smuggled into the conclusion.