Example · Undergraduate
Terms
| Term | This example | Why |
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| propositional logic |
$p, \; q \;\therefore\; r$, which is not valid
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In propositional logic, the three statements of the Socrates argument are unrelated units $p$, $q$, and $r$, so the argument is not valid: the truth assignment with $p$ and $q$ true and $r$ false makes the premises true and the conclusion false.
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| first order logic |
$\forall x \, (H(x) \implies M(x)), \; H(s) \;\therefore\; M(s)$, which is valid
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In first-order logic, the Socrates argument is valid, because the formulas show the shared parts of the statements: taking $x = s$ in $\forall x \, (H(x) \implies M(x))$ gives $H(s) \implies M(s)$, and with $H(s)$ this gives $M(s)$.
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