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What were Chrysippus’s five indemonstrable inference patterns?
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Ancient logic
Zeno's paradox, illustrated by Achilles' racing a tortoise.
Chrysippus, a central figure in Stoic philosophy, identified five basic inference schemata that he considered indemonstrable. These patterns served as the foundation for his propositional logic, which focused on inferences from hypothetical propositions rather than the term logic favored by the Aristotelians.12
The five indemonstrable inference patterns are:
- If the first, then the second; but the first; therefore, the second.
- If the first, then the second; but not the second; therefore, not the first.
- Not both the first and the second; but the first; therefore, not the second.
- Either the first or the second; but the first; therefore, not the second.
- Either the first or the second; but not the second; therefore, the first.
Chrysippus used these five principles to prove the validity of numerous other inference schemata, as the Stoics believed that all valid logical inferences could be derived from these foundational patterns.12