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What are Chrysippus’s five indemonstrable inference schemata?
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History of logic
Zeno's paradox, illustrated by Achilles' racing a tortoise.
The Stoic philosopher Chrysippus identified five basic inference schemata, which he termed "indemonstrables." These schemata served as the foundation for his propositional logic, using ordinal numerals as variables to represent entire propositions.12
The five indemonstrable schemata 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 utilized these five principles to demonstrate the validity of more complex arguments, as the Stoics believed that all valid inference schemata could be derived from these basic forms.12