Britannica
Sources used in this answer
How did Chrysippus use the five indemonstrables to prove further inferences?
Created from Britannica articles
using AI.
AI can make mistakes, so verify using Britannica articles.
History of logic
Zeno's paradox, illustrated by Achilles' racing a tortoise.
Chrysippus, the most prominent Stoic logician, utilized five basic inference schemata known as "indemonstrables" to establish the validity of more complex logical arguments.12
These five foundational principles 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.12
By employing these indemonstrables as building blocks, Chrysippus proved the validity of numerous further inference schemata. While the Stoics claimed that all valid inference schemata could be derived from these five, this assertion is considered incorrect by modern standards. Unlike Aristotelian logic, which focused on term logic, the Stoic approach centered on propositional logic, using ordinal numerals as variables to represent entire propositions rather than individual terms.12