Before the Stoics taught inner calm, they trained sharp thinking. Their logic is a switchboard: flip the right connections, and messy talk lights up with clarity.
WHAT IS SAYABLE?
Stoics distinguished sound from meaning. The spoken words 'It is day' are an utterance; the meaning grasped is a sayable (lekton). Among sayables, an assertible (axiÅma) is the kind that can be true or false; commands and questions are not. Think of sheet music (utterance), the melody (lekton), and the actual concert (the external thing).
Lekta are incorporealsālike time, place, and void. Only bodies act or are acted upon in Stoic physics; sayables 'subsist' and bear truth without pushing anything around.
FROM WORDS TO CONNECTIVES
Building on sayables, Stoics pioneered propositional logic: reasoning with whole statements. Their key connectors are if...then (conditional), both...and (conjunction), either...or (disjunction), and not (negation). This lens captures everyday arguments better than cataloging 'All A are B'ābecause life speaks in claims, not just categories.
“Guard your assent; propositions knock all day, but you choose which to let in.”
ā Stoic exercise, after Epictetus
THE FIVE INDEMONSTRABLES
Chrysippus canonized five basic valid moves. (1) If p then q; p; therefore q. (2) If p then q; not q; therefore not p. (3) Not both p and q; p; therefore not q. (4) Either p or q; p; therefore not q. (5) Either p or q; not q; therefore p. Example: If it is day, it is light; it is day; therefore it is light.
Stoic 'either/or' is exclusive: not both. Thatās why from 'Either p or q' and 'p' they could conclude 'not q'.
WHEN DOES 'IF' REALLY BIND?
The Stoics asked when an if-then is genuinely tight. Chrysippus wanted a secure conditional: it should be impossible for the antecedent to be true while the consequent is false, not merely unlikely. In practice, they tested by seeing whether 'p and not q' clashes with how the world hangs togetherāso 'If it is day, it is light' passes, but 'If it is day, Iām a poet' does not.
Practice by abstracting content: replace claims with p, q, r to see the form, then restore the sentences and ask whether the conditional link is genuine rather than accidental. Donāt assent until both checks pass.
- Works with whole statements and connectors (if, and, or, not).
- Excels at conditionals, dilemmas, and everyday argument flow.
- Ancestor of modern logicās truth-functional thinking.
- Works with terms and predication (All, Some, No).
- Excels at classification and essence-based inferences.
- Foundation of medieval syllogistics and taxonomy.
- Sayables (lekta) are meanings; assertibles are the truth-evaluable ones.
- Stoic logic reasons with whole propositions connected by if/and/or/not.
- Five indemonstrables capture core valid argument forms.
- Their disjunction is exclusive; sound conditionals demand a real tie.
- Test form first, then content, before giving assent.