Philosophy Models

Stoic logic, elaborated by Chrysippus (297-206 BC), is one of the two major systems of logic (the other one is Aristotelian logic) in the classical world and can be characterized by:

• It is propositional logic (unlike the Aristotelian [1.3.9], which is term logic), because analyses the relations and truth values of assertibles (or propositions). Here logical variables are propositions, while in Aristotelian logic terms.
• It is concerned more with particulars (unlike the Aristotelian logic, which is analyzing categorization and universals) reflecting thus the stoic view that only particulars are real existents (see also [2.2.5]).

The stoic logic, represented in the OntoUML diagram below, operates with the following main classes and relationships:

Class	Description	Relations
Sayable	Sayable (lekta) (see also in [2.2.2]): “are the underlying meanings in everything we say and think, but… also subsist independently of us. They are distinguished from spoken and written linguistic expressions: what we utter are those expressions, but what we say are the sayables.”
Assertible	“Assertibles (axiômata) are sayables having a truth value: at any one time they are either true or false. So truth is temporal and assertibles may change their truth-value. They can never be true and false at the same time (law of non-contradiction) and they must be at least true or false (law of excluded middle).”	subkind of Sayable
TruthValue	The truth value of an Assertible might change over time, so each value is valid from the startTime to endTime.	characterizes Assertible
SimpleAssertible	Simple assertibles include propositions like: “it is cold”; “it is raining this morning” and “no one is running.”	subkind ofAssertible; component of Non-simpleAssertible
Non-simpleAssertible	Non-simple assertibles are compound of simple assertibles linked with logical connectives, like: if.. than, and, either.. or, since, because. E.g. “if it is winter than it is cold”; “either it is day or night”; and “I am moving since I am working”.	subkind of Assertible; is component of SimpleAssertible
Premise	Premise is an Assertible, e.g. “it is winter”; “if it is winter than it is cold”.	role of Assertrible; deducts conclusion
Conclusion	Conclusion is an Assertible, e.g. “it is cold”.	role of Assertrible
Argument	Arguments relates two (or more) Premises to a Conclusion as cause and effect. At least one Premise has to be a Non-simpleAssertible. E.g. Premise1: “if it is winter than it is cold”; if P than Q Premise2: “it is winter”; P Conclusion: “it is cold”; therefore Q	mediates between Premise and Conclusion; if Argument is valid can be reduced to StoicSyllogism
StoicSyllogism	Stoic syllogism “is best understood as a… natural-deduction system that consists of five kinds of axiomatic arguments (the indemonstrables) and four inference rules, called themata. An argument is a syllogism precisely if it either is an indemonstrable or can be reduced to one by means of the themata. Thus syllogisms are certain kinds of formally valid arguments. The Stoics explicitly acknowledged that there are valid arguments that are not syllogisms; but assumed that these could be somehow transformed into syllogisms.”
Indemonstrable	The five indemonstrables are: 1/ Modus ponens: If p, then q.  p. Therefore, q. 2/ Modus tollens: If p, then q. Not q. Therefore, not p. 3/ Not both p and q.  p. Therefore, not q. 4/ Modus tollendo ponens: Either p or q. Not p. Therefore, q. 5/ Modus ponendo tollens: Either p or q.  p. Therefore, not q.	member of StoicSyllogism
Themata	“Complex syllogisms could be reduced to the indemonstrables through the use of four ground rules or themata. Of these four, only two have survived. E.g. when from two assertibles a third follows, then from either of them together with the contradictory of the conclusion the contradictory of the other follows.”	member of StoicSyllogism

Sources

• All citations from: Bobzien, Susanne, “Ancient Logic“, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.)
• Bobzien, Suzanne, Stoic Logic, Cambridge Companions Online © Cambridge University Press, 2006

First published: 13/6/2019
Updated: 15/1/2022