Ancient Greek Logic

April 15, 2025

Both the Stoics and Aristotle developed logical systems in ancient Greece that competed during their time. But how do these systems compare? What distinguishes one from the other?

In simple terms, Aristotelian logic focuses on what can be deduced from a set of given statements. Stoic logic, by contrast, is concerned with the structure of the statements themselves—what truth values they can have and how those values relate to one another.

Consider this classic Aristotelian argument:

Premise 1: All men are mortal.
Premise 2: Socrates is a man.
Conclusion: Therefore, Socrates is mortal.

Here, we begin with premises—statements assumed to be true—and use them to derive a conclusion. Aristotelian logic relies on quantifiers like all or some, but it doesn’t involve logical connectors such as and, or, or if…then between the premises.

Now let’s look at an example of Stoic logic:

If it is day, it is light.
It is day.
Therefore, it is light.

At first glance, this may seem similar. However, the Stoic approach treats the entire argument as a compound statement built from smaller parts connected by logical operators like if…then. Unlike Aristotelian logic, Stoic logic does not use quantifiers—it works instead with propositional connectives and focuses on how statements combine and what follows logically from their structure.

One helpful way to distinguish them is this: to formally analyze an argument, we often need both systems. Aristotelian logic helps us infer new conclusions from general principles, while Stoic logic allows us to evaluate how statements connect and whether an argument is valid based on the truth of its components.

Both systems laid the foundation for modern logic. Aristotelian logic evolved into first-order logic, which includes quantifiers and predicates. Stoic logic, on the other hand, developed into propositional logic, also called zeroth-order logic, which operates on whole statements and their truth values.

So, rather than asking which system is “better,” it’s more accurate to say that they serve different purposes—and both are still highly relevant today. In fact, both are typically taught in undergraduate logic and computer science courses.