The need to modernize Stoicism for the contemporary era is pressing. To achieve this, we must first grasp the essence of ancient Stoicism. In the previous article, we delved into Stoic physics, one of the three core areas in classical Stoic thought. This time, we will briefly explore the second area: Stoic logic.

Rest assured, this won’t be a tedious, overly technical discussion. Logic is essential for Stoics and for anyone who thinks critically. As Epictetus articulated:

“Someone in the audience asked, ‘Convince me of the usefulness of logic.’ ‘Shall I prove it to you?’ ‘Yes, please.’ ‘Then I’d better use a demonstrative argument, shouldn’t I?’ The individual agreed, prompting Epictetus to ask, ‘How will you determine if my argument is fallacious?’ The man remained silent. ‘Do you see,’ Epictetus replied, ‘that you are acknowledging the necessity of logic, since without it, you can’t even ascertain its necessity?’” (Discourses, 2.25)

Now that we’re on the same page, let’s proceed, as we did previously, using the insightful article on Stoicism by Marion Durand and Simon Shogry in the Stanford Encyclopedia of Philosophy as our guide. For deeper exploration, feel free to consult that resource.

Rhetoric and Dialectic

Initially, Stoic logic encompassed not only what we now consider formal logic but also a wide array of related disciplines that contribute to sound reasoning, such as epistemology, grammar, philosophy of language, and rhetoric.

The two primary branches of Stoic logic were rhetoric and dialectic. Rhetoric was defined as “the science [or knowledge, epistêmê] of effective speaking,” while dialectic was described as “the science [or knowledge, epistêmê] of what signifies and what is signified” (Diogenes Laertius, Lives of the Eminent Philosophers, 7.42).

A significant Stoic innovation was the concept of lekta, typically translated as “sayables.” This term encompasses everything that can be articulated, referring to the substance of our thoughts, rational impressions, and judgments—elements of utmost importance to the Stoics.

The Stoics posited that the only carriers of truth in logic are propositions, often termed “assertibles,” which are a subset of sayables; not everything expressible qualifies as a bearer of truth. For instance, the assertion that unicorns possess a single horn is regarded as undecided by Stoics, given that unicorns do not exist. Hence, while the assertion itself is a sayable, it is not an assertible.

It is crucial to note that the truth value of a Stoic assertible can fluctuate based on context. If I state, “It is currently daytime,” and it is indeed day, the proposition holds true. However, it will not be true later tonight, and it will hold true again tomorrow morning.

Stoic logic further developed the truth conditions for combinations of assertibles: conjunctions (p and q), disjunctions (p or q), and conditionals (if p then q).

A key distinction exists between Stoic logic and the more familiar Aristotelian framework: Stoic logic is rooted in propositional logic, while Aristotelian logic pertains to predicate logic. This means that Stoics focused on the logical structure of sentences, whereas Aristotle analyzed the logic of terms. The two frameworks are not mutually exclusive; Stoic logic was extensively studied during the Middle Ages and Renaissance, representing the cutting edge of logical scholarship until the advent of Gottlob Frege’s predicate logic in the 19th century. Technically, predicate logic builds upon propositional logic. [1]

The Fundamental Axioms of Stoic Logic

Stoic propositional logic was founded on five axioms, which the Stoics referred to as “indemonstrables.” Here they are:

• if p then q; p; therefore q (modus ponens);
• if p then q; not-q; therefore not-p (modus tollens);
• not both p and q; p; therefore not-q;
• either p or q; p; therefore not-q;
• either p or q; not-p; therefore q.

Starting from these indemonstrables allowed the development of Stoic syllogistics, which are the principles of valid propositional reasoning. A syllogism, as defined by the Stoics, is a structured argument that is valid. An argument is sound if it is valid and its premises are true.

For example, consider the following valid argument:

Premise 1: All philosophy courses are incredibly exciting; Premise 2: All logic courses are philosophy courses; Conclusion: Therefore, all logic courses are incredibly exciting.

While this argument is valid, it is not sound because the first premise is false: not all philosophy courses are exciting!

The Master Argument

A significant focus of the ancient Stoics, inherited from Aristotle and the Megarians, was modality—the distinction between logical possibility and logical necessity. One of the most renowned examples is the so-called Master Argument, attributed to the Megarian logician Diodorus Cronus.

The Master Argument posits that out of the following three propositions, only two (at most) can be true (Epictetus, Discourses, 2.19):

1. Past truths are necessary;
2. Nothing impossible follows from something possible;
3. Something is possible which neither is nor will be true.

Modern logicians debate whether these three propositions are genuinely partially incompatible, and unfortunately, Diodorus’s proof for this has not survived. Nevertheless, the ancients had differing opinions on which of the three propositions had to be discarded.

Diodorus himself argued for the rejection of (iii), suggesting that what is possible is confined to what is or will be true at some point. Cleanthes of Assos, the second head of the Stoa, controversially preferred to reject (i), viewing past truths as contingent. Meanwhile, Chrysippus of Soli, one of antiquity’s most significant logicians, rejected (ii).

Chrysippus’s position is intriguing because it allows him to maintain the necessity of the past (unlike Cleanthes) while also asserting that some possibilities may not actualize (unlike Diodorus). As noted by Durand and Shogry, Chrysippus introduces a distinction between metaphysical necessity (everything is predetermined by prior causes) and logical necessity (some things are logically possible yet do not occur). This distinction is central to his argument for compatibilism between determinism and free will, a perspective widely accepted in Stoic philosophy and contemporary thought. Who said logic lacks engaging implications?

Stoic Epistemology

The final significant topic to address within Stoic logic is epistemology, or their theory of knowledge. In this regard, they largely diverged from the views of their long-standing rivals, the Academic Skeptics.

Stoic epistemology aimed to define knowledge (epistêmê), which they regarded as the pinnacle of intellectual achievement for humanity. According to the Stoics, attaining true knowledge means that one will not waver in their beliefs; this is not due to stubbornness but rather to achieving sagehood. Thus, the stakes are high!

Crucially, knowing something for the Stoics encompasses not just grasping a single truth but understanding how that truth integrates with our broader knowledge of the world—an early version of what we would now refer to as scientific knowledge.

Moreover, since virtue is a form of knowledge (concerning “human and divine matters,” as Cicero eloquently states in De Officiis, 2.5), it follows that only those who possess knowledge can be truly happy. This sets a high standard, as even the various leaders of the Stoa did not claim to be sages, and thus did not possess knowledge or happiness. [2]

The Stoics distinguished between knowledge (epistêmê), cognition (katalêpsis), and ignorance (agnoia). Only the sage possesses true knowledge, while the rest of us remain ignorant. However, both the sage and laypersons can experience cognition.

Katalepsis refers to a specific mental state, introduced by Zeno of Citium, the founder of the Stoa. Kataleptic impressions are sensory or mental perceptions that are so compelling they are practically undeniable. For example, I am currently experiencing two kataleptic impressions: that the square root of nine equals three, and that it is sunny outside my window.

No amount of persuasion could convince me otherwise about these impressions; they seem stable and thus qualify as knowledge. The distinction between a sage and myself lies in the fact that I could still be mistaken about these kataleptic impressions. It is possible I might misunderstand the square root of nine or misinterpret the weather. In contrast, the sage can confirm the truth of these impressions because they possess an unarticulated criterion distinguishing genuine kataleptic impressions from false ones.

Academic Skeptics like Arcesilaus and Carneades countered this view, arguing that no definitive criterion of truth exists, leading to a blurred line between the sage and the average person. They asserted that we deal not with absolute truths but with probabilities. Truth is not simply binary; it exists on a spectrum, and adjusting one’s beliefs in light of new evidence reflects an open, inquisitive mindset rather than a weak one. In this instance, I believe the Skeptics were correct.

[1] More advanced forms of logic fall under a third category known as higher-order logic. [2] In contrast, Epicurus had no such reservations and openly declared himself a sage.