From ancient to new Stoicism: II—Stoic logic
A conceptual map of where Stoicism came from and where it may be going
We are in need of updating Stoicism for the 21st century and beyond. But in order to do that, we want a clear sense of what ancient Stoicism was about. In the first entry in this series we have looked at Stoic physics, one of the three areas of study in classical Stoic philosophy. This time we examine (briefly!) The second area: Stoic logic.
Don’t worry, this isn’t going to be a boring, heavily technical treatment. Then again, logic is fundamental not just for the Stoics, but for every thinking person. Here is how Epictetus explained why:
“Someone in the audience said, ‘Convince me of the usefulness of logic.’ ‘Shall I prove it to you?’ ‘Yes, please.’ ‘Then I’d better use a demonstrative argument, hadn’t I?’ His interlocutor agreed, and Epictetus went on, ‘So how will you know if my argument is fallacious?’ The man said nothing. ‘Do you see,’ Epictetus said, ‘that you are yourself admitting that logic is necessary, since without it you can’t even find out whether or not it’s necessary?’” (Discourses, 2.25)
Right? Okay, then, let us proceed, like last time, using as a guide the excellent article on Stoicism by Marion Durand and Simon Shogry, published in the Stanford Encyclopedia of Philosophy. You can go there if you need to dig deeper.
Rhetoric and dialectic
To begin with, Stoic logic included not just formal logic as we understand it today, but a broad range of disciplines related to sound thinking, including epistemology, grammar, philosophy of language, and rhetoric.
The two major branches of Stoic logic were rhetoric and dialectic. The first one was defined as “the science [or knowledge, epistêmê] of speaking well,” while the second one was “the science [or knowledge, epistêmê] of what signifies and what is signified” (Diogenes Laertius, Lives of the Eminent Philosophers, 7.42)
An important Stoic innovation was the introduction of what they called lekta, usually translated as “sayables.” The term covers everything that can be said, and therefore refers to the content of our thoughts, to our rational impressions, and to our judgments—pretty much what really matters to the Stoic.
The Stoics thought that the only bearers of truth in logic are propositions, often referred to as “assertibles,” a subset of sayables, since not everything that can be said is a bearer of truth. For example, is it true that unicorns have one horn? For the Stoics the question is undecided, since there are, in fact, no unicorns. The question itself, then, is a sayable but not an assertible.
Notice that a Stoic assertible can change truth value depending on the circumstances. If I say “it is day now” and it is in fact, day, the proposition is true. But it won’t be true tonight, and it will be true again tomorrow morning.
Stoic logic developed the truth conditions for combinations of assertibles: conjunctions (p and q), disjunctions (p or q), and conditionals (if p then q).
There is an important difference between Stoic logic and its more familiar Aristotelian counterpart: the Stoic system is one of propositional logic, while the Aristotelian one concerns predicate logic. That is, the Stoics were focused on the logic governing sentences, while Aristotle was occupied with the logic of terms. The two are not mutually exclusive and Stoic logic was much studied during the Middle Ages and Renaissance, representing the forefront of logical scholarship until the introduction in the 19th century of Gottlob Frege’s predicate logic. Technically, predicate (or first-order) logic is founded on propositional (or zeroth-order) logic. [1]
The basic axioms of Stoic logic
Stoic propositional logic was based 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.
Taking the indemonstrables as a starting point led to the development of Stoic syllogistics, i.e., of the rules of sound propositional reasoning. A syllogism is defined by the Stoics as a valid (i.e., correctly structured) argument. A sound (i.e., true) argument is then a valid argument the premises of which are true.
For instance, here is a 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 the argument is valid, it is not sound, because the first premise is not true: alas, not all philosophy courses are incredibly exciting!
The Master Argument
A major interest of the ancient Stoics (which they inherited from Aristotle and the Megarians) was modality, which deals with the difference between logical possibility and logical necessity. Arguably the most famous example was their discussion of the so-called Master Argument, attributed to the Megarian logician Diodorus Cronus.
The Master Argument says that of the following three propositions, only two (at most) can be true (Epictetus, Discourses, 2.19):
(i) Past truths are necessary;
(ii) Nothing impossible follows from something possible;
(iii) Something is possible which neither is nor will be true.
Modern logicians are uncertain about whether the three propositions are truly partially incompatible with each other, and unfortunately Diodorus’s proof for this has not survived. But assuming this to be the case, the ancients disagreed on which of the three propositions had to be abandoned.
Diodorus himself argued for the rejection of (iii), which means that what is possible is limited to what either is or will be true at some point in the future. The second head of the Stoa, Cleanthes of Assos, rather strangely preferred to reject (i), making past truths contingent. Finally, the third head of the Stoa, Chrysippus of Soli—one of the most important logicians of antiquity—rejected (ii).
Chrysippus’s move is interesting because it means that he retains the necessity of the past (unlike Cleanthes) as well as the notion that there are things which are possible but do not happen (unlike Diodorus). In other words, as Durand and Shogry point out, Chrysippus introduces a distinction between metaphysical (all things are fated and pre-determined by antecedent causes) and logical necessity (some things are logically possible but do not happen). This is at the core of his argument for compatibilism between determinism and free will, which is the standard Stoic view on human agency, as well as the one most widely accepted by contemporary philosophers. Who said logic doesn’t have interesting consequences?
Stoic epistemology
The last big topic that we need to tackle within Stoic logic is epistemology, their theory of knowledge. Which, I think, they got largely wrong by contrast with what their longtime rivals, the Academic Skeptics, were arguing. Let’s take a look.
The point of Stoic epistemology was to provide an account of knowledge (epistêmê), which they considered the highest intellectual achievement available to human beings. If you acquire true knowledge, according to the Stoics, you will not change your mind (i.e., your position with regard to something you know will be “stable”). This is not because you have become stubborn and close-minded, but because you have achieved sagehood. So, the stakes are high!
Importantly, knowing something for the Stoics doesn’t just mean grasping one particular truth. It also involves the understanding of how that truth fits with everything else we know about the world, an early definition of what we would noways call scientific knowledge.
Moreover, since virtue is a a type of knowledge (of “things human and divine,” as Cicero beautifully puts it in De Officiis, 2.5), if follows that only those who possess knowledge are truly happy. That’s a high bar, as not even the various heads of the Stoa claimed to be sages, and therefore to have knowledge and be happy. [2]
The Stoics made a distinction between knowledge (epistêmê), cognition (katalêpsis), and ignorance (agnoia). Only the sage has knowledge, while the rest of us are ignorant. However, both we and the sage can experience cognition. Let me explain.
Katalepsis (often translated as cognition) refers to a particular mental state, introduced by the founder of the Stoa, Zeno of Citium. Kataleptic impressions [3] are the sort of sensory or mental impressions that are so strong as to be for all effective purposes undeniable. For instance, I am right now having two kataleptic impressions: that the square root of nine is three, and that it is sunny outside my window.
No matter how hard you try, you will not convince me that either of those two impressions is incorrect. They appear, therefore, to be stable for good reasons, and hence to qualify as examples of knowledge. The difference between a sage and myself, however, is that I could still be wrong even about kataleptic impressions. It may very well be that I actually don’t know the square root of nine and that I am hallucinating the sunny day. The sage, by contrast, will know for sure that those two impressions are true, because she is somehow (the Stoics never explained exactly how) able to distinguish the “mark” or “criterion” that differentiates a true kataleptic impression from a false one.
Baloney, replied Academic Skeptics like Arcesilaus and Carneades. There is no criterion of truth out there in the world, and therefore no sharp distinction between the sage and the rest of us. All we have available are not Truths (with the capital T) but rather probabilities. Truth is not either/or, but a matter of degree, and changing one’s mind in the face of new evidence is not the hallmark of a feeble mind, but rather of an open one set on inquiry rather than dogma. As I said, I think the Skeptics got it right, this time.
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[1] More complex types of logic belong to a third class, known as higher-order.
[2] Epicurus, by contrast, had no such compulsion, and openly declared himself a sage.
[3] On the concept of impressions see our discussion of Stoic psychology under the general rubric of physics.
[Previous installments: Stoic physics. Next time: Stoic ethics.]
This was a fantastic read. Thank you
Kudos, Massimo...even with all my agnoia! 😄