Category Archives: Logic

Becker’s A New Stoicism, IV: normative Stoic logic

Larry Becker’s A New Stoicism, which I have discussed over three previous posts, is now getting into the heavy lifting of the second part of the book, “The way things might go,” comprising chapters 4-7 on normative logic, living according to nature (“follow the facts,” in Becker’s rendition), virtue, and happiness. This post comprises chapter 4, on normative Stoic logic.

Admittedly, this bit is not for the philosophically faint of heart, as the material is difficult to get through, despite (or maybe because) the brevity of the chapter itself. Still, it is very well worth the effort, as one gets, among other things, the beginning of an explanation of how Stoics bridge the so-called is/ought (fact/value) divide, which David Hume allegedly thought unbridgeable, but that any naturalistic ethics has, in fact, to bridge.

The first issue that Larry approaches in this context is defining norms and normative propositions, since ethics is a prescriptive (i.e., normative) discipline (as opposed to a descriptive one, like psychology). Norms — in this context — are simply facts about the behaviors of agents, i.e., about their goals, projects and endeavors. Normative propositions, then, are representations of facts about norms, and they can be true or false but can acquire no other truth value (i.e., Stoic logic is classical logic, not, for instance, paraconsistent).

Any logic is characterized by “operators,” i.e., by the logical equivalents of things like “plus,” “minus,” “divided by,” “multiplied by,” and so forth in mathematics. Standard deontic logic (a major modern approach to the use of formal logic in ethics) has operators like “obligation,” “permission,” and “prohibition.” Stoic moral logic, instead, uses operators like “requirement,” “ought,” and “indifference,” to which we now briefly turn.

Beginning with the definition of requirement:

“To say that an agent is required to do (or be) x is to say one or more of three things: (i) it may be to say that her doing or being x is in some sense a necessary condition for her pursuing some endeavor she has; (ii) it may be to say that within the terms of some endeavor, she ought to be (or it is required that she be) sanctioned for doing or being non-x; or (iii) it may be to say that her doing or being non-x would be a ‘nullity’ in her endeavor.” (p. 39)

For instance, if my endeavor is to become a better person, then I am required to practice the four cardinal virtues of practical wisdom, courage, justice, and temperance; I should be sanctioned if I do not practice those virtues (the word “sanctioned” here does not refer to formal punishments, it could simply be the result of me chastising myself when writing my evening diary, for instance); and if I do not behave virtuously then I am not in the process of becoming a better person.

Next, ought:

“To say that an agent ought to do or be x is to say that her doing (or being) x is advisable (but not necessarily required) in terms of some endeavor that she has.” (p. 38)

Notice that “ought,” here, does not have anything like the standard meaning that it has in modern moral philosophy, where it indicates an imperative. We as Stoics cannot make sense of moral imperatives that are detached from specific goals or endeavors, hence the “advisable rather than requires” bit above. Think of these as conditional imperatives, of the type: IF I want to do x, THEN I ought to do y.

Finally, indifference:

“The indifference operator is interpreted as a logical remainder. To say that it is a matter of indifference whether an agent does x is to say that her doing x is neither advisable nor inadvisable, neither required nor prohibited.” (p. 39)

In the case of my endeavor to become a better person, it is indifferent whether I am wealthy or not, as wealth has nothing to do with being a good person.

Becker then proceeds to distinguish three sets of possibilities to be used in our reasoning: logical, theoretical, and practical. Logical possibility is the largest set, and it includes the other two. It refers to things that are possible because they do not entail a logical contradiction. For instance, insisting in attempting to square the circle is futile, since we know that this is logically impossible.

Theoretical possibility refers to things that may be done, because they are not logically impossible, though whether they will be done depends on a set of pragmatic considerations. It is certainly logically possible to establish a human colony on Mars, for instance, but it may not be advisable to do so. Which means that practical possibility is the smallest set, contained by the other two, and refers to things that are logically and theoretically possible as well as, in fact, pragmatically realizable. My writing this commentary series on Larry’s book falls, obviously, in this latter category, as it is compatible, in practice, with a number of other endeavors I am currently engaged in. (Having another meeting with my Dean, by contrast, is pragmatically impossible, or so I tell myself right before politely declining his invitation.)

One more piece of the logical puzzle before we get to bridging the is/ought gap: it will often be the case that there will be conflicts among some of our endeavors and goals. Stoic logic comes built in with a way to resolve at least some of these conflicts from the get go: requirements take precedents over oughts, and both of these take precedence over indifferents. This is practically very important, because, among other things, it makes sense of what Stoics mean by “preferred indifferents.” If my goal is to become a more virtuous person (as it should be, if I’m a Stoic), then it is a requirement for me to practice the cardinal virtues, and that requirement overrides oughts related to other projects that may interfere with my main goal; both requirements and oughts related to compatible projects, in turn, override my pursuit of preferred indifferents, if that pursuit conflicts in any way with the requirements and oughts that have logical-ethical precedence. If pursuing wealth, say, is something I can do only by compromising my practice of virtue, then it is required of me, as a Stoic, not to pursue wealth.

We now get to how Stoics bridge the is/ought gap. Becker begins his treatment of this topic with an analogy: if I want to play a game, say chess, and win, then I ought to follow its rules, as well as to implement certain defensive and offensive strategies. If I don’t follow the rules, then I’m not playing the game. And if I don’t implement good strategies then I will not win at the game. Similarly with any kind of naturalistic philosophy, like Stoicism: IF I want to be a productive member of the human polis and live a flourishing human life, THEN I should be engaging in certain behaviors and not others (e.g., practice virtue, not comport myself like a psychopath). This conditional imperative follows from certain facts about human nature and human society, and it is the result of deliberate reflection on my part, “all things considered,” i.e., once I have evaluated all my priorities and goals in life.

As Larry puts it, for Stoics means/ends reasoning of the type just outlined is the underlying form of all practical reasoning. Most of our normative propositions, however, will be of the “nothing else considered” type, i.e., they will apply to local goals or endeavors. For instance, if my goal tonight is to have a romantic dinner with my partner, then I ought to buy some wine and flowers, and perhaps the ingredients to cook a good meal. But this sort of normative propositions can be in contrast with other normative propositions, e.g., tonight I really ought to grade my students’ papers, as a result of my commitments as a teacher and a professional. But I cannot both grade papers and set up a romantic dinner on the same night, for pragmatic reasons.

Stoic logic, as laid out by Larry, provides various means to resolve conflicts between normative propositions. Specifically:

“We resolve such conflicts by means of rules for generating superordinate normative propositions that dominate the conflicting ones. … When one endeavor is embedded in a more comprehensive and controlling one, the latter’s norms are superordinate. … When we recognize one endeavor as subject to assessment and correction by another, the latter’s norms are superordinate. … Sometimes norms of the same ordinal rank conflict. We resolve such conflicts with forced choices.” (pp. 43-44)

So, for instance, if I think of the need to spend a romantic evening with my partner and of the need to grade my students’ papers as on the same ordinal rank, then I juts have to make a forced choice between the two. But more likely then not, one norm will actually be superordinate: in this case, grading papers is part of my duty, both ethical and contractual, toward my students and employer. By contrast, spending a romantic evening is pleasant, but not a duty toward my partner, certainly not on that particular night. I should, then, grade the damn papers and promise to my partner that I will make it up to her the following night (at which point I will have an additional ethical duty to fulfill a promise made). Of course, the final level of superordinacy is represented by my duty to be a moral, virtuous person. That duty overrides everything else, including grading papers, should the two norms come into conflict.

The chapter ends with a succinct statement of four axioms of Stoic logic. These are explained in more depth, together with some additional axioms, in the appendix to the book devoted to formal logic, but the brief description that follows is sufficient for the general reader:

Axiom of Encompassment. The exercise of our agency through practical intelligence, including practical reasoning all-things-considered, is the most comprehensive and controlling of our endeavors.

Axiom of Finality. There is no reasoned assessment endeavor external to the exercise of practical reasoning all-things-considered.

Axiom of Moral Priority. Norms generated by the exercise of practical reasoning all-things-considered are superordinate to all others.

Axiom of Futility. Agents are required not to make direct attempts to do (or be) something that is logically, theoretically, or practically impossible.


On the nature of the Sage: II. How to transition to sagehood

While discussing René Brouwer’s The Stoic Sage: The Early Stoics on Wisdom, Sagehood and Socrates (Cambridge Press), we have encountered the two Stoic definitions of wisdom: (i) “knowledge of human and divine matters,” and (ii) “fitting expertise.” In chapter 2, Brouwer turns to the issue of what happens when someone transitions into sagehood. A note of caution: according to Seneca, this event (if it occurs at all) is as rare as the mythical bird, the phoenix, i.e., it takes place every half millennium or so. The chances you’ll personally achieve sagehood, therefore, ain’t that high. Still, I think that if one is interested in Stoic philosophy this is a topic worth briefly discussing.

Plutarch (who was not particularly sympathetic to the Stoics, and whose writings need, therefore, be interpreted with caution) says in “How a man may become aware of his progress in wisdom,” with barely veiled sarcasm:

“The sage changes in a moment or a second of time from the lowest possible inferiority to an unsurpassable character of virtue; and all his vice, of which he has not over a long time succeeded in removing even a small part, he instantaneously flees forever.” (Stoicorum Veterum Fragmenta, 3.539).

If taken seriously, this makes the transition to sagehood sound very much like revelation for a Christian (say, on the way to Damascus), or enlightenment for a Buddhist, with the difference that the source of the Christian transformation is external, while for both Stoics and Buddhists it is internal. It is also irreversible, as I think it is in Buddhism, but not necessarily in Christianity (where one can lose one’s way; perhaps precisely because the transformation was triggered from the outside in the first place?).

Much of Brouwer’s discussion here is based on the Synopsis of “The Stoics talk More Paradoxically than the Poets,” again by Plutarch. According to Plutarch’s Synopsis, then, two things immediately characterize the transition to sagehood: its speed, and the fact that it is a change between opposite states (vice and virtue).

The Synopsis also states that the Sage may be ugly rather than beautiful, and a beggar rather than a rich king. So don’t expect wisdom to correspond to external attributes, such as beauty and wealth or power.

Moreover, the Sage does not hold “opinions,” meaning changeable convictions about whatever matters he contemplates. That is because he has reached the pinnacle of human epistemic power: he does not have superhuman knowledge, but does have the best knowledge any human being can possibly achieve. His cognition, so to speak, is stable. Needless to say, from a contemporary standpoint this is simply nonsense, and it should be abandoned by modern Stoics. There is no human ideal of knowledge because knowledge is always context-dependent, and moreover it encompasses far too much for a single human mind to actually hold and comprehend. On these bases alone we may conclude that Sagehood — if so defined — is not just rare, it is unachievable.

Interestingly, Plutarch says — and Brouwer confirms that this is found also in other ancient texts on the topic — that the Sage is not “like” Zeus, he actually is divine. As Sextus Empiricus puts it, in his non-Stoic friendly “Against the Professors” (7.423):

“According to them [i.e. the Stoics] the sage possesses an infallible criterion, which makes him in all respects divine because he never holds opinions, that is assents to what is false, wherein lies the height of unhappiness and the ruin of the inferior person.”

This may struck the modern reader as just bizarre, until we remember that the Stoics did not literally believe in the Olympian gods, as for them god was the same as nature itself. And human beings participate in the Logos, so they are, in a sense, divine. Brouwer again: “Chrysippus explains in allegorical fashion that not only the Olympian gods such as Zeus, Ares and Hephaistos are to be ‘assimilated’ to, respectively, reason that rules over everything, war or the principle of order and disorder, and fire, but also that the sun and moon are gods. What we thus seem to have is an interpretation of the gods of traditional religion in terms of natural phenomena and an interpretation of natural phenomena in terms of the divine.” Ancient Stoicism, in other words, was pantheistic.

A further characteristic of the transition to sagehood is its radical nature. That is because the ancient Stoics maintained that there is nothing between vice and virtue, and that all bad deeds are equal. (I commented on this strange idea before, in terms of the famous drowning man metaphor.) Another way to explain this is summarized by Brouwer in this fashion: “According to Chrysippus in his fourth book Ethical Questions [see Diogenes Laertius 7.120, SVF 3.356], just as it does not matter whether the pilgrim is a hundred or a few miles away from Canopus [a sanctuary in the Nile delta which flourished in the third century BCE], as they are both not in Canopus, so it does not matter whether one makes a big or a small mistake: in either case, one is not virtuous.”

Well yes, technically, but really, the only charitable interpretation we can give of this, and the only reason we may entertain retaining this notion in modern Stoicism, is as a call for humility, along the Christian lines of “we are all sinners.” If taken literally, the analogy has very little force.

What about logic and knowledge? As we have seen above, the transition to sagehood also means that the Sage no longer holds to mere opinions, he actually has knowledge based on stable cognition. But even this is open to dispute, as Brouwer reminds us of the famous (and actually useful, I think) analogy of the hand: “Zeno is said to have compared the open palm of his hand with an impression, the fingers of his hand a bit contracted with assent to the impression, his fingers made into a fist with a cognition and the tight and forceful gripping of his other hand over the fist with knowledge.” It’s a “handy” (literally!) reminder, worth spelling out in sequence:

Open palm = Impression
Contracted fingers = Assent to the impression
Fist = cognition (which, however, may be unstable, if one is not a Sage)
Other hand over fist = knowledge (i.e., stable cognition, typical only of the Sage)

Finally, there is yet another weird thing about the Stoic Sage: he may be unaware of actually having achieved sagehood! Philo of Alexandria writes:

“They say that it is impossible that those people who have reached the highest wisdom and touched upon its borders for the first time, know their own perfection; for the two things do not happen at the same time, namely the arrival at the border and the cognition of arrival; in between the two there is ignorance of such a sort that is not far removed from knowledge, but close to it and on its doorstep.” (SVF 3.541)

Brouwer elaborates: “wisdom consists in the special disposition of character. As this disposition is the (only) condition for wisdom, the virtuous (or expert) disposition of the Sage need not be accompanied by the awareness of the fact that it is a virtuous disposition.”

This sounds to me rather odd, but I do wonder whether a Buddhist practitioner knows he has achieved enlightenment at the very moment he has, or whether a Christian mystic is aware of a state of divine bliss as it begins. Perhaps, again, the difference lies in whether the transition is triggered externally or the result of an internal change?

The Stoics tried to explain this by way, as usual, of an analogy. Let’s say you have been practicing for a long time a particular craft, for instance playing the flute. It is possible that you achieve “perfection” (whatever that means) at that craft without — again, initially — realizing it. Does it matter? No, because the earliest known characterization of wisdom, Brouwer tells us, goes back to Homer, and it implies that it is the mastery that counts, not the awareness of it.

Despite all the problematic aspects outlined above of the transition to sagehood, Brouwer concludes that in a very important sense the Sage remains a human being: “the sage is in a way ordinary, in the sense that he remains doing what he did before, that is judging each impression and placing it in the overall scheme of things. As it turns out, Stoic wisdom is very much a this-worldly affair: the person who becomes a Sage, will continue to live life as he did before, dealing with judging impressions.”

Becoming a Sage is, in effect, a type of initiation. In the Great Etymological Dictionary edited in 1848 by T. Gaisford, and cited by Brouwer, we find:

“Chrysippus says that the doctrines [logoi] on divine things are rightly called initiations: for these should be the last things to be taught, when the soul has found its stability and has become in control, and is capable of keeping silent [amuetous] towards the uninitiated. For it is a great reward to hear the correct things about the gods and to gain control.”

Notice the reference to “keeping silent to the uninitiated,” which sounds very much like it reflects some mystical approach to knowledge. Brouwer’s comment is intriguing: “Chrysippus apparently considered it prudent that the real truth about the nature of the gods should be kept secret. Chrysippus does not tell us why, but a suggestion is that bringing out truths that reduce the traditional gods to a force in nature did not go down well with the traditional supporters of Athenian civic religion.” This is a tantalizing hint that the Stoics, while not atheists, were potentially considered “impious” by the standards of their culture. And you know what happened to Socrates when that charge was raised against him…

Philosophy vs rationality vs therapy

stop and thinkStoicism is a philosophy, which means a general framework for navigating one’s life. It has a body of theory (e.g., the three disciplines) and a set of practices. Stoicism is just one particular philosophy of life, others include some of its Hellenistic competitors, such as Epicureanism, as well as bodies of ideas coming from outside the Western tradition, especially Buddhism. As Bill Irvine argues in his A Guide to the Stoic Life, the advantages of adopting or developing a more or less coherent philosophy of life is that one has always available a handy reminder of how to interpret things, what to prioritize, and how to behave. Not bad, if you ask me.

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Epictetus and the Master Argument

Phidias: Athena Parthenon, ~450BCE

Phidias: Athena Parthenon, ~450BCE

Epictetus, even more so than most Stoics, thought that philosophy has to be useful, or it becomes the kind of sterile intellectual exercise (some would dare say mental masturbation) that it is notorious for in certain quarters of the modern academy.

His attitude is perhaps most explicitly and fascinatingly on display in Discourses II.19, where he tackles the famous “Master Argument,” originally proposed by Diodorus Cronus in the III century BCE (i.e., about four centuries before Epictetus).

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Stoic logic

spockSusanne Bobzien’s chapter of the Cambridge Companion to the Stoics makes for a tough read, but it is definitely worth it for anyone seriously interested in Stoicism. It covers the basics of Stoic logic, and then some. I will only hit on some of the highlights, skipping much of the more technical details which Bobzien (rightly) gets into.

She begins by reminding her readers that Stoic logic was a type of propositional logic, concerned with what they called “assertibles,” the primary bearers of truth values. This makes perfect sense, given Stoicism’s concern with practical applications of philosophy: after all, human beings communicate by way of propositions, and the goal was to establish under what conditions what we say may or may not be truthful.

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