In this past two years, I’ve had over 7,000 readers who have viewed nearly 17,000 posts. Thank you very much for your interest in Stoicisim, for making me a part of that, and for contributing to the blog.
Here’s a to a few more, eh? (;
— The MountainStoic
Our classic Stoics often spent a good deal of time on Logical problems. As I wrote yesterday about the question regarding ‘right reason’ (Gr: ὀρθὸς λόγος), the foundation of Stoic epistemology requires that true understanding is possible, via the idea of katalepsis (Gr: κατάληψις). The idea of the Sage necessitates it, and without the Sage there isn’t a measure for our own knowledge and progress.
One such issue is the “Sorites Paradox,” so named for the Greek word for ‘heap’ which is σωρίτης. The basic paradox has two forms.
First:
If I place down a single grain of sand, is it a heap? “No,” you will say. I will continue placing down grains and asking the question, until at some point you admit, “yes, that’s a heap.” Then I remove one. ‘Is this still a heap?’ Thus the paradox, that one grain of sand cannot determine heapness.
Second:
I start with a heap of 10,000 grains of sand, since the absence of one grain cannot unmake a heap (see above), we will recursively remove grains until there is 1, and then 0. Both of these would necessarily qualify as heaps per the above. Paradox. We can even logically go further to negative numbered grains still being heaps if Heap-Number minus 1 always yields a new Heap-Number.
We can see this same problem with baldness, plucking the hairs from the head one-by-one, at what point would we call him bald? The English form of the word “balding” might provide us with a logical escape here, in that he is in the process of becoming bald, but that’s neither here nor there.
We can also see it in the issues of collective nouns for groups of animals, as shown by this joke image, on the right. A murder being the collective noun for a group of corvidae, this image presents the question and pun of ‘attempted murder.’
This problem is not localized to quantities of sand, hairs, and crows, as we will see shortly.
Chrysippus’ answer to the heap paradox is recorded in Cicero’s Lucullus/Academic Prior, and amounts to suspending judgment:
“You value the art [of logic], but remember that it gave rise to fallacies like the sorites, which you say is faulty. If it is so, refute it. The plan of Chrysippus to refrain from answering, will avail you nothing. If you refrain because you cannot answer, your knowledge fails you, if you can answer and yet refrain, you are unfair.”
—Cicero, Lucullus/Academic Prior §§ 91—98.
Chrysippus suggests that before the vagueness of the question causes doubt, one should withhold judgment until it’s sure. This prevents the incongruency between 17 not being a heap, but 18 being one.
However, this is not really a solution, merely a way of avoiding the dialectal trap, as History of Philosophy notes. In the podcast, the example is given that before one is forced into the logical corner of arguing that 24 is not a heap, and 25 is; we should begin to withhold judgment sometime around 20, before the doubt is clear. I suspect any argument partner would infer, however, the logical paradox in silence; but Chrysippus was more concerned with protecting the epistemology of the Stoics than he was at winning 6th Grade debate points.
The issue at hand is one of vagueness, and the imprecision that is manifest in human language. Language is made up of arbitrary symbols, for instance, nothing about the sounds of the English word ‘tree’ ( /t͡ʃɹi:/) contains anything which carries a universal understanding of the conception of ‘tree.’ It’s a symbol, agreed upon by all English speakers, but it is arbitrary.
Some of the solutions to the paradox rely on this trait of human language. Some, by means of technical resolution, affirm a boundary which is fixed (like 10,000 units makes a heap), and others posit that there are boundaries for heaps, but they are unknowable. Still more rely on specific types of many-value logics, and similar types of reasoning.
The colloquial phrase, “I know it when I see it” is often disparaged as simplistic understanding or ‘folksy cleverness’, but in fact it relates a truth about vagueness, subjectivity, and the symbols available to us through human language.
It is possible to make a case for the subjectivity of a heap:
Say we have boulders the size of a mini-van. Five of these would make quite a formidable pile… one we could reasonably describe as a heap. 50 sesame seeds, however, might not be a heap. What about 500 motes of dust?
That is not my position, however. Rather, I want to look past the sign of the word ‘heap,’ and try to get at the thing which it symbolizes.
In grammar and linguistics we can discuss ‘mass nouns,’ which are also called no-count nouns. Liquids tend to fall in this category. Many languages have a partitive case (sometimes a function of the genitive) which deals with these. See: English “some tea,” or Russian “чаю.”
The core premise of the paradox is that a heap is a certain number of objects grouped together, but this premise is not explicitly stated, and its suppression causes the logical issues seen here. So, I will bring that out, and state that such a definition is not accurate, and show how a more accurate definition alleviates the paradox.
‘Heap,” I argue, is a similar no-count word as above. A heap describes the manner of ordering and/or generally parabolic shape of the bodies of the items in question, and in which the specific number of items is not the operative determiner of the disposition. Example, 10 shirts in the corner of my bedroom are deemed by my girlfriend to be a heap, as in “Can you please clean up that heap of clothes.” The very same number of shirts, (even the exact same shirts themselves) folded and stored in a stack in the closet, are no longer a heap, it seems. The operative determiner, then, is the relatively unordered manner of stacking, and the parabolic shape which results.
Remembering that bodies according to the stoics can even be “matter disposed in a certain way,” as in the difference between ‘a hand’ and ‘a fist’, ‘heap’ seems to be one such disposition. Thus, heaps exist, and do have an objective definition.
The issue which then needs to be explicitly pointed out is the count-requirement of the paradox. Applying a count-criteria to a no-count problem necessarily creates a paradox, and it’s not that this particular paradox in questions needs a count-resolution, it’s simply an inappropriate question.
Inappropriate questions are easily formulated, such as “How many waters does that bottle hold?” or “What is the number five’s favorite color?” These are certainly sayable, and even intelligible utterances. Yet, they lack any relevance to the universe as we know it. They have no clear answer, because the type of answer requested doesn’t fit the proposition.
Whether one agrees that heap is a count or no-count word, the paradox provides an interesting avenue of exploration. The chance to apply Stoic ontology, that of bodies and disposition, to the subject was a fun thought experiment. I don’t recall ever seeing this position stated before, possibly because relying on definitions is a weak point in propositional logic. As this is my first attempt to wrestle with a classical paradox, I’ll accept that it’s a baby step. So far as surety can go with the Sorites Paradox, the thing I’m most sure of is that I ought to fold my shirts before they become a heap in the corner. (:
Seneca,
“[I]f you would put off all worry, assume that what you fear may happen will certainly happen in any event; whatever the trouble may be, measure it in your own mind, and estimate the amount of your fear. You will thus understand that what you fear is either insignificant or short-lived.”
It is interesting to find here the example of the premeditatio malorum, which I think is usually attributed to Marcus.
“Remember, however, before all else, to strip things of all that disturbs and confuses, and to see what each is at bottom; you will then comprehend that they contain nothing fearful except the actual fear… We should strip the mask, not only from men, but from things, and restore to each object its own aspect.”
And here we have the muse of Objective Description, that practice which is often attributed to Marcus. You’ve laid out, if not the letter of the practice, the spirit of it.
It’s Socrates via Plato who says, “…those who practice philosophy in the right way are in training for dying, and they fear death least of all men.”
This is still an issue I’m wrangling with, and so I won’t do either of us the disservice of speaking overly long on it. When I first started studying Stoicism in earnest, not as a mere interest or hobby, I don’t think I really grokked the importance of the measure against death, the memento mori. I read about it, thought about it superficially, but even then it was hard to truly hold in my mind.
The young really do feel immortal. Whether the realities of the situation are finally starting to settle in, or I’m just becoming more comfortable with the ideas of entropy, I don’t know. But the memento mori is becoming something new for me which it wasn’t even two years ago.
I would like to read more of Cato, even though your letter suggests maybe Lucillius was fed up with that story. I’ll try to file that away for future reading. Thank you for the letter, and I look forward to the second part tomorrow.
Farewell.
I’m reading the Fragments of Zeno and Cleanthes, and I’ve come across a phrase that either I didn’t register before, I’d forgotten, or I skipped somehow. That is ‘right reason’ (Gr: ὀρθὸς λόγος).
One of the binary distinctions that exist in Stoicism is between the actions of the Sage versus that of the the layman or ‘untrained person’ (Gr: ἰδιώτης):
The layman’s actions (even when appropriate) are always insane or mistakes. When they are according to his nature, they are kathēkonta (Gr: καθήκοντα), ‘appropriate actions.’
The Sage’s actions (even if outwardly the same as the above, are katorthōmata (Gr: κατόρθωματα), or ‘perfect actions.’ Only the Sage has ‘perfect actions.’
The Sage comes about this distinction, the ability to make perfect actions, because her actions are focused to the good, and that comes about through ‘right reason’ (Gr: ὀρθὸς λόγος). This concept of ‘right reason’ is interesting to me, and I was wondering if anyone had seen any longer, more in-depth studies on that?
Logos can be a tricky term in Stoic jargon, but in my reading, it’s being used here in the common understanding of “logic, or reason,” and not the capital-L Logos type.
If anyone has any resources on ὀρθὸς λόγος, shoot them my way in the comments, please.
Seneca,
It’s entirely possible that I am guilty of “blue car syndrome,” yet I still find myself surprised to find evidence of ascetic training in your Letters.
“The frail body, also, even though we can accomplish nothing without it, is to be regarded as necessary rather than as important; it involves us in vain pleasures, short-lived, and soon to be regretted, which, unless they are reined in by extreme self-control, will be transformed into the opposite.”
Of course, the “Cynic holiday” is your as well, but the issue comes when those of us in my time look back at one of the wealthiest men in the empire, and extols so highly frugality and simple living. It appears to many to be a contradiction.
When Diogenes tells us from his barrel the same, it has a certain authority which is lacking when heard in the villa retreat. Ah well, this is more our problem than it is yours.
The more and more I read, the firmer becomes my thesis that you classic Stoics require an austere ascetic regimen as part of training, and then as a part of life. I’m reading elsewhere the Fragments of Zeno and Cleanthes, and in the introduction, the author states that Zeno’s “frugal” diet was determined by detractors to be on account of his weak digestion. The author editorializes, however, and states that philosophical motivations are likely just as much the cause.
Many moderns discount what we left of the early Stoa as being “on the tail of the dog,” as if this is argument enough to cast aside the very foundations of the school! If it is under closer influence of the Cynic school, what of it? That doesn’t make it wrong. In fact, it might be closer to the truth. Epictetus deems the calling of the Cynic as ordained by God, and the hardest charge possible to be given.
It may be that the cultural attitudes of the west are more similar to that of Rome than they are of Greece, esp. those who even then were pushing the envelope. It’s much more comforting to discount an entire branch (the foundation, no less) as “too Cynic,” when such a discounting protects us from all manner of difficulties, labors, and obligations.
My thoughts have been heavily towards this bent the past few weeks, and receiving your Letters titled “On the futility of half-way measures” and the content of this one seems fortuitous.
Farewell.
Seneca,
Your point today on how we handle “future” philosophy is well taken. It is an easy and all too common excuse to put off what we know we should do for some later date, but as you said, “Men do not care how nobly they live, but only how long, although it is within the reach of every man to live nobly, but within no man’s power to live long.”
There is certainly motivation enough in the words of the classic Stoics, but most of us are too frightened to embrace them wholesale. Indeed, we do all manner of mental gymnastics to try and justify to ourselves that we can cut out whole chunks of it, and be left with something just as valuable.
But that’s not the case, is it?
Indeed, no. In fact, the lie that we can remove the hardship, or (even worse yet) that they Stoics didn’t mean what they said meant, and still have Stoicism proper is the common stance today. I, too, know what I need to do. But I’m putting it off, fiddling about with half-way measures and excuses, distracting myself with studies and readings.
It is fair to say I’ve made some progress, myself. But that progress has been stalled, or plateaued for some time. Maybe, even, it has slipped back somewhat in the past couple months. I need a firm kick in the butt, some focus and motivation.
Seven weeks into our letters, and I’ve seen it a number of times. Yet… still stalled.
Farewell.
Seneca,
“From business, however, my dear Lucilius, it is easy to escape,
if only you will despise the rewards of business.”
That’s the crux of it, isn’t it? It’s pretty easy to talk a good (and consistent) Stoic game, but do we walk the walk? The modern student is rightly focused on handling impressions, on reading about logic and ethics, and social duties. But does she spurn the indifferents which captivate the ἰδιώτης (untrained persons)? Very rarely.
Half-way measures indeed. Thank you for the letter, it is providing much food for thought today.
Farewell.
Seneca,
I do think Epicurus’ point about removing desires is well taken. That seems in line with Stoic ἀπάθεια and Epicurean ἀταραξία both.
Still, the basic premise that pleasure is a good results in unacceptable consequences. Epicurus may have been able to subsist on barley and water and find pleasure there, but the modern world is so hedonistic, that such practices are seen ascetic, and dismissed.
I still find Musonius argument, that even were pleasure the highest good, nothing would be more pleasurable than self-control, and if pain the highest evil, nothing more painful than the lack of self-control.
I still very much enjoyed the content of the first half of this letter, from yesterday. I will write to you again next week. Thanks.
Farewell.
Seneca,
The section of your letter which resonates with me the most today, is the observation that “conversion” (for lack of a better term) to a philosophical life is a promotion.
I think you are 100% correct that we do not fully understand our need for progress, or even the path there. If we did, we’d throw ourselves into it with reckless abandon. We’d leave everything of the common world behind (so far as we needed to do), and embrace the rigors of the school.
But we don’t.
Thank you for the letter; farewell.
Seneca,
“Poverty will keep for you your true and tried friends; you will be rid of the men who were not seeking you for yourself, but for something which you have. Is it not true, however, that you should love poverty, if only for this single reason, – that it will show you those by whom you are loved?”
I take your letter today in good spirits. Your recommendation speak to what I myself already know, but for reasons aplenty but slim, have avoided doing. I can look back to my own life, and see what difference relative wealth can make in regards to “friends.” Your point is well taken.
As you know, I’ve been interested in the teachings of Musonius, yet I need to become more interested in the practices of Musonius.
“Believe me, your words will be more imposing if you sleep on a cot and wear rags. For in that case you will not be merely saying them; you will be demonstrating their truth.” — Epicurus
Some of us by nature or nurture, are easily captivated by ideas. We can chew on a theoretical or hypothetical concept for days or weeks. We can twist it, wring it out, and get every last drop from it. And all without even for a moment practicing or emulating the idea.
For those of us, philosophy can be a constant example of how we need to correct our impressions and our work.
“Every man, when he first sees light, is commanded to be content with milk and rags. Such is our beginning, and yet kingdoms are all too small for us!”
Thank you for the letter. Farewell.
Mountain Stoic 
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