Logic: Sorites Paradox


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.

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.

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.  (:


Impressions and the OODA Loop


If you hang around .mil, LEO, or civilian self-defense circles you’ll eventually hear reference to the OODA Loop.  OODA Loops are not the most recent in a line of tactic-cool cereal for the cool guys.  The OODA Loop is a mental model for human decision making, especially in crisis.  Now, professionals in psychology and decision making make take issue, but as a pedagogical tool and mental model for the non-specialist, it’s the standard of training.

A quick and dirty primer on the OODA Loop:
The OODA Loop is a decision making loop that one must go through to come to action in times of crisis.  It is broken down into four parts which give it the acronym.



Image Credit: ArtOfManliness.com

  • Observe
  • Orient
  • Decide
  • Act

First, you must make an observation.  This is a witnessing of some fact about reality.  It might be “A man is approaching me,” or “An object rests on the sidewalk,” or “I’ve fallen to the ground.”  The observation is neutral.  It simply is.

Next, is the orienting phase.  You must put the observation into the proper context.  You must come to know ‘what the observation means.’

  • “A man is approaching me.”
    • Observation:  A man is walking in a baggy jacket, hands in his pockets, shoulders rolled forward.  He is on a vector to cross paths with me.  We make eye contact, and he speeds up.
      • Orientation 1:  I’ve just exited a store, his jacket is light, appears to be unlined.  It’s winter, and the wind and snow are driving.  This man is cold, and is going inside.
      • Orientation 2:  I’m lost on a city street at night.  The street is practically empty, and I’ve seen this man before two blocks back.  He might be threat.

Next comes the deciding phase.  Once you have oriented to the situation, and you understand the context in which the observation occurs, you must decide on the proper course of action.

  • “A man is approaching me.”
    • Decide:
      • O1:  Step aside and hold the door as courtesy.
      • O2:  Options…
        • A:  Cross the street.
        • B:  Speak to the man, “Hey buddy, nice night, eh?”
        • C:  Speak to the man, “Watch out for that bus!”
        • D:  Prepare to fight

Now, the action.  You do the thing.

The thing about the OODA Loop is that we engage in this hundreds of times per day, and if for some reason the loop gets interrupted, it must start over.  So, if we can ‘get inside’ the OODA Loop of someone else, we’ll catch them off-guard.  Most folks take between 0.25 and 1.5 seconds to go through one OODA Loop.  Speaking to a would-be attacker my kick his or her OODA Loop back to the start, giving you more time to act.

So, what does this have to do with Stoicism and with φαντασία in particular?  I think the Cycle of Assent matches up fairly well:

  1.  The ἡγεμονικόν (hêgemonikon) is presented with an impression. (Observe)
  2.  An almost-instantaneous value judgment is attached, and a proposition is made. (Orient)
  3. The proposition is weighed, you either assent, deny, or suspend judgment. (Decide)
  4. You either experience a passion, form an intention, desire or aversion, etc.  (Act)

This is a modification of Sellars’ distillation of the four stages of Assent:

1. The soul receives an impression via the sense organs or the mind/memory;
2. An “almost” involuntary and unconscious value judgment is attached;
3.  The ruling faculty is presented with a proposition composed of the perceptual data and the unconscious value judgment from #2;
4. One either assents or denies the impression/proposition.

As practicing Stoics practicing the Discipline of Assent, if one is already familiar with the OODA Loop (or finds it a useful mnemonic device), this similarity in models may be helpful.


A box of my favorite things, with “STOICISM” scrawled on the side



– My political beliefs
– My ideas of family
– My nationalism
– My support for a state
– My theism or atheism (sometimes anti-theism)
– My support for popular causes
– My dislike of certain “indifferent things”
– My like of other “indifferent things”


How many of us have a box of our favorite things which we’ve haphazardly scrawled “STOICISM” across the side?  Inside this box of decades’, generations’ worth of baggage, is there much room leftover for the ideas of Epictetus?

How about Marcus’s reminders to himself?

The lectures of Musonius, do those have a home in this box of my favorite things?

Maybe, this thing I’m calling Stoicism, is simply a label for a new demagoguery, that reinforces all my biases by applying a systematic slant to them.  “See!”  I can say, “there’s a good reason that I should prefer this to that, treat this as indifferent, and lobby for my favorite politician of choice!”  Fate forbid, call it a vice, it’s indifferent!

“Watch your own conduct thus and you will discover to what school you belong. You will find that most of you are Epicureans and some few Peripatetics, but with all the fibre gone from you. Where have you shown that you really hold virtue to be equal to all else, or even superior?

Show me a Stoic if you can! Where or how is he to be found? You can show me men who use the fine phrases of the Stoics, in any number, for the same men who do this can recite Epicurean phrases just as well and can repeat those of the Peripatetics just as perfectly; is it not so?

Who then is a Stoic?

Show me a man moulded to the pattern of the judgements that he utters, in the same way as we call a statue Phidian that is moulded according to the art of Phidias. Show me one who is sick and yet happy, in peril and yet happy, dying and yet happy, in exile and happy, in disgrace and happy. Show him me. By the gods I would fain see a Stoic. Nay you cannot show me a finished Stoic; then show me one in the moulding, one who has set his feet on the path. Do me this kindness, do not grudge an old man like me a sight I never saw till now.”

— Epictetus, Discourses II.19

Am I studying Stoicism, am I trying to be a Stoic?  Or am I taking refuge in a label?  Am I being a Stoic, or am I just saying I’m a Stoic?  Do I really try to inculcate virtue as the sole good, or am I an undercover Epicurean?  Can I show it, in my every day life?  Can I see the skill with which I weigh impressions and assent or deny them?  Can the others in my life say, “There’s something good going on there,” ?

Not here.

“Nay you cannot show me a finished Stoic; then show me one in the moulding, one who has set his feet on the path.”

On Musonius Rufus and law suits.


In Musonius’ Lecture X, he makes the claim that a good philosopher ought never to levy a civil suit against another for personal injury.  This is because all of the things which the civil authority might bring to a plaintiff are indifferents; and no accused person has it in their power to take anything good from nor foist anything evil on a philosopher.

This level of commitment to intellectual integrity is not often seen.  While the questions of society, the state, and communities are very close to Stoicism, this is a particular poignant recommendation.  But did Musonius live up to his own advice?

In the year 70 CE, Musonius went to court and assisted in the conviction of Publius Egnatius Celer, a fellow Stoic.  Celer has betrayed Barea Soranus to his death during the reign of Nero; one of the three so-called Stoic Martyrs.  court

Is this a problem for the unity of Musonius’ teachings?

No.  Musonius’ suggestions that a philosopher avoid suits of personal injury is well-grounded in Stoicism, but so too is his participation in the Celer’s trial.  Musonius was seeking justice to a man betrayed.  Justice, being one of the four constituent parts of Virtue; his endeavor was thus in accord with his own teaching.

It seems that we can infer a difference in his thinking between the personal injury claims of civil or equity law; and the laws of the state (malum in se, if not malum prohibitum) and criminal law.

Granted, this is an interpretation between what we have of his teaching and the way he lived his life.  We have it from our sources that The Roman Socrates was especially known for practicing what he preached.  It is reasonable, then, I think, to infer this dichotomy between the civil and criminal law.

What are your thoughts?
– Is Musonius suggestions that philosophers expressly avoid personal injury suits relevant to our modern times; or is this a core aspect of how our society now dispenses justice?
– Do you think this dichotomy between civil and criminal law is well grounded, or is it splitting fine hairs?

On Ritualized Daily Stoic Practice


My academic background is anthropology and linguistics.  Although my current job is pretty far from these, that perspective is still one lens through which I view culture and societies.  To my knowledge, no culture exists without rituals.

For most folks, the term ritual evokes the image of religion (which is a borderline four-letter word on some sites and blogs these days).  While it’s true that religions generally have rituals, we have many secular ones as well.  Getting a driver’s license tends to have ritual significance as a coming of age rite, graduations are heavily and careful prescribed activities (even with ritual garments, gestures, talismans, and music).  Weddings, even at the court house, and on and on.  The story of human life is punctuated with ritual.

There are several reasons why a modern Stoic should consider ritualizing his or her practice.  Ritual and symbolism speak to the human mind in a way that overt, language-based impressions do not.  Rituals build a sense of seriousness and solemnity to activities; like the Japanese Tea Ceremony.  Rituals help make sure that we are doing complex things in a prescribed manner.  How many of us learned to tie our shoes and cross the street with ritualistic formalism?   Maybe even a parable about a rabbit?

When we undertake certain things with a ritual mindset, we learn it in a way that fossilizes the thing acquired.  In doing “philosophy as a way of life” we are endeavoring to untrain and retrain certain reactions which we have spent decades reinforcing.  No small thing, that.

Ritualizing our daily practices will build regularity, seriousness, and competence in our chosen endeavors.  Just like we train in a gym or a dojo in a specific manner before we’re expected to use those skills in a more serious context, rituals will help us prepare in the relative security of the philosophical school before we go out into the world to test what we’ve learned.

If we want to learn to box, we start in a gym; we don’t go pick a fight with Ronda Rousey.

Epictetus advises us to “Practice yourself, for heaven’s sake in little things, and thence proceed to greater.

Ritualizing our practice is one way to do that.

It’s not my intent to lay out an entire scheme of things to ritualize, that’s the kind of nitty-gritty work most folks would rather do on their own.  But everything from clothing, meals, scholarly activities, etc. can be imbued with that special quality and signification of the ritual.

One of the biggest challenges for me, is figuring out how to inculcate Stoic practice, and effectively “automate” their use.  When it occurs to me use a Stoic technique, I’m pretty successful at using it.  The hard part, is gaining that little bit of time to remember to do the thing!  Ritual helps with that.

Musonius was big on habits.  It’s fair to say that Musonius believe that building good habits was the foundation of virtuous living.  While the classical Stoics all agreed that virtue was a sort of episteme or knowledge; building that justified belief into real actions is also important.  For Musonius, that was habits, hands down.

Ritualizing our practice builds habits.

As many a coach has said, “perfect practice makes perfect, practice just makes permanent.”  By building specific and prescribed rituals we will be doing the former, and hopefully the latter.

Do you already have something akin to “Stoic rituals” in your daily practice?  If so, what are they?  If not, what are some fertile grounds for that particular seed?

The Philosopher’s Cloak


So, one of the things I’ve been thinking about quite a bit is socratesthe philosopher’s cloak.  This will be the topic of one of the Episodes of the nascent TubCast, and I’m still working through my thoughts and ideas on the issue.  The philosopher’s cloak is the simplest of garments, really.  The basest protection from the elements, the minimum required for modesty, and requiring very little care and very little to make.

It calls to mind the Spartans, classic philosophers such as Socrates and Diogenes of Sinope, and other fundamental figures in the intellectual history the west.

The philosopher’s cloak has become a symbol of wisdom so powerful in western culture that we apply it to folks who really have no right to it.  washigntonTake this photo of a statue of the first US President George Washington (right).  Here, a man of the late 1700s is depicted in the classical garments which are, truly, as far removed from his period as they are from our own.  Yet, to drape Washington in the mystique, the tradition, and the heritage of the west, of democratic republicanism, one has but to drape him also in the philosopher’s cloak:  and that heritage becomes self-evident to all in the west.

The pallium or tribōn was ubiquitous for Hellenic philosophers, and it had fallen out of fashion in favor of the chitton, and other garments.  (Sidebar:  Musonius mentions the chitton, sort of an extra-long, tunic-like shirt in his lectures; stating folks should wear one, not two.  And better yet, a philosopher’s cloak).  As it had fallen out of fashion amongst the laity, it stands to reason that we can say it made the philosopher stand out.  Diogenes referred to his cloak, small bag, and staff as his uniform, and I think for practicing philosophers that’s an appropriate model of thought for it.

This got me thinking on the ideas of a ‘philosophical uniform,’ and what that means for modern practitioners.  Anciently, the cloak can had several functions, firstly that it meets the barest natural needs of the human creature.  Secondly, it calls out clearly to all who would see it that “this person lives differently.”  It might also have other messages attached to it that a related: this person is wise, this person is studying virtue, this person is religious or holy, etc.  But, It is also a message to one’s own self:  “I chose to discard fashion.”  “I’m focused on other things.”  “I am intentionally living.”  “When I put this on, and take this off, I will do so with virtue in mind.” Of course, there is the ever-present risk of vanity in such things as well: ‘I want to be seen in a certain way.’  ‘I want a certain kind of attention.’  ‘I want to look special.’

If we look at philosophical and religious clothing the world over, generally it causes a person to stand out, but I suspect that in the times these traditions were established, that may not have been the prominent reason.  Instead, rather, it generally hearkens back to an early time viewed as closer to nature, closer to “real living,” and closer to our telos of practice.

From the prayer shawls of the Jews, to the robes of a Buddhist monk, to the Roman collar of the Catholic priest:  all of these set one apart, and say, “I’m doing something important.”  “I’m doing something different.”  “I’m living intentionally.”

Stoicism has had a hiatus of approximately 1500 years.  The traditions which are now accepted as common place for other creeds, schools, and faiths are notably absent for we prokoptontes.  That puts us in a tough position.  We necessarily must interpret, create, and change things which otherwise might have already been handed down.  In the eyes of many, that weakens our claims to legitimacy.  However, we who feel called should not be turned aside by such impressions, but we should take to heart the warning that such things can also carry.

No Stoic that I know of believes unequivocally that he or she is doing things in exactly the way that Epictetus, Marcus, or Musonius did, or suggested.  Such a claim is on the face, silly.  We should, however, be wary of interpretations that change core doctrines to the point that we should call it something else.  There is a hedonic element in much of the conversation we see on online Stoic communities, which is a serious departure from the tradition.  We do have a duty to the tradition to enrich it, while maintaining its core.  Drifting too far away might be the right path for some, Stoicism has never claimed to be the one, only, and true path anywhere, but we should have the integrity to call that, then, something else if that’s what we’re doing.  But I digress…

Should we, if we adopt a philosophical uniform, consider whether or not we would stand out?  Or should we instead focus on blending in.  Should we choose something which sends a message to us, every day, while dressing and undressing “I choose to live my life differently than most,”  and do so in such a way that the passerby is none the wiser?

Is it vanity for us, absent the 2,000 year tradition, to stand out?  Should we be like Diogenes, calling out to the passerby to change his ways by our mere presence?  Or should we quietly work to show how our lives have changed, without ostentation or performance?

What say you?
Should a modern Stoic philosophical uniform stand out, or blend in?

21-Aug-2015:  Please see the continuation of this train of thought:  The Philosopher’s Cloak (MK-II).

2015 Stoic Commencement Address


In this post, someone asked what a Stoic commencement address would look like.  I thought this would be an interesting thought experiment in couching Stoic lessons in that format without the technical jargon that often features in our discussions.

To the graduating class of 2015:

Congratulations on your achievement, and I wish you excellence in your coming endeavors whatever they may be.  Some will enter the workforce immediately, others will commit themselves to some form of national service like the armed forces, and some will go on to college or university.  You are preparing yourselves, regardless, for big changes, new adventures, and exciting challenges.

High school, however, is a microcosm of the larger world.  For instance, while all of you here have made this achievement, your paths have been very different.  Some of you struggled and fought to make Bs, others acquired As easily.  Some maybe skated by, “D is for diploma,” right?  Classes varied from remedial, grade level, to honors and Advanced Placement.  You each took a different journey.  The same will be true in your coming fields.

I have something uncomfortable to tell you.  Soon, this achievement will fall by the wayside.  Enjoy today, but tomorrow, this will be in the past.  Once you’re in college your high school GPA is of little importance.  The same for the workforce or military.  Once you take the next step, the previous one matters less.  Each new challenge becomes the focus, and previous victories will become smaller in comparison.

For those going on to higher education, once you leave those institutions and enter the workforce your college GPA will become less important.  At your first ten year work anniversary, no one will say “Remember when she got a 4.0 four semesters in a row?”  It will fade.

But one thing, however, will not fade.  One thing is far more permanent.  The character you build in yourself while working hard for a B, or cruising easily in a cake class for an A will stick around.  You will, day by day, step by step, build and create the person you will be for the rest of your life.  Character.  Character development is not something that happens in the future.  It is not an activity one takes up once “things are settled.”  Character development happens regardless, the only question is, will you do it consciously or accidentally?

Many of us have a person, maybe a grandparent, neighbor, or family friend.  Some good, older person.  We admire their character and think, “I’d like to be like that one day.” If we want that, the time is now, because if we wait until the future to work on that, it will be too late.

Character is like a boat or a ship.  We take the rude and rough materials that we are presented with.  We start with a tree, which is felled and carried to the worksite.  Once we begin to examine and work with the tree, we find defects, burls, gnarls, and knots.  These are not up to us, we don’t chose them.  Maybe someone or something else had, but that is not important.  We have what we’re given.  Ours is to make the best of it.

So we take out our tools and begin to work the tree, ripping planks and boards from its trunk.  These planks are rough, splintery, and not too pretty to look at.  This is where we are now.  You’ve made choices, built habits with new and green wood, still wet from the earth.

Next, we begin to plane down the planks, smoothing the surface, taking off the rough parts, and producing a useful plank.  This is a lot of work.  Based on the grain, the shape, the bend, the flexibility of this plank we choose to use it for the hull, or decking, or a decorative handrail artfully carved.  Each one, its natural character determining its use can be taken and fitted to our ship.  And when it’s finished, we have one plank, with many more to go.  Each of these choices, these planks helps build our ship.  But if done haphazardly, what kind of vessel will we have?  It is only by conscious, focused, and neutral judgement that each part can be fitted to its appropriate use.

A shoddy ship might float in the harbor, where it is safe, but that’s not what ships are made for.  We must take it out into the wild and fierce waves, test it against the untamed seas of real life.

When you go into the world, as a worker, manager, teacher, or other role:  you will find folks doing the minimum, doing less than, and other yet excelling.  It is not yours to compete with them but to compete with yourself.  To quietly, doggedly, and determinedly do better tomorrow than you did today.  You might end up with the same salary, the same awards, and the same qualifications of these others, but those things are temporary and transient.  They will pass.

But that character you build in the process is yours for the rest of your life.  Did you do your work with honor?  Did you do it with determination and discipline?  Did you do it with kindness, lend a helping hand?  Did you cheat?  Did you lie?  Did you steal?  Which ship are you building?

You have a short period of time where it is slightly easier to change course, the degree of change is small here, but further into the journey it will be many and many miles to correct your course.  If you’re headed in a rough direction, change now, at the beginning.  Suit your ship for the seas ahead, build it well, and track your right course.

I leave you with this, congratulations on this achievement, and there is the possibility for glory on the horizon for you.  Your ship stands in the yards, not yet complete, but its shape is beginning to become visible.  Which one will you build?