61 - Nobody’s Perfect: the Stoics on Knowledge

Posted on

The Stoics think there could be a perfect sage, so wise that he is never wrong. Is this a big mistake? Peter investigates their epistemology to find out.



Further Reading

• J.E. Annas, “Stoic Epistemology,” and G. Striker, “The Problem of the Criterion,” in S. Everson, Epistemology (Cambridge: 1990).

• S. Bobzien, “Chrysippus and the Epistemic Theory of Vagueness,” Proceedings of the Aristotelian Society 102 (2002), 217-238.

• M. Frede, “The Stoic Notion of a Lekton,” in S. Everson, Language (Cambridge: 1994), 109-28.

• M. Frede, “Stoics and Skeptics on Clear and Distinct Impressions,” in Frede, Essays in Ancient Philosophy (Oxford: 1987), 151-78.

• M. Mignucci, “The Liar Paradox and the Stoics,” in K. Ierodiakonou (ed.), Topics in Stoic Philosophy (Oxford: 1999), 54-70.

• F.H. Sandbach, “Phantasia Kataleptike,” in A.A. Long, Problems in Stoicism (London: 1971).


Ted on 13 September 2013

The Sorites Paradox and a 5 year old


I was listening to your podcast on the Stoics and Epistimology on the way home from work one day, and when I got home, I told my 9 year old daughter and 5 year old son the Sorities paradox. As I went through it, my daughter said that adding the 18th grain would make a heap, so I asked, of course, how can adding just one grain make a heap, and my son Ollie said, "no dad, you're not adding the one grain to the pile, you're adding the whole pile to the one grain; that's why it's now a heap". I may be as impartial as I am classically educated, but that's the best solution I've heard. If nothing else, it shows an amazing grasp of the commutative property of addition, and is a lot more ballsy than Chrysippus's solution!

You may not feel the same, but I can't wait for your summer break to end!

Thanks again for your podcasts.

In reply to by Ted

Peter Adamson on 13 September 2013

Out of the mouths of babes

Thanks, that's a great story! Maybe you have a future philosopher in the making there. I agree, it's admirable that unlike certain Stoics we could name, Ollie was at least ready to take a stand.

The next episode goes up Sunday!


peter l on 16 June 2014

every hair is numbered ...

I think the answer to this 'adding a grain of sand to create a heap problem' is simply to say ...

"you asked me to decide when I would call this a heap if you added sand grain by grain so I did. in this situation x grains isn't a heap but x+1 is ... i'm not saying I would apply the same principle in a different situation.
for instance, i'm not going to ask someone ... 'who left that heap of sand on my desk? well at least there's a lot of grains there. i'm not sure because obviously I haven't counted the grains ...' "

In reply to by peter l

Peter Adamson on 16 June 2014


That's a nice idea: it sounds a bit like just biting the bullet and accepting one of the supposedly absurd claims, namely that n grains is not a heap but n+1 is. But you might be right that the context in which one would admit this could be crucial. Actually I recently heard an episode of the Elucidations podcast that argued for a version of this solution, arguing that one could perhaps solve the paradox by invoking context as you are doing. Worth a listen. Here is the link.

Robert on 9 November 2016

Viable Solution?

If adding or subtracting a grain does not change heap status, then it is possible to disperse any heap without changing the number of grains in the heap by repeatedly adding a grain at the outer rim and removing one from the center.

Does this not show that the sorites paradox is wrong in assuming that the number of grains solely defines what constitutes a heap?


In reply to by Robert

Peter Adamson on 10 November 2016


Oh, that's clever! I like it. The only thing is that I guess it is less a solution than a way of reframing the paradox: just as we can ask when the heap is no longer a heap because the grains are too few, we can ask when the heap has lost its "heap" status by being dispersed. Clearly not from moving just one grain to the rim, or two, or three... but at some point.

Thus I think that your point shows not a flaw in the sorites reasoning, really, but that "heaps" are defined by two features: quantity (the number of grains) and arrangement (as a pile, not scattered all over the room or whatever). And the argument can be applied to either of these two features.

In reply to by Peter Adamson

Robert on 20 November 2016

Apples and Oranges

My example shows conclusively that any number of grains capable of forming a heap are also able to form a non-heap at the same time.

This does not mean that the concept of heap is paradoxical in nature.

It means that the paradox makes an error by trying to replace an indefinite quantifier like heap with a concrete number because it fails to consider the impact of other characteristics of the heap like distribution and outside factors such as the observer.

Those variables are not negligible.

Another error occurs when the paradox wants to attribute all change to the last step performed.

If you add one grain to a pair, you cannot claim that it is only the last grain added that makes it a trio and ignore the other two.

All three grains contribute equally to form a trio, but the paradox wants you to forget that you were already two thirds of the way.

As my example has shown that part is unquantifiable in nature for heaps since the contribution of a grain hinges on others factors than pure numbers.

When the paradox claims over and over again that adding yet another grain is not enough, it is essentially moving the goalposts.

In reply to by Robert

Peter Adamson on 22 November 2016


I think you may be missing the point of the paradox. The whole idea is indeed that there is no concrete number that makes a heap, and that adding just one grain cannot make a non-heap into a heap - yet, at some point between (say) 1 grain and 1 million grains, we somehow have made a transition from non-heap to heap. In other words you are treating one half of the paradox (heaps cannot be sharply defined) as if it were the solution to the paradox.

Wayne Burt on 9 December 2020


adding a grain of sand to a pile when does it make it a heap. I can see where a impressionist who is looking at it ,not knowing the cognitive process would say at a certain ( unknown advanced stage ) would say "thats a heap of sand "(again that would be as recognizing the form(Platonic ) as being large (Aristotle ) in comparable to form of small and middle ( in this case Aristotle would not  get to the heap as he would keep a middle way . The impressionist  at a earlier point would say "thats a pile of sand " or a hand full  of sand  A scientist would use a scale as would a seller at the marketplace to determine a agreed upon definition .

another paradox is  "thats the  straw that broke the camels back "   as not the first or any other one but the last one " 

( meaning to me as losing knowledge as going over the edge causing a collapse . This than indeed have a tipping pt ,as to metaphysical  cause and effect of matter to collapse .

  Anyways , so far i have listened to all 61 podcasts and enjoyed them all . I feel " without gaps " is the important part .as is the golden means ones knowledge advances in equal proportions with each podcast . Thanks for your tremendous efforts ,

In reply to by Wayne Burt

Peter Adamson on 9 December 2020


Thanks, glad you like the series! Actually I think the straw that breaks the camel's back is crucially different from the heap case. In the straw case, the camel's back does break at some point (or if this example is too hard to really imagine, then adding one gram weights to a table until it falls). So there is a sharp cut off point there, where we go from not breaking to breaking. By contrast, vagueness cases like heaps, baldness, etc are, well, vague: there is no one step that makes the difference.

Carroll Boswell on 28 February 2022


I think that vague terms like "heap" are statistical terms. They do not refer to a specific amount at all but to an average amount with a standard deviation around that mean that gradually dissipates, a normal distribution. The world is an inherently vague place, that is, it is an inherently statistical place. In statistics, for example, we would say a man is "tall" if his height is more than one standard deviation above the average height of all men of his age. Perhaps this helps?


In reply to by Carroll Boswell

Peter Adamson on 28 February 2022


Well, I'm no expert on statistics but it sounds a little like your solution is simply to declare an arbitrary line ("more than one standard deviation") which just bites the bullet on the paradox. So if we have a man who is half a millimeter below that height which the statistician takes as the beginning of "tall," he is not tall, but if he grows that half millimeter, he is tall. This seems counterintuitive as a description of any real property out in the world. Of course you might be willing to do this for practical purposes but it seems arbitrary. And you might not want the concepts you use to describe the world to be arbitrary; as you say, pretty well all our empirical concepts are subject to vagueness in this way, and so it could suggest that all our descriptions of the world are in some sense unmoored from any external reality. That is the worry, at least.

Vagueness is now a whole sub-branch of philosophy so it gets to be a very complicated topic, which I am not really competent to explain but you can check out this overview: https://plato.stanford.edu/entries/vagueness/. The Stoics are important, I think, not because they had a good solution already but because they are the first European philosophers we know about to have grappled with the problem. (I say "European" because I think vagueness was thematized in classical Indian thought from early on too, especially by the Buddhists.)

In reply to by Peter Adamson

Carroll Boswell on 9 March 2022

statistics again

The "more than one standard deviation" is not at all arbitrary. It arises "naturally" out of the mathematical investigations of randomness. I suppose by natural I mean that mathematically it is inevitable, automatic, obvious. And the proof is in the pudding. Adopting the standard deviation as the right measure is what makes statistics work, and it is spectacularly successful, it underpins all our technological achievements. It is true that it will still seem counter-intuitive, but that is frequently the case with mathematical conclusions. A mathematician is comfortable with the belief that intuition is not reliable. Intuition is based on sensory impressions and as the Stoics realized this means that intuition can't be infallibly reliable. Since our language is created based on sense impressions, it is inevitable that language can't have precise meaning either. Our empirical concepts are subject to vagueness and are unmoored from any external reality, unless something like statistics can be used to moor them to external reality. Then we are left with the rather unsatisfying conclusion: we know it is true because it works.

But this brings up the question: what did the Stoics think of the reality of such mathematical ideas as circles, etc? I assume they would deny that mathematical concepts are real. Are they just sayables? Is circle in the same category as majestic? It seems to me that mathematical ideas are in between in some sense the real and the sayables like majestic, etc. There would seem to be a whole range of classification necessary to delineate the various kinds of reality. Then having sorted out this spectrum of realities, would there be also vagueness in specifying what kind of reality we meant? Perhaps we might need to statistically specify the range of various types of reality? This could easily get out of hand, but it is amusing to speculate.

I have had cognitive impressions in the sense that I have had impressions that I find it impossible to doubt. I am not sure that knowledge is the right term to use for those impressions, but I don't have an alternative suggestion..

Thanks for the link about vagueness.I am very interested.


Ravi on 10 November 2023

I can't play this episode

For some reason, I'm able to play every previous episode, except this one. I tried to listen to it on Spotify and on the site, but both just load forever. Maybe the file is corrupted or something?

I can even play the next one, seems to be just this one that has this problem.

In reply to by Peter Adamson

Jefferson on 19 March 2024

Streaming the episode

I'm having the exact same problem. I've tried streaming this episode a few days ago but it didn't download the file. I've also tried listening on different apps, and through a direct link to the mp3 file in the feed, but it still doesn't work.

By the way, I'm really enjoying this podcast, thanks for all the effort you've put into it.

In reply to by Jefferson

Peter Adamson on 19 March 2024


Sorry about that - I just tried it and it seems to work. Not sure why this is happening! You could also try it on Spotify, the Podbean RSS feed, or something, if this happens again?

In reply to by Peter Adamson

Jefferson on 20 March 2024


This is weird, I tried again all of the options you mentioned, but it still doesn't work. I even tried using my mobile data instead of my home WiFi, to no avail.

But since you're able to stream it, I decided to try a free web proxy to download the file through a US server, and it worked!

It is extremely unlikely that this specific episode is being deliberately blocked in my region (São Paulo, Brasil), so the only reasonable explanation I can think of is that the file is being served through some sort of CDN. When I try to download it, I end up accessing a server that is closer to me, but there is some problem with the copy of this file located there. When you try to download the same file, you end up accessing a different server that is closer to your location, where everything works fine.

So even though I was able to download this episode through a proxy, it is possible that other people are having the same problem.

If you ever find a solution, I could check for you if I'm able to download the file without the proxy.

Andrew on 31 January 2024

Sayables about sayables?

Unless I am missing something, sayables seem very fragile to a self applicability objection. Sayables are meant to act as bridges between us and the world? Then how can we talk about the sayables? Are there sayables about sayables? This creates a two problems for me.

1. It is now clear that there are an infinity of sayables, since for every sayable there are sayables about that sayable. To be fair though, I can't think off the top of my head why they couldn't bite the bullet on this, although it seems weird to say there are an infinity of semi existent things just hanging around.

2. A stronger argument. If there are sayables about sayables, I assume that truth is applicable to them. But that would mean we can say true and false things about things that don't really exist! While not the exact same, this seems dangerously close to the problem of how we can talk about nonbeing.

Last two thing that isn't related to sayables about sayables, but it seems that to say that something can "subsist" rather than fully existing seems both ad hoc (does anything else subsist in their view? Side note but maybe this could help solve the Sorites paradox somehow?) and also a violation of the principle of bivalence. Did the stoics subscribe to the principle of bivalence? If they do, how could they argue that subsisting isn't a third value between being and nonbeing?

In reply to by Andrew

Peter Adamson on 31 January 2024


Nice points. On the first one, I agree there should be an infinity of sayables and also that it is not a problem (I mean, they aren't bodies, or even beings, so we won't run out of room as it were). On the second point, it's clear that we can say true (and false) things about items that subsist; e.g. that they subsist, or that void is not the same thing as a sayable, or that two sayables are distinct. Again I don't see any obvious problem with this.

On the principle of bivalence, at least as you set it up, again I see no obvious problem: sayables are straightforwardly non-beings, because subsisting is different from being. Subsistence isn't, like, a compromise or mixture between being and non-being. (So your objection would be like saying that being blue is a third value between being white and non-white.)

And yes there are other subisting things, like void and time.

Not sure about the sorites idea, I guess you'd need to spell that one out for me!

In reply to by Peter Adamson

Andrew on 1 February 2024

For points 2 and 3, do the…

For points 2 and 3, do the stoics give an account of how we can talk about nonbeing then? That would seem like a very controversial claim for the time period, just snuck under the label "subsistence".

As for the sorities (and this might explain the bivalence objection more) I had in mind that subsistence was either a third thing or, how shall I put it, the gap between being and non being. Kind of like a gradient with the second idea. So my idea for the sorities was that would give you a theoretical backing to answering "kind of" when it becomes unclear that there is a heap or not. That the heap (with the gradient in mind) is now subsisting, if not fully existing yet. The heap is not fully there yet. That was the idea anyway. But if subsistence is just purely nonbeing, then that idea doesn't work as much.

In reply to by Andrew

Peter Adamson on 1 February 2024


Right, I think if we don't conceive of the subsistent as a semi-being, then it wouldn't be relevant to the sorites problem.

On the first point, the Stoics' basic idea is that "to be" means being able to exert or under causation (this is taken from Plato's Sophist), and they think only bodies can do that. So everything else we might want to talk about is a non-being. However we do want to postulate some non-bodies in our metaphysics (for lack of a better term), like sayables, time, and void. Why exactly we want/need to do that is a matter of scholarly debate, but a first stab might be simply that there are some true propositions that refer to these items, e.g. "the cosmos is surrounded by infinite void". Hence they "subsist" (enough to be truth-makers) but are not "beings" (because they don't exert causation). That's how I understand it anyway.

Philip Riske on 11 February 2024

Stoics and Early Christian apologists?

I listened to this episode a few years ago and just finished reading the corresponding chapter in one of the books.  I couldn't help thinking that 1st and 2nd century stoics would be very susceptible to Christian apologists because of their "hand over fist" theory of knowledge and the search for the perfect sage.  Educated Christian converts would have argued that the followers of Christ had various open palm impressions of seeing Christ risen from the dead, resulting in a fingers together consensus and then a closed fist.  When Christ appeared to all of them together, including the skeptical Thomas, that would have been the hand over fist.  Of course, Christ would have been presented as the perfect sage providing certain ethical and spiritual knowledge about the one true God.  Perhaps there are some ancient things I either haven't read or read once and forgot about.   I've learned about the 2nd century figure of Justin Martyr and his background in Stoic and Platonic philosophy but I don't remember or know if he used an argument like this.

In reply to by Philip Riske

Peter Adamson on 11 February 2024

Stoics and skepticism

Yes that’s a nice example and of course the “demanding proof” vs “being satisfied with faith” idea is one that runs through Christianity longer term as well. I don’t know of a text that looks at this story philosophically but it would be worth checking the church fathers!

Add new comment

The content of this field is kept private and will not be shown publicly.