Skip to content


by Bill Meacham on April 4th, 2011

Imagine a heap of sand. It contains, let’s say, 100,000 individual grains. If you remove one grain, is it still a heap? Certainly, we would say. What if we remove one more? And then one more? Is it still a heap at 99,997 grains? Yes. What if we keep going and get down to one grain of sand? Is it still a heap? Well, no, one grain of sand is not a heap. So at what point did the collection of grains of sand cease to be a heap? It is impossible to say.

This is an example of a paradox called Sorites (pronounced so-rite-ees), a Greek word meaning “heaped up.” Here is the paradox stated as a logical argument:

100,000 grains of sand constitute a heap.
Removing one grain of sand from a heap does not cause the heap to cease to be a heap.
Hence, if 100,000 grains constitute a heap, then 99,999 grains constitute a heap.
If 99,999 grains constitute a heap, then 99,998 grains constitute a heap.

If 2 grains constitute a heap, then 1 grain constitutes a heap.
Therefore, 1 grain of sand constitutes a heap.

The logical paradox is that from apparently true premises by seemingly uncontroversial reasoning we arrive at an apparently false conclusion. One grain of sand is obviously not a heap. But the logic is sound and none of the premises are false. How can this be?

Buckets of ink (and, more recently, heaps of electrons) have been spilled over this problem ever since Eubulides, a contemporary of Aristotle, first posed the paradox. A standard objection is that the paradox is due to the vagueness of language. The term “heap” has no exact definition, and neither does its opposite. But when used in logical argument “heap” and “non-heap” are treated as precise, black-and-white terms. The clear-cut logic does not apply to the fuzzy concept.

It’s not just a fuzzy concept, however; it’s a fuzzy reality as well. And our drive for linguistic precision can get us in trouble when we try to impose categories on reality that obscure important facts.

For example, at a recent symposium at the University of Texas at Austin (which I found quite stimulating and enjoyable) Harvard professor Dr. Christine Korsgaard, reading one of her papers, made the following assertions:

  • Plants are different from animals, since plants don’t move but animals do. Specifically, following Arisotle, she said that plants do not have locomotion guided by perception.(1)
  • Human beings are like animals in that both, unlike plants, have evaluative attitudes toward their own functioning.(2)

That second point is a bit obscure, and I will return to it in a moment. The first point, that plants don’t move but animals do, is observably false. Plants do move, just more slowly than animals. Plants grow toward the sun and toward sources of water. A small tree that is overshadowed by a larger one grows in a curved fashion, as if trying to get out of the shade. If you remove the larger one, after a while the smaller tree will be growing more directly straight up. Some plants, such as the Venus Flytrap, move quite suddenly when presented with food. It would be more accurate to say that plants are not ambulatory, but you could quibble with that as well.(3)

The second point needs some unpacking in order to understand it. What does it mean to have an evaluative attitude toward your own functioning? Korsgaard says two things:

  • Animals have desire and aversion, pleasure and pain, interest and fear, toward things that affect their functioning. For instance, they like to eat when they are hungry, they fear their enemies, and so forth, so they perceive food as attractive and predators as repulsive or fearful.(4)
  • Animals monitor their own functioning. They care about themselves.(5) An animal can “be conscious of itself as healthily alive.”(6)

Human beings certainly have both of these abilities. We say “I’m feeling sick today” or “I’m feeling great.” In so doing, we are observing and evaluating our own physical functioning. (The evaluation is unstated, but obviously we don’t like being sick and prefer feeling great.) Similarly when we say “my mind is fuzzy right now” we are observing and evaluating our own mental functioning. Korsgaaard is saying that non-human animals do something like this as well, although they don’t think about their condition as humans do. She means that animals have some sense of the overall way they feel and are motivated to do something about it, to prolong it if it is pleasant or to change it if it is unpleasant. In other words, non-human animals have capacities similar to those of humans, albeit in a more primitive and less developed form.

The problem with this is the opposite of her assertion about plants. There she was making distinctions that don’t quite apply. Here she is lumping too many things together, failing to make distinctions that really do apply.

To some extent she is right. It is now fairly uncontroversial to assert that some animals – chimps and bonobos, elephants, whales and dolphins, perhaps others – have an interior life with emotions and thoughts. They have a sense of morality: a preference for fairness, an urge to help others in need. They can use tools. They have conceptual language, more complex than mere emotive grunts. They can think ahead and cooperate with others to get things done. They have some idea of themselves as separate from other beings, as evidenced by their ability to recognize themselves in a mirror.

And if they can think of themselves as separate then it is not too big a stretch to imagine that they can have evaluative feelings toward their own well-being, toward their own functioning.

But surely not all animals are so talented. It’s hard to imagine an ant, for instance, with such capacities. Certainly it shows no evidence of being able to recognize itself in a mirror. Even less so, an amoeba. And dogs, friendly and helpful as they are, fail to pass the mirror test as well. So do these animals have evaluative attitudes toward their own functioning?

Assertions about the interior state of non-human animals must be a bit speculative, but if we take “evaluative attitudes” in the first sense, meaning desire or aversion toward things in the environment that affect the animal’s functioning, then it is plausible to say Yes. But if we take the phrase in the second sense, to be conscious of itself, then on the basis of observable evidence the answer for most animals is No.

And the same is true of plants. If we take “evaluative attitudes” in the first sense it is quite plausible to assert that plants have them. My wife, an avid gardener, says that plants are happy when they are watered, and that some like full sunlight and others prefer shade. If we take “evaluative attitudes” in the second sense most of us would say they are certainly not conscious of themselves.

So where do we draw the line?

We carve up the world conceptually, lumping some things together and distinguishing others, in order to achieve results. The results we want may be practical, such as the ability to grow sufficient food. They may be theoretical, aiming for pure understanding. Or they may be moral, so we can figure out how to act in a given circumstance or what kind of person to be.

In the moral realm of concern we can make a hard-and-fast distinction between humans and animals, thereby relegating animals to mere means of satisfying our ends. Or we can loosen the distinction, as Korsgaard does, to include animals as worthy of moral concern, but not plants. Or we can loosen it still further to extend our concern to all living beings. How shall we decide where to place the boundaries? The available evidence suggests that plants are not outside the pale, that they do indeed experience their world and respond to it.

Which of these stances resonates better with your experience? Which would be more likely to afford you and your loved ones a healthy and fulfilling life? How big is your heap of compassion?

(1) Korsgaard, “The Origin of the Good and Our Animal Nature,” p. 16.

(2) Ibid., p. 17.

(3) You could object that grasses are, in a sense, ambulatory. They grow by sending out horizontal runners that take root and send up shoots at a distance. If the originating shoot is killed, the others, rooted elsewhere, can still live, and you could say that the plant has travelled from its original position.

(4) Korsgaard, “The Origin of the Good and Our Animal Nature,” pp. 17 and 31.

(5) Ibid., p. 31.

(6) Ibid., p. 33.


Hauser, Marc D. Moral Minds: The Nature of Right and Wrong. New York: Harper Perennial, 2006.

Hyde, Dominic. “Sorites Paradox.” Stanford Encyclopedia of Philosophy. On-line publication, URL = as of 9 March 2011.

Keim, Brandon. “Elephants Lend a Helping Trunk, Pass Cooperation Test.” On-line publication, URL = as of 7 March 2011.

Korsgaard, Christine M. “The Origin of the Good and Our Animal Nature.” On-line publication, URL = as of 4 March 2011.

Kranak, Joseph. “Eubulides’ Paradoxes.” On-line publication, URL = as of 9 March 2011.

Wikipedia. “Eubulides.” On-line publication, URL = as of 9 March 2011.

Wikipedia. “Mirror test.” On-line publication, URL = as of 11 March 2011.

Wikipedia. “Sorites paradox.” On-line publication, URL = as of 9 March 2011.

From → Philosophy

  1. I was watching Sunday Morning with my daughter yesterday. One report was about a man who had attracted a goose while walking the park. The goose became smitten and every time the man came to the park the goose would find him and walk with him. The goose even tried to fly with him as he rode his bicycle back home.

    I had a similar experience when I lived on a farm outside of Dallas. A couple of white German shepherds came over from a neighbor’s house one day and found me out for my daily walk. Every day after that they came at the same time every morning expecting to go for a walk. They would howl and walk around on the deck until I came outside to join them. Sometimes they would hang out all day with me lying in the shade while I gardened. Those dogs were my friends. The female shepherd became very attached to me and wouldn’t let the other dog walk next to me, and she didn’t like it when I when my partner would come for a walk with me.

    I believe the plants in my garden grow better (are happier?) when I give them my undivided attention.

    I had a lovely conversation with a lizard while gardening the other day. When I spoke to him (seemed like a male) he jumped toward me instead of away from me so I kept talking.

  2. Salila permalink

    Logic is a gradient scale, not black or white. One apple never equals another apple because they are never the same. Absolutes are only obtainable in theory, not life. In addition, we have different realities. At some point, the sand quits being a heap, but that point will differ from person to person.

  3. Anonymous permalink

    Dogs may not recognize themselves visually but have a keen sense of smell and recognize themselves that way. As for a heap of sand, it seems to me that, by definition, it is an expression of quantity and must be at least or more than a few grains of sand. Two grains of sand would be quantified as a couple of grains of sand. They say, “two is company and three is a crowd.” Similarly, a very slight “heap” may require a set of elements with at least three countable elements. There is no such thing as a heap of milk or water, despite the fact that liquid can be counted as “drops” and a drop of water can be said to be constituted of a heap of molecules. It is more likely for drops of water to form a pool of water but never a heap of water as the surface of water is usually level. So, the term ‘heap’ not only signifies quantity but also a form. 🙂

    As for organisms such as oysters, mussels and clams which lack the central nervous system, I sometimes wonder if they are not like plants (with mechanism like the venus flytrap) rather than animals. They can move, but are usually attached permanently to their habitat. I would feel heaps better about eating them if the delineation were not so fuzzy.

  4. Parmenides permalink

    > Imagine a heap of sand. It contains, let’s say,
    > 100,000 individual grains. If you remove one grain, is it still a heap?

    Maybe, but it’s not the same heap.

    > Well, no, one grain of sand is not a heap.

    I dunno; you can have a one-element linked list, so why not a one-element heap?

    > Human beings are like animals in that both, unlike plants,
    > have evaluative attitudes toward their own functioning.

    Quite a few garden plants you don’t want to water too much at the wrong time or they won’t set fruit. Some plants, when under stress, make more pollen or seed. It would seem that both types are evaluating their situations and acting differently because of that evaluation.

    > An animal can be conscious of itself as healthily alive.

    What does “conscious” mean? Is a fruit fly conscious? A flea? A worm? A bacteria? A virus?

    I would say yes to all, but some of them have more levels of consciousness than others.

    And plants have some of those levels.

    > They have some idea of themselves as separate from other beings,

    There are plants that secrete chemicals that inhibit the growth of other plants. My aunt made a career out of studying that sort of thing. It’s called ecology.

    And that’s why these kinds of hard and fast divisions into abstract categories aren’t very useful: they’re not how the world actually works. Plants and animals and people co-evolve.

    > How big is your heap of compassion?

    Well, if you’re a Republican, it’s me and my family. That way lies further slipping into oblivion if not a dark age.

    The Greeks managed to bring on a dark age by cutting down all their trees. Maybe they should have had compassion for plants.

    • Good points. I think you are actually agreeing with my thesis, that certain conceptual divisions are not useful. Or useful in some contexts, but not others. For instance, by and large you don’t have to build a fence around your plants to keep them penned in, but you do have to build one around most animals. Anyway, thanks for the comment!

  5. Tim permalink

    My answer to why the sand paradox is illusory.

    Part of the definition of heap is that it is plural. So one grain of sand cannot be a heap. Two grains of sand together can be, but we would not normally say so. That we can start with 10,000 grains of sand, subtract one, and still call it a heap simply demonstrates that the most basic definition of “heap” is “more than one of something together.” Both 10,000 and 9,999 are greater than one, so small additions and subtractions of grains of sand are inconsequential. The paradox arises only because it seems necessary to allow for the reduction from 2 grains of sand to 1, but this is precisely the reduction that requires us to stop using “heap” to describe what is there.

Trackbacks & Pingbacks

  1. Considering Ayn Rand | Philosophy for Real Life

Leave a Reply

Note: XHTML is allowed. Your email address will never be published.

Subscribe to this comment feed via RSS