In this blog post, we will look at how the Stoics faced the limits of knowledge and chose silence through the paradox of the heap.
Can a single grain of wheat make a heap of grain? No. Then what about two grains? No, still not enough. Three grains? Still no. What about ten thousand grains? It is clear that if enough grains are piled up, they will form a pile of grain. However, a single grain cannot form a pile of grain, and adding another grain will not instantly turn it into a pile. If we think about it this way, no matter how many grains are piled up, it would be ambiguous to call it a “pile,” wouldn’t it? We call this situation, in which it is difficult to set a standard point for when “small changes” lead to a “qualitative change,” the “paradox of the heap.” This paradox is said to have been devised by the philosopher Eubulides in the 4th century BC. The “paradox of the heap” is not a simple logic puzzle. It is a profound thought experiment that connects everyday life and philosophy, and was used as an important tool in ancient philosophy, especially by skeptics to criticize the dogmatic epistemology of the Stoics. Through this paradox, they break down the boundary between clear and unclear perceptions. According to the Stoics, the process of acquiring knowledge begins with “agreement” on “sensory impressions.”
In other words, when we agree that the sensory impressions we receive about an object match that object, only then can “knowledge” be established. At this point, the clearer the impression, or the more clearly we feel its truth, the stronger the agreement will be. On the other hand, if the impression is unclear, the power to induce agreement weakens.
The Stoics argue that ordinary people tend to rush into agreement even when their impressions are unclear, leading them to fall into speculation, but that wise people, who have steadily trained themselves to discern sensory impressions, can reach true knowledge only by agreeing with clear impressions. Skeptics counter this with the “dummy paradox.”
In order to blur the line between clear and unclear impressions, they present a series of impressions that are so similar to each other. Each impression cannot be clearly distinguished on its own, but through gradual accumulation, they construct a process of impression alteration, putting the Stoic school of thought to the test. They question the continuity of perception and the ambiguity of its boundaries by asking, “How far does a clear impression extend?”
The Stoics strictly apply the law of the excluded middle, a basic principle of classical logic. This is the principle that all propositions must be either true or false. Therefore, the Stoics must answer a series of questions such as “Is n small?” and “Is n+1 small?” in a consistent manner. At first, the answer “yes” is repeated, but at some point, the answer ‘no’ must be repeated. Otherwise, it would violate the law of excluded middle. According to this logic, there must be a clear boundary, or “reference point,” between “n is small” and “n+1 is not small.” The Stoics believe that such a reference point exists and insist that it must exist.
However, the problem is whether we can know exactly where that reference point is, even if it exists. Even wise people may not be able to clearly recognize that boundary. If so, where is that boundary? The Stoics believe that true knowledge is established by agreement on clear sensory impressions, so they adhere to the principle that when something is unclear, one should not agree and remain silent. Speak only what you know. If you don’t know, don’t say it. This is the Stoic ethic of knowledge.
So what does it mean to answer “I don’t know”? It means that you know that you don’t know, which, ironically, is an acknowledgment of your own ignorance. In other words, according to the principle of “agreeing only with clear impressions,” even the judgment “I don’t know” can only be made when “it is clear that the impression is unclear.” However, as pointed out earlier, when clear impressions and unclear impressions are too similar, it becomes difficult to distinguish whether the impression is unclear or not.
Then, it becomes impossible to even say “it is unclear.” The Stoics believe that discernment can be improved through training and practice. However, no matter how much training one undergoes, humans cannot achieve perfection. Therefore, even skilled sages sometimes refrain from hasty agreement even in the face of clear impressions in order to prevent mistakes.
However, if they judge everything to be “unclear,” even wise people are exposed to the risk of making mistakes. Therefore, in some cases, they choose to remain silent without even saying “unclear.”
Chrysippus, the third leader of the Stoics, explained this attitude metaphorically. He likened himself to a wise charioteer pulling back his horse before a cliff, and advised people to remain silent until they reach a clear conclusion. In other words, when you cannot answer “yes,” it is better to remain silent even if you can say “yes.” This is a philosophical attitude that chooses to err on the side of caution rather than excess, and it is a virtue of prudence.
However, the question remains. When should one remain silent? If you are a skeptic, you should stop judging and remain silent whenever you have doubts. Of course, such doubts will not easily disappear. On the other hand, in the case of Chrysippus, one must remain silent when one cannot even distinguish between “clear” and “unclear.” However, even that is difficult because it may be impossible to determine whether the situation is indeed “indistinguishable.” Ultimately, even at the level of determining whether something is distinguishable, we are faced with the possibility of remaining silent.
If we continue to retroactively apply logic in this way, even the judgment that “falling short is better than going too far” loses its validity. In trying to avoid going too far, we fall into the trap of falling short, and when even that falls short, the necessity of silence becomes meaningless. When that happens, the distance between philosophical judgment and practice becomes infinitely wide.
