I&#x27;m not sure what the big deal here is. This has an obvious solution.<p>&quot;Heap&quot; is a word. Words have meaning to people. Different people ascribe different meanings to the same word.<p>Each grain added to a pile of grain measurably changes the probability that an observer will classify the resulting collection as a heap. While it&#x27;s not a linear function, it&#x27;s generally a positive correlation, more grains means a higher probability of any individual calling it a heap.<p>That is a collection of grain of size n+1 has a probability of being classified as a heap that is usually greater than the probability of a collection of grain of size n being classified as a heap.<p>Where&#x27;s the paradox?