Removing a single grain from a heap of sand does not convert the heap to a non-heap. This principle entails that if a million grains of sand make a heap, then one grain of sand makes a heap. This paradox arises from the vagueness of language. Vague language is used to express vague thoughts. Vague thoughts are thoughts that are neither fully satisfied nor fully unsatisfied by certain states of the world, but instead may be satisfied to varying degrees. Strictly speaking, vague thoughts do not express propositions. Nevertheless, we often appropriately pretend that they do, because they come close enough to expressing propositions. This causes logical problems when we also incorporate into our reasoning the very facts that prevent our thoughts from expressing propositions.
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