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It seems obvious that there are vague ways of speaking and vague ways of thinking – saying that the weather is hot, for example. Common sense also has it that there is vagueness in the external world (although this is not the usual view in philosophy). Intuitively, clouds, for example, do not have sharp spatiotemporal boundaries. But the thesis that vagueness is real has spawned a number of deeply perplexing paradoxes and problems. There is no general agreement among philosophers about how to understand vagueness.