Abstract
Peter Unger argues that his puzzle of the problem of the many leaves us with having to accept either countless embedded objects of the same kind or a Parmenidean rejection of distinct entities. This dilemma can be avoided if objects truly have vague boundaries. It is metaphysically impossible for an entity with a vague boundary to be embedded within an entity of the same kind. A cloud's parts (that is, cloud stuff) cannot be clearly embedded within the vague boundary region of another cloud, for the latter region is defined as possessing neither cloud-stuff nor non-cloud-stuff. Likewise, there cannot be a cloud with a vague boundary embedded in the middle of another cloud because there would then have to be a population of water droplets dense enough to compose part of the larger cloud which was nevertheless insufficient in density to compose part of the embedded cloud.
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