Abstract
There are various puzzles that set our intuitions about composition and identity against one another. Four that are particularly well known are the Growing Argument (also known as the Paradox of Increase), the Ship of Theseus Puzzle, the Body-minus Argument (usually presented by way of Peter Geach's story about Tibbles the cat), and Allan Gibbard's puzzle about Lumpl and Goliath (a piece of clay and a statue, respectively). Such puzzles have received a great deal of attention in the literature over the past thirty years, and there is an impressive and growing variety of solutions available for each of them. Surprisingly, however, no one has really discussed how all of the different puzzles, and their solutions, are interrelated. On the surface, they seem to raise different problems; but clearly the puzzles are related somehow. They raise similar questions and generate similar sets of possible solutions. But, as yet, nothing has been said about how far the similarities extend.
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