AbstractUnder what conditions are material objects, such as particles, parts of a whole object? This is the composition question and is a longstanding open question in philosophy. Existing attempts to specify a non-trivialrestrictionon composition tend to be vague and face serious counterexamples. Consequently, two extreme answers have become mainstream: composition (the forming of a whole by its parts) happens undernoorallconditions. In this paper, we provide a self-contained introduction to the integrated information theory (IIT) of consciousness. We show that IIT specifies a non-trivial restriction on composition: composition happens when integrated information is maximized. We compare the IIT restriction to existing proposals and argue that the IIT restriction has significant advantages, especially in response to the problems of vagueness and counterexamples. An appendix provides an introduction to calculating parts and wholes with a simple system.