We argue that intelligence, construed as the disposition to perform tasks successfully, is a property of systems composed of agents and their contexts. This is the thesis of extended intelligence. We argue that the performance of an agent will generally not be preserved if its context is allowed to vary. Hence, this disposition is not possessed by an agent alone, but is rather possessed by the system consisting of an agent and its context, which we dub an agent-in-context. An agent's context may include an environment, other agents, cultural artifacts (like language, technology), or all of these, as is typically the case for humans and artificial intelligence systems, as well as many non-human animals. In virtue of the thesis of extended intelligence, we contend that intelligence is context-bound, task-particular and incommensurable among agents. Our thesis carries strong implications for how intelligence is analyzed in the context of both psychology and artificial intelligence.