A naturalistic theory of intentionality (in the sense of 'aboutness') is proposed that differs from previous evolutionary and tracking theories. Full-blown intentionality is constructed through a series of evolvable refinements. A first, minimal version of intentionality originates from a conjectured internal process that estimates an organism's own fitness and that continually modifies the organism. This process produces the directedness of intentionality. The internal estimator can be parsed into intentional components that point to components of the process that produces fitness. It is argued that such intentional components can point to mistaken or non-existing entities. Different Fregian senses of the same reference correspond to different components that have different roles in the estimator. Intentional components that point to intentional components in other organisms produce directedness towards semi-abstract entities. Finally, adding a general, population-wide means of communication enables intentional components that point to fully abstract entities. Intentionality thus naturalized has all of its expected properties: being directed; potentially making errors; possibly pointing to non-existent, abstract, or rigid entities; capable of pointing many-to-one and one-to-many; distinguishing sense and reference; having perspective and grain; and having determinate content. Several examples, such as 'swampman' and 'brain-in-a-vat', illustrate how the theory can be applied.