Daniel Dennett:

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Dennett's theory of intentionality is based on the folk concepts of belief, desire, intention and expectation.
In order to explain and predict the behavior of a system one can employ three strategies: a "physical stance", which infers the behavior from the physical structure and the laws of Physics; a "design stance", which infers the behavior from the function for which it was designed (we know when a clock alarm will go on even if we don't know the internal structure of the clock); and an "intentional stance", which infers the behavior from the beliefs and desires that the system must exhibit to be rational.
The "intentional stance" is the set of beliefs and desires of an organism that allow an observer to predict its actions. Belief and desires are not internal states of the mind which cause behavior, but simply tools which are useful to predict the behavior. No system is really intentional.
The process that defines how beliefs and desires are shaped, and how they affect the organism's behavior, has biological roots. If an organism survived natural selection, the majority of its beliefs are true and the way the organism employs them is the most "rational" (beliefs are used to satisfy its desires).
From a biological standpoint, the intentional stance defines the relationship between an organism and its environment. The organism continously reflects its environment, as the organization of its system implicitly contains a representation of the environment.
Intentional states are not internal states of the system, but descriptions of the relationship between the system and its environment. An intentional state is not separate from the others, but, holistically, it makes sense only to deal with the cognitive state of an organism as a whole, and with its relationship as a whole with the environment. The propositional attitude is defined by a "notional attitude", which is independent of the real world, and a component which depends from the real world.
A notional attitude is defined in a "notional world". An agent's notional worlds are the worlds in which all the agent's beliefs are true and all the agent's desires are feasible. Me and my doppelganger on Putnam's twin Earth have the same notional world, but different propositional attitudes (because we live in two different environments).
Intentionality defines an organism as a function of its beliefs and desires, which are products of natural selection. The more an agent's notional worlds stride away from the real world, the less the agent is capable of adapting to it.
What creates beliefs and desires is the biological function of cognitive mechanisms. Beliefs must be true and desires must be feasible to be useful to survival.
However, Brentano's thesis (that the intentional is irreducible to the physical) is true, because strickly speaking there are no such things as beliefs and desires.
Dennett's theory allows for an interpretation within an ecological context, in agreement with Gibson's and Neisser's theories; within an ethological context (cognitive profile of a species); and within a philogenetic context (how an organism evolved do adapt continously to its environment).

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