Quine's instrumentalist theory refused intentionality, considering it merely a linguistic trick. Quine thus denied Psychology (that deals with desires, beliefs and hopes and so forth) the status of science.

Dennett reached a similar conclusion: the intentional stance is simply one of the possible ones, and it is just that, a stance. It is useful to attribute intentional states to other humans, and maybe even to non-human systems.

Intentionality is only a feature of our language, a tool. The mind is not intentional because it does not exist, it is only a term in the vocabulary of folk psychology. The brain is not intentional because its states do not refer to anything: they simply are what they are, just like in any physical system.

Jerry Fodor's representational theory, instead, posits that the brain literally contains the intentional state that we ascribe to the mind. For Fodor, the vocabulary of folk psychology "is" a scientific language: it describes facts that are really happening in the brain, not just linguistic tools.

Ruth Millikan's teleological theory claims that intentionality is an objective, natural, biological feature of humans, that evolved over millions of years just like any other organ or limb of the human body. Intentionality is no more than the biology of belief, desire, hope and intention, which must be treated like any other biological object. Propositional attitudes (beliefs, hopes, desires, intentions) are biological devices, designed by evolution to have some effects on us. That effect is its content. Thus the effect has been determined by evolution. This strategy of treating intentionality as a biological feature can be extended to treating meaning as a biological phenomenon ("biosemantics"), because each sentence can be viewed as having a biological function (typically, helping us live in the world). "Sentences are basic intentional items". Intentionality is grounded in the relationship with the environment, a relationship determined by evolution. A mental content is the effect of a biological system designed by evolution to have that effect. Presumably, Millikan believes that desires and beliefs are physiological features of the brain, because they have evolved from generation to generation just like any other bodily organ has. On the other hand, the contents of these beliefs and desires are located outside the brain, and can be understood only by understanding their biological function, i.e. their evolutionary history. A belief is similar to the dance of a bee, a biological feature designed by evolution that refers to an object outside the head of the bee.

McGinn's externalist theory is an extension of Millikan's teleological theory. The mental contents of humans is external to their minds for the simple reason that it was set by evolution and it refers to the environment. The cognitive life of humans has been shaped by evolution to cope with an external object, the environment. Beliefs and desires are brain states whose content is a relation to the external world.

Fred Dretske's information-processing theory was based on the assumption that cognitive life consists in transforming analogue information (that comes from the sensory system) into digital information (that can become the processed as knowledge). For example, a smell per se is only a set of sensory data. Once it is analyzed and turned into the information that it corresponds with the smell of a particular flower, we "know" a fact about the world. This transformation from analogue to digital is what creates a "belief". A belief is therefore a neural structure. This is what the system "believes". The content of that belief is thus defined by its informational origin and not by its behavioral effect. A concept is the link between the information origin and the behavioral effect. The semantic content becomes a cognitive content when it is transformed from a representational unit to a functional unit.

Brian Loar's functionalist theory beliefs and desires are real physical states with real causal powers, but they are wholly defined by and within the overall network of beliefs an desires. A belief is defined by its functional role within the network of the person's beliefs. In a sense, the mind "is" the network of prepositional attitudes.

As for his own theory of intentionality, Lyons views the brain as a store of semantic structures, but not as an interpreter of such structures. In other words, the representations that are in the brain are not capable of understanding themselves.

Lyons distinguishes four levels of intentionality that children go through as they grow up: brain-level (analogue representation of sensory inputs), sensory-experience (representation of connection between events), linguistic, and prepositional attitudes.