Philosophy of languages discusses the two concepts of extension and intension. Since the 1960ies Putnam published a series of papers on topics like the meaning of meaning. He argues against the view that meaning exists in the brain only: “ ’meanings’ just aint’t in the head!” By the famous thought experiment of water on the twin earth he clarified his point of view, that the meaning of a term has to take into account more than just brain states.
In the meantime, neuroscience has established itself as a player in the domain of philosophy of mind. Some researchers with a strong capability in neurobiology and philosophy have presented new models of the mind; e.g. Gerhard Roth: Das Gehirn und seine Wirklichkeit. 1994 (in German).
The philosophical approach employs a constructivist epistemology. On the other hand, neuroscience emphasizes that the content of our mental processes solely results by pattern recognition and pattern processing from the net of neural activity in the brain. The brain is deaf and blind. It neither hears nor sees nor smells nor touches etc.
It is our cognitive system, which classifies the neural input as visual, auditive, olfactoric or sensual due to the brain areas where the input comes from and due to its time-related pattern. Herefrom the brain constructs a world-model with the relevant features of our environment. This world-model is permanently updated. All our perceptions refer to this model. But the model itself stays transparent. It is invisible to our conscious awareness: We perceive the inner world-model as if we had direct contact to the things from the outside world.
The meaning of a term is the relation between two mental structures, both of which form part of our world-model. One structure is the pattern of the term, the other is a combination of several other patterns (the intension).
In particular, all meaning is in the brain because the world-model is in the brain.
Added: What are possible objections?