For cognitive neuroscience to go forward a more explicit effort is needed to use neurophysiology to constrain how the brain produces human mental functions. This review begins with the suggestion that two fundamental features may be critical for this effort. The first is the connectivity of the brain, which occupies an intermediate position between complete redundant interconnections and independence. The term semniconnected is presented as a designation, which is an obvious derivation of the term semiconductors as used in engineering. The second is transient response plasticity where a given neuron or collection of neurons may show rapid changes in response characteristics depending on experience. Response plasticity is a ubiquitous property of the brain rather than a unique characteristic of "neurocognitive" regions. These two properties may be brought together when brain areas interact such that their aggregate function embodies cognition. Three examples are used to illustrate these general principles and to develop the idea that a particular region in isolation may not act as a reliable index for a particular cognitive function. Instead, the neural context in which an area is active may define the cognitive function. Neural context emphasizes that the particular spatiotemporal pattern of neural interactions may hold the key to bridge between brain and mind.