The idea of cognitive psychology replacing epistemology is akin to medical anthropology replacing anthropology. In essence, cognitive psychology is a sub field of psychology, as is epistemology, and both originate in philosophy. A mother science cannot be replaced by a sub field.
In definition, cognitive psychology originated in the 1950s when scientists broke away from the behavioral traditions of psychological theory and began to focus on the thinking processes. The field was heavily populated with scientific processes, models and paradigms as what some have come to call the “cognitive revolution”. The methodologies of the behaviorists were retained, while the restrictions that were imposed by behavioral approaches were abandoned with glee.
While very little is known about the mechanics of the brain, and how those mechanics serve to make cognitive functions work, a lot of progress has been made. With such new technology as brain imaging, where the actual structure and electrical and possibly chemical activity of the brain can be detected in relation to certain cognitive functions, the field is making some incremental breakthroughs, creating even more subfields of cognitive psychology such as cognitive neuroscience.
With cognitive psychology it is about the brains technology.
Epistemology is a field of philosophy that deals with all knowledge, how we come to know and retain knowledge, what it is that we know, and how we come to believe things, whether we have a lot of knowledge or not. Epistemology relates the above issues with belief, justification and truth, which is a far broader field of study than the technical aspects of the way in which our brains process information and knowledge.
Epistemology deals with knowledge generally under the concept of “propositional knowledge”, which means that we are interested in “knowledge that”, instead of “knowledge how”. The famous math problem: 2+2=4, is the easiest way to explain the difference between “knowledge that”: we know that 2+2=4; but how do we know how to add two numbers to get to a third number, or to attain “knowledge how”? We can study all of the physics of bicycle riding that we want to, but actually learning to achieve the physical balance and control necessary to control an actual bike is another matter of knowledge. This can be called a “justified true belief” form of knowledge.
Another way of doing epistemology is to get away from propositions and to look at the individual’s intellectual virtues or abilities and deeper into the idea that knowledge comes from other places than proposition and testing of proposition. Belief is the core of human knowledge, and we all know how it can affect the whole of what a person will admit to knowing. We forecast and decide likely future outcomes based on our beliefs.
With humans, the issue of studying the subjective nature of and issues concerned with knowledge will always be as important, in dealing with the internal truth, as will be dealing with external truth.
As a result, one field will not supplant the other, and both will be of interest to thinkers and scientists for some time to come.
John Robert Anderson, “Cognitive Psychology And Its Implications”, 6 ed, 1980, Worth Publishers, and .WF Freeman and Co.