A neural network is usually programmed to learn from datasets to solve a specific problem. Essentially, they perform non-linear regression.
Could a neural network be programmed to receive input from a human, like a terminal, to begin to grow and learn (similar to how a child learns)?
A program that neither knows it's purpose nor specific data sets but is given enough information to learn based off of input, ponder the input, and ask questions. A child discovers their purpose (in destiny based philosophy) through experience. Thus, could an AI be created that would learn its purpose over time?
Grow both by continued development, maybe adding extensions that add image recognition, speech analysis, etc., and through user interaction. Eventually learning "moral imperatives" or simple the do's and don't's and how to interact with data.
A case scenario would be a Question & Answer session with the neural network and a large data set. Where the human operator knows the answers. At first, the question and the answer are supplied to the neural network. Giving it the ability to find the answer supplied through deep learning. A guaranteed confidence score of (1) - as the question is pondered the closer it gets to the answer the more it "learns".
The next step is supplying the question and waiting for the answer. The human still knows these answers but is testing the "learning machine" to see if it is truly learning and not "repeating the answer". The answer is supplied by the machine and the human returns with either a percentage that the machine is right (hopefully and eventually matching its confidence score). and after an amount of failure provides the right answer to the machine to repeat the first step and improve learning.
The last step is being able to have the machine answer the question with the human not knowing the solution, thus completing the learning cycle. The human would test the solution and report the results to the machine and the machine would adapt the process and continue learning. However, this time it would begin learning from a data set of results. Hopefully learning "data mining" during its question and answer session.