A central problem in understanding the brain concerns how knowledge is stored in synaptic connections among neurons. In artificial neural networks this phenomenon is modeled by connection weights, which determine how much of the activation of one neuron is passed to another neuron. The goal of this project is to understand how knowledge is stored in a set of connection weights, and to use this understanding as the foundation for an epistemology that is directly grounded in what we know of the brain. Our understanding of the brain and of the neural networks that model it, including those used for artificial intelligence purposes, will be limited until we understand how to correlate specific changes in connection weights with specific changes in stored knowledge. For similar reasons, psychological explanations of cognitive processes and the philosophic theories of epistemology that build on them both rely fundamentally on understanding what knowledge is stored, and under what conditions, within a neural network.