This chapter explores computation as the systematic execution of operations over formalized data, governed by explicit rules. We examine how computational complexity theory classifies problems into classes such as P—those solvable in polynomial time, and NP—those whose solutions can be verified in polynomial time, although potentially requiring exponential time to solve. At the heart of this lies the P vs NP question: whether every problem whose solution can be efficiently checked can also be efficiently solved. Deterministic and nondeterministic Turing machines are introduced as abstract models defining the theoretical limits of computability. In parallel, early neural network models, notably the McCulloch-Pitts neuron, demonstrated how basic logical operations could be mechanized, though challenges like the XOR problem revealed the need for multi-layer, non-linear architectures. By interlacing these foundations—from logic and algorithmic limits to biological inspirations—the chapter positions computationalism not only as a framework for artificial intelligence but also as a deeper philosophical claim about the mechanistic nature of cognition.