What are the limitations of computer models and why do we still not have working models of people that are recognizably human?  This is the principle puzzle explored in this book where ideas behind systems that behave intelligently are described and different philosophical issues are touched upon.  The key to human behaviour is taken to be intelligence and the ability to reason about the world To approach this scientifically, it is necessary to understand what a scientific approach could mean in the context of both natural and artificial systems.  A theory of intelligence is proposed that can be tested and developed in the light of experimental results.  The author illustrates that intelligence is much more than just behaviour confined to a unique person or a single computer program within a fixed time frame.  Some answers are unravelled and some puzzles emerge from these investigations and experiments.  Natural and Artificial Reasoning describes a few steps on an exciting journey that began many centuries ago with the word ‘why?’.