Natural science and psychology are distinct from each other. Natural science is about material objects and the changes that they undergo because of their material nature. But psychology need not be about material things. If immaterial objects such as souls or angels existed, then they would be subject to psychological understanding. They could not be subject to scientific theorizing because immaterial objects are incapable of substantial change, cannot be created or destroyed naturally and cannot be altered by outside forces. So it is least possible for natural science and psychology to cover different individuals.
Psychology is the science of activity. Activities are different from mere changes. A is alive because it continues to do thing required to live. It gains nutrients from the outside, expels waste and grows. But all of those actions are things that happen from within the organism and are directed at the organism itself. These kind of actions are activities and living things are the things that can do them. In short, an activity is an action done by an individual that is directed at that same individual
Plants and animals may have a special kind of activity, but psychology is particularly concerned with rational activity. Thinking about something is one kind of rational activity, desiring something is another and planning something is a third kind. Any of these kinds of activities are subject to psychological scrutiny. They are outside of the domain of natural science because matter on its own cannot express rational activity. In other words, human beings do not have the ability to reason, desire and plan because their brains are special. No brain, no matter how special, could ever give anyone that kind of power. Instead, human beings have special brains because these brains are used by our rational powers. But the powers themselves are not found somewhere in the brain.
All of this means that psychology is in a similar position to theology. In order for it to be a discipline separate from natural science, it must demonstrate that the powers of matter cannot create a rational being. If this argument succeeds, then psychology is a separate discipline from natural science. If the powers of matter can create a rational being, then psychology is simply a subdivision of biology.
Arguments that attempt to show that matter cannot give rise to rational activity are numerous. They include arguments from qualia, arguments from intentionality and arguments from the nature of reason and morality. There are also arguments from consciousness and zombie arguments. An evaluation of all of these arguments is withing the sphere of philosophy as these arguments are about substance in general.
Next, I will discuss the science of sociology.