Below you will find a question someone asked me on Quora, and my response.

Question: "Is psychology scientific? Or speculative? Are premises like 'sexual repression leads to psychosis' facts ? Have the Jungian concepts of anima and shadow been proved?"

My response: 

Different branches of psychology involve very different implicit or explicit worldviews. For example, neuropsychology tends to view psychological disturbances more through a materialistic lens, with causes attributed to chemical imbalances in the brain. Jungian psychology (also called analytical psychology), as well as depth psychology, can be considered to be on the opposite end of the spectrum, involving concepts like the “archetypes” and the “soul” that are non-quantifiable and nonphysical in origin. These types of psychology have more to do with meaning, purpose, and emotion—things that are in the mind (experience) rather than in the brain. 

In regards to having “proof” for psychological theories, when dealing with human experience directly, we cannot prove anything. For example, if you say that you love someone, and you describe that love experience as being a particular way, there is no way to prove that experience. From a neurological standpoint, we can measure the chemical processes that occur when you say you are in love in this certain way and compare those measurements with ones from a sample set of people who also say that they are in love in that way, but there is no way to prove the actual experience. Subjective experience cannot be proved, nor can it be accessed through a microscope. That doesn't mean that all of our feelings, complex thoughts and dreams don't mean anything, just that the only way that we have access to those experiences are through the reports of the individuals who have them. And so, we have therapy—people who listen and talk things out in order to help figure out what is going on with an individual subjectively.

Much of analytical psychology is based on the notion of an unconscious mind (psyche) and what, exactly, is to be found in that unconscious mind (which, again, is not the same “thing” as the brain). It became obvious early on that people had an unconscious. When Freud and Jung conducted simple word association tests they noticed that the test subject's response time would consistently be longer given the prompt of certain words (like “mother” for example), and that the subjects were not aware of their different reactions to some words over others. Hence, something was happening “within” the subject's mind that was “beyond” their conscious awareness. This lead to the notion of a “complex,” which is an idea or image in the unconscious that is “surrounded by” or “embedded in” emotional charges. 

There is no way to prove there is a complex in the same way the you can prove something in the laboratory, but you can infer it with a large degree of certainty. Complexes can become evident in many ways, not just through word association tests. A therapist can gain an impression of patients' complexes just by talking with them about their experiences and inner life, observing their behavior, and by exploring the content of their dreams. 

We all have complexes. If you are irrationally afraid of the ocean; that is a complex. If you see someone whom you don't know, but automatically hate, that is a complex. You are experiencing a series of emotional charges that are associated with a certain idea and image. Through therapy or analysis, you can figure out the meaning of what is going on there. For example, if an image of a certain type of man activates strong negative emotions in someone, through analysis, we might discover that the person is really responding to his or her internalized father image. Coming to understanding of this will help the individual learn how to be less reactive, and also to reintegrate some essential masculine qualities that have been dissociated with that image. 

As time went on, Jung and others greatly expanded the theories about what constitutes the postulated structures of the unconscious. For example, the notion of Anima was developed, which is the unconscious feminine side of a man. You can't prove the existence of the Anima, but you can infer its existence by the countless reports of individual men (and the thousands upon thousands of analyzed dreams in therapy sessions), as well as through artifacts from our collective culture—movies, literature, theater, and so on. So analytical psychology isn't a “hard science,” per say. When dealing with subjective experience itself, there is no hard science: the only gateway into that content is through the personal reports of the individuals themselves. Direct human experience is qualitative, not quantitative. This does not mean the psychologists haven't been methodical, or even empirical, in their studies and recordings of people's subjective patterns—the countless reported dreams, experiences and behaviors of their patients.