Situating Solipsism in Philosophy Branches of Philosophy

Despite the large number of philosophical schools and subtle nuances between many, all philosophies are said to fall into one of two primary categories, which are defined in contrast to each other: Idealism vs. Materialism.

1. 
   What does reality consist of? (Metaphysics) 2) Where does it originate? (Epistemology)
   

In consideration of the above, it is good to keep in mind that you can’t be an Idealist and a Materialist, and you can’t be a Rationalist and an Empiricist. On the other hand, you can be an Idealist and a Rationalist or an Idealist and an Empiricist. You can also be a Materialist and a Rationalist, or you can be a Materialist and an Empiricist.

That is because Idealism and Materialism are statements of metaphysics, which means they are statements about what you believe is real. Rationalism and Empiricism are statements of epistemology, which means statements about what is the best way to know what is real.
The "Inside-Out" Tradition

In the history of Metaphysics, there are two quite distinct traditions about the nature of the relationship between our self and the world we see around us  -  between what we think we perceive and what believe is real; and centrally, between the meaning of "perceive" and the meaning of "real".  They are the Idealist, or the "Inside-Out" tradition and the Materialist or "Outside-In" tradition. The difference between the two traditions is the difference in their approach.  The Outside-In tradition sets out what must in a very general way be the case about the world and about ourselves if the world exists independent of our consciousness of it.  The Inside-Out tradition holds that only things answering to certain criteria are real with the result that there are distinct realms to be called "appearance" and "reality" respectively. 

Philosophers of the Inside-Out tradition maintain that our modes of consciousness and cognition constitute, modify, or process what we perceive as sensory inputs.  What our consciousness is aware of as sensory evidence must be regarded as the products of our consciousness rather than unbiased evidence of reality.  In that event, goes the inescapable logical conclusion, either we can know nothing about the "True" nature of an alleged external reality, or anything that we can know about such an alleged external reality must be provided through other means than our senses.  The proponents of the "Inside-Out" line of reasoning assume that consciousness, as prior and primary to the sensory evidence, must generate our understanding from the evidence provided by our processes of perception.  Perception is a separate process from our conscious awareness of what we perceive.  Our understanding of what we perceive is not a pure product of our senses.  Therefore, what we understand about our perceptions cannot be trusted as evidence for a separate reality.  We have no independent basis from which to validate the evidence provided by our senses.  All we have is the evidence of our perceptions.  And our perceptions are highly processed information from our senses.

There is, therefore, no logically valid line of reasoning that can proceed from the basic axiom that consciousness is the fundamental given, to the conclusion that there is a reality outside of, or separate from one's own consciousness.  Since there is no way to validate the evidence of the senses (the senses being the only source of information), there is no basis from which to conclude that the sensory evidence is valid evidence of an external reality.  There is no way to distinguish between "reality" and a dream or hallucination.  Philosophers of the Inside-Out Tradition therefore almost universally conclude that all that is perceived (ie. all the evidence), as well as all the contents of consciousness, is actively a product of consciousness.  As it is impossible to logically derive the existence of a reality beyond our subjective experience, therefore there can be no knowledge of such an external objective reality.  Hence, there is no acceptable proof that there is such an external objective reality. 

The inescapable consequence of this conclusion is that there can be no possible logical foundation for any constraints on the nature of the contents of a particular person's consciousness.  There can be no logical foundation for any standardization or similarity of the contents of consciousness from one person to another.  For this reason, the Inside-Out tradition logically results in what is referred to as "Subjectivist" (or sometimes "Anti-Realist" ) notions of Truth, Knowledge, and Ethics.  And, ultimately, to metaphysical "Solipsism".
Idealism (“Inside-Out”) vs. Materialism (“Outside-In”)

Let us consider some very basic features of our being. We sit, for instance, on a chair. We can see the chair, we can touch it, and the other senses can, as well, perceive of the chair. Now, these perceptions all occur within our brain, where the input data of the sensory organs come together and form an "image" of the thing we perceive (the chair in this case).

Solipsism comes from the Latin "Solus ipse"  - the sole self.  Anthony Flew defines solipsism as "The theory that I am the sole existent.  To be a solipsist I must hold that I alone exist independently, and that what I ordinarily call the outside world exists only as an object or content of my consciousness."⁽¹⁾  Thomas Mautner defines it as "(1-metaphysics) the view that nothing exists except one's own self and the contents of its consciousness; (2-epistemology) the view that nothing can be known except one's own self and the contents of its consciousness."⁽²⁾

The challenge that Solipsism raises for the study of philosophy is that while it seems to be a logically sound theory of existence, no one likes the implication that they are completely alone in the Universe.  It is also universally (and frequently offensively) rejected by philosophers as an acceptable basis of metaphysics.  Yet given certain popular metaphysical premises, philosophers have difficulty in rationally supporting this rejection.  Hence the challenge that Solipsism presents.

Solipsism is a huge problem for anyone interested in promoting introspection as a way to understand the mind. You can only introspect on your own mind, not anybody else’s. So technically, all you really know for sure is your own mind. The existence of any other minds is purely hypothetical.

Remember, all this started with the fundamental premise of the Inside-Out Tradition that consciousness is primary, that the mind is something separate from an objective reality, that we have a direct knowledge only of our minds and its contents and not of the source of our sensory perceptions, that there is a dichotomy between "reality" and "appearance".  This was combined with the Empiricist premise that all human knowledge derives from our sensory experiences.  So, if you don't like Solipsism as a metaphysical theory of what actually exists, adopt alternative premises.  Either, like Aristotle and other "realists", the premise of the Outside-In Tradition that existence is primary, that the mind is a product of the prior existence of reality, that we have as direct an access to the source of our sensory perceptions as we do to the contents of our mind, that there is no dichotomy between "reality" and "appearance".  Or, like Descartes and Kant, the Intuitionist premise that the mind has access to sources of knowledge other than our sensory experiences  -  innate pre-programmed ideas and concepts, or an ability to "intuit" a priori knowledge without the contribution of the senses .  Or, like Descartes and Berkeley, the Theistic premise that there is a benevolent God to bridge the gap between my mind and the "other", that we can gain from "divine revelation" knowledge not available to our senses.