Here is my current thinking about idealism vs. realism. I am in my home office looking at my computer, surrounded by my books. This room I am in, my body, my activity, etc....all of this is real. How do I know this: I cannot absolutely, but it seems reasonable, at least right now, to deny every alternative hypothesis (for example, that I am actually looking at a virtual reality world). I am, as Dewey puts it, a live creature interacting with my environment. Let's just take that as a given. The world I experience around me as I am walking, for example, is a world that exists and to which I have access through my senses. It is one part of a larger world to which I do not have access through my senses, for example the sub-atomic aspect of that world. Modern science is the best way to understand the world I have access to through my senses, and also the larger world to which sometimes I have no access through my senses. Yet, the the world of modern science is not, and here I am following Nelson Goodman, the only way the world is. There are other ways, and this brings in the issue of idealism.
So where is there room for idealism? There is room on two levels, these having to do with two different meanings of "idealism." First, as soon as I represent this world, either in language or by some other means, I create a second world, i.e. a representation of the first world: it is a way the world is.
Much of my life is spent contemplating and making such representations. These representations are all ways of seeing the world, and they present ways the world is. Moreover, although I have access to the world sensuously, I only focus on those aspects of the world that are of interest to me and that fit into certain categories I commonly use. So, although what I see and otherwise experience is the world, the arrangement that comes from choosing what I look at, and how I construct my own internal map of this world, is influenced by ideas. One could say that I view the real world through various idea worlds, where the second "world" refers to world maps. To ignore the pervasiveness of all of the representations that mediate my relations with the physical world is to ignore this fundamental truth, the real intuition of idealism. Moreover, since much of the physical world within which I live is made up of artifacts which themselves are either representations or are the result of human non-representational thinking and activity, the meaning content of that aspect of the world is also subject to idealism.
An interesting problem for strict realists (realism that excludes the intuition of idealism) is that I cannot say or think anything about the real world without using representations. Even if I say that "this is a chair" I am using ideas such as "chair" and all of the complex grammatical ideas associated with the formula "this is a" to do this. And so my experience is two-sided: there is the side that is real and physical, the chair in front of me, which I have access to by way of my senses, my brain, and my bodily behavior, and the chair as described, as thought of, as having meaning content (even if that meaning content is entirely expressed in physicalist terms and is the result of a physicalist philosophy!).
A second aspect of idealism is belief in something like Plato's Forms. Don't get me wrong, I do not believe that Plato's Forms themselves exist, i.e. as eternal and unchanging, except possibly in the way the certain mathematical entities may exist (I am agnostic on whether there is an eternal Form of "circle") The point here, with respect to a defense of something vaguely like Plato's Forms, is that there is a legitimate activity, a philosophy language game, that asks "what is the essence of X" and that gives us competing answers that can generate dialogue with some resolution. On my view, essences are real but within the domain of representation and its interaction with the real physical world, especially with those aspects of the real physical world that are also implicated in human activity and interpretation. As opposed to Plato's Forms, essences evolve historically. I grant to Plato that they have an ideal as well as a real aspect, but this ideal aspect is always of the form of an unrealized and ultimately unrealizable goal: the ideal aspect has no content of its own and simply marks the ideal of resolution of debates over essences. I have written about this elsewhere in detail.
Wikipedia says "In philosophy, idealism is the group of philosophies which assert that reality, or reality as we can know it, is fundamentally mental, mentally constructed, or otherwise immaterial." I am not an idealist in that sense, and yet there is a fundamentally mental aspect of the world in that there is not only the level of physical objects but also the level of multiple interpretations of those objects especially as evidenced in the language game of philosophy its search for truth, or, as I would put it, essences.
Nor do I accept the idea that something mental or spiritual is the foundation of all things. And yet, in a strange way, I am as much an idealist as a realist. Paul Guyer and Rolf Peter Horstmann in their Stanford Encylopedia article on idealism make a point of distinguishing between idealism of this sort and epistemological idealism, which they describe in this way: "involves a theory of the nature of our human knowledge; and various decidedly different theories are called by this name in view of one common feature, namely, the stress that they lay upon the ‘subjectivity’ of a larger or smaller portion of what pretends to be our knowledge of things." Yet, atlough attracted to idealism, I would not say that knowledge is essentially subjective. There is, of course, a subjective aspect of all knowledge, and yet we can still speak of degrees of objectivity, and this is just based on the fact (assuming we are willing to accept it as fact) that there is a real world in which we live, and that that world is what it is independent of our thoughts about it, although of course our thoughtful representations, once made, also become an important part of that world. Moreover, there is some truth to ontological idealism, both in terms of the existence of an emergent world of representation and interpretation and also the ideal but indescribable aspect of the world represented by the philosophy language game. Essences are real beings, although not reducible to the realm of the sciences nor identifiable with eternal unchanging Forms. To reject idealism of the traditional form that posits a separate metaphysical world is not the same as rejecting all ontological implications for the intuition of idealism. My point: interpretation and representation animate our world, and the world experienced through that animation is what is important to us, and the search for essences is one way to animate the world as was the search for gods previously. Thus creating new mythologies, writing poetry, done in a way that is deep, and also respectful of the physical world in which we live and respectful of the way it grounds our experience (the pragmatist intuition of Dewey, I think) is the way to respond to our present crisis of spirit. Nietzsche, of course, saw this.
Guyer and Horstmann say "An inclination toward idealism might even arise from considerations pertaining to the ontological status of aesthetic values (is beauty an objective attribute of objects?) or from the inability or the unwillingness to think of the constitution of social and cultural phenomena like society or religion in terms of physical theory." and this seems to describe my attitude or the reason why I would consider idealism as having equal status to realism as long as restrained to include only the world as represented through language and art. Physical theory is not and can never be sufficient for explaining social and cultural phenomena since these all involve many levels of interpretation and are complex evolving entities that are, as Joseph Margolis would put it, emergent upon but not reducible to physical phenomena.