Is there just one fundamental thing in the world? Or are there many? Perhaps the world is a dichotomy or dualism, for example, between the Ideal and the Material? Some philosophers prefer to think of "three worlds," often adding a third world between the Ideal and the Material.

The "problem of universals" is the existential status of such a shared property. Does the one universal property exist apart from the many instances in particular objects? Plato thought it does. Aristotle thought it does not.

Consider the property having the color red. Is there an abstract concept of redness or "being red?" Granted the idea of a concept of redness, in what way and where in particular does it exist? Nominalists (sometimes called anti-realists) say that it exists only in the particular instances, and that redness is the name of this property. Conceptualists say that the concept of redness exists only in the minds of those persons who have grasped the concept of redness. They might exclude color-blind persons who cannot perceive red.

Realism is the view that a "reality" of physical objects, and possibly of abstract concepts like redness, exists in an external world independently of our minds and perceptions.

Platonic Realism is the view that abstract things like numbers, perfect geometric figures, and other things that Plato called the Forms or the Ideas, have a real and independent existence, though they are not material objects.

But for his student, Aristotle, these "universals" exist only in the concrete objects which share some property. For him, the universal idea of a perfect circle is a shared property of the many actual circles in nature.

Naive realists think that we can access concrete physical objects directly and fully with our perceptual sense data. This is sometimes called the "copy theory." Our perceptions are fully apprehending the physical objects, so that the content of a perception is the same as the object of perception. In information philosophy terms, naive realism mistakenly assumes that the information in the perceived sense data (or the representation in the mind) is (quantitatively) equal to (a copy of) the information in the physical object. In the case of the abstract concept of redness, it may be that the copy-theory is most tenable. The perception of a red object may in a strong sense bring the concept of redness into existence (at least in the observer's mind).

Historically, realism is a metaphysical claim about this independently existing world where redness might be found. Since Aristotle's Metaphysics, two kinds of metaphysical questions (ontological and epistemological ) are raised - what exists, and how can we know what exists.

The ontological status of abstract concepts is a completely different question from the ontology of concrete physical objects, though these questions have often been confounded in the history of philosophy.

Information philosophy provides distinct answers to these two ontological questions. Physical objects exist in the world of space and time. They are information structures embodied in matter and interacting with energy. Abstract concepts (like redness) are pure information, neither matter nor energy, although they need matter for their embodiment and energy for their communication.

The contrast between physical objects and abstract concepts can be illustrated by the difference between invention and discovery.

We discover physical objects through our perceptions of them. To be sure, we invent our ideas about these objects, their descriptions, their names, theories of how they are structured and how they interact energetically - with one another and with us. But we cannot arbitrarily invent the natural world. We must test our theories with experiment. The experimental results select those theories that best fit the data, the information coming to us from the world. This makes our knowledge of an independent external world scientific knowledge.

By contrast, we humans invent abstract concepts like redness. We know that these cultural constructs exist nowhere in nature as physical structures. We create them. Cultural knowledge is relative to and dependent on the society that creates it.

However, some of our invented abstract concepts seem to have an existence that is independent of us, like the numbers and the force of gravity.

Critical realists, like scientists, start with observations and sense data, but they add hypotheses and experiments to develop theories about the physical objects and the abstract concepts in the external world. Nevertheless, the abstract representation in the mind is (quantitatively) much less information than the information in the physical object represented.

The "axiom of independent reality" claims that "Knowledge unconditionally presupposes that the reality known exists independently of the knowledge of it, and that we know it as it exists in this independence." (H. A. Prichard.)

The British empiricists Locke and Hume argued that what we were "given" in our perceptions of sense data was limited to so-called "secondary qualities." These are properties that produce the sensations in the observer's senses - color, taste, smell, sound, and touch. Knowledge that comes from secondary qualities does not provide objective facts about things "in themselves."

Kant described these secondary qualities as "phenomena" that could tell us nothing about the "noumena," which the empiricists called the "primary qualities." These are properties the objects have that are independent of any observer, such as solidity, extension, motion, number and figure. These qualities exist in the thing itself (Kant's "Ding an sich"). Kant thought that some of these qualities can be determined with certainty, as "synthetic a priori truths. Some of these qualities are analytic truths, defined by the logical meanings of linguistic terms. For example, a round circle cannot be a square.