Richard Dawkins begins his popular "The Magic of Reality" (Free Press, 2011) with the sentence "Reality is everything that exists". This is a good definition of "reality" if we can agree on what the verb "exists" means; and a good definition of "exists" if we can agree on what "reality" means. Unfortunately, strictly speaking, neither is the case, although for those who use the terms only for everyday purposes - and Dawkins' book is after all aimed at them - this does not represent a problem.
On a different level, the NewScientist ended its recent series of ten articles entitled "What is Reality?" rather inconclusively:
"Do we make reality, or does it make us? Probe the existence of the universe's supposed building blocks - quarks, electrons, neutrinos and the rest - and you eventually end up back in your own mind. Alternatively, discount everything human and settle for 'a world without us' - a reality that might also be unknowable by us …These options are as viscerally unsettling as they are intellectually challenging".
What is then the nature of reality? This is one of the questions also Stephen Hawking and Leonard Mlodinow ask at the very beginning of their book "The Grand Design" (Bantam Press, 2010), followed by the often quoted "philosophy is dead" claim. Taken as such, this claim is obviously an exaggeration ad absurdum. However, if in the actual context one replaces it with an ellipsis, we get "traditionally these were questions for philosophy, but philosophy … has not kept up with modern developments in science, particularly physics", a criticism that many of us can agree with. So what are the insights from physics offered by Hawking and Mlodinow? They call it "model-dependent realism" that I think could represent an intriguing contribution of physics to philosophy, (misunderstood by many, although already hinted at by Einstein when he wrote that reality was merely an illusion), and best expressed by:
"According to the idea of model-dependent realism ..., our brains interpret the input from our sensory organs by making a model of the outside world. We form mental concepts of our home, trees, other people, the electricity that flows from wall sockets, atoms, molecules, and other universes. These mental concepts are the only reality we can know. There is no model-independent test of reality. It follows that a well-constructed model creates a reality of its own."
What this means is that physics/science cannot provide any guarantee ("evidence") that there is a reality independent of what "model", i.e. physical theory, one uses to represent (describe) it with.
Nevertheless, and the authors admit that much, for practical purposes one cannot live without the assumption ("belief"?) that there exists such a reality, that there is a "truth" about this reality, that scientists are striving to know. In philosophy (of science) if this assumption is explicit, one speaks about scientific realism. On the other hand, a strict adherence to model-dependent realism of Hawking and Mlodinow would correspond more or less to the position of constructive empiricism of Bas C. Van Fraassen: "Science aims to give us theories which are empirically adequate; and acceptance of a theory involves as belief only that it is empirically adequate".
Another approach is to first look not so much at what is "reality" and what "exists" but to start with the three worlds - mental, mathematical, physical - of Roger Penrose (see e.g. The Road to Reality, Alfred A. Knopf, 2004). It is related to, and inspired by, but not identical to, Karl Popper's three worlds, mental, objective knowledge, physical. Penrose's model is primarily aimed at explaining the role of mathematics in our understanding of the structure of reality studied by physics, but it could perhaps be extended by adding other conceptual constructions to the mathematical world, thus ending more or less in Popper's world of "objective knowledge". I shall not consider this generality, so that also the mental world will be restricted mainly to ideas (what is understood either by a particular individual or by humanity as such) related to physical reality and mathematics.
There is no need for an a priori assumption about the "independent existence" (although here "irreducibility " is a better word) of these three worlds of Penrose, although many scientists and mathematicians believe that neither of them is reducible to any of the other two. For instance, many, probably most, mathematicians (so called Platonists or realists) believe in a world of mathematical concepts and relations independent of the human mind. For practical purposes, i.e. in order to better understand the interrelatedness of these three worlds, it is better to formally assume this mutual irreducibility. (Actually, one could similarly think of a fourth world, spiritual or transcendental, with some people believing in its irreducibility, and others seeing it as reducible to - if not contained in - the mental and/or physical worlds.)
There is a rich literature on the interrelations between these three worlds. I shall mention here only the three enigmas, or mysteries, that haunt our attempts to properly understand them:
The Wigner enigma, haunting the mathematical-physicalworlds interrelation. It is about the "unreasonable effectiveness of mathematics", meaning that most of the seemingly purely mental constructions in mathematics find applications as models describing some features of thephysical world, including making verifiable predictions.
The working mathematician's creation/discovery enigma haunts the mathematical-mentalworlds interrelation. Does a mathematician create his mathematics, or does he/she discover something that pre-exists in the "objective" world of mathematics? The answer is that both, although it is not easy to tell whether in a particular situation the creation or the discovery aspect prevails.
The quantum enigma haunts the mental-physicalworlds interrelation. It concerns the situation in modern physics, where observations seemingly create the physical reality observed, or in Wigner's words, the situation when "it was not possible to formulate the laws of quantum mechanics in a fully consistent way without reference to the consciousness". This hints at the Copenhagen interpretation of quantum mechanics, but even if abandoned, and replaced by Everett's many world's interpretation, as seems to be the preference among contemporary physicists, the enigmatic nature of this, or other interpretations, remains.
And perhaps the greatest enigma of them all is the following. In spite of all these uncertainties and ambiguities - concerning the nature of reality, its structure and the working of consciousness - when we need a level of understanding sufficient for everyday life, common sense is a practically reliable (albeit in most cases) guide.