Is the classical world an illusion? In the paper

Zeh, H. D. The Wave Function: It or Bit? In Science and Ultimate Reality, eds. J.D. Barrow, P.C.W. Davies, and C.L. Harper Jr. (Cambridge University Press, 2004), pp. 103-120.    arXiv:quant-ph/0204088

does Zeh state the classical world is an illusion or that our sense of locality in the classical world is an illusion? Is he correct?
 A: First of all one should define what  illusion  means.   

1)
a) obsolete : the action of deceiving
b) (1) : the state or fact of being intellectually deceived or misled : misapprehension 

(2) : an instance of such deception

2)
a) (1) : a misleading image presented to the vision
(2) : something that deceives or misleads intellectually
b) (1) : perception of something objectively existing in such a way as to cause misinterpretation of its actual nature
(2) : hallucination 
(3) : a pattern capable of reversible perspective 

If one uses the "deceptive" part of these definitions, the answer is yes, the classical world is an "illusion".
BUT, when one starts being philosophical about our perception of the world one should keep in mind that everything that defines our existence can then be called an illusion. All information we have about the world around us reaches us through successive levels of proxies.
By level of proxies for example: we observe the world through our five senses, they depend on a level of cells organized to send information and store it, and that level depends on the organization of atoms and molecules, which depends on the quantum mechanical substratum of protons and neutros, which protons and neutrons depend on the substratum of quarks.
Another example: when we walk, we sense the earth beneath our feet as solid. It is an illusion because it is composed by a level of atoms which are mostly empty space as far as mass goes, and those atoms are composed by protons and neutrons .....
Nevertheless we do manage to walk, and are sure we exist because we ride as a biological pattern supported by forces over a complex stratum also supported  by forces we have studied utilizing all these "illusionary" levels;we have also acquired an understanding of  this in depth.
This happens because, as Vladimir concisely says, the everyday world is emergent from the complex levels  of matter and forces beneath the dimensions we can measure every day compatible with our size : millimeters or at most microns for length, seconds, or at most microseconds for time.  It is when our focus goes to smaller dimensions that the concept of "illusion" pertains.
A: Classical world is an inclusive picture with a certain time resolution. In this sense it is an illusion since made of sets of bits of information.
A: There's a misleading urban myth spreading around virulantly these days. It says decoherence shows how the classical world can emerge and solve the measurement problem.
Decoherence doesn't do anything of this sort! Note careful thinkers always use the word quasiclassicality instead of classical in this context. Interference may be exponentially suppressed after coarse graining, but the superposition still remains! Exponentially small off diagonal terms are still there, and there's still the problem of definite outcomes!
The classical world is an illusion! Quasiclassicality is the best we can do! We're all Wigner's friend!
