  It is well known that mean-field theories fail to reproduce the
experimentally known critical exponents. The traditional argument which explain
this failure of mean-field theories near a critical point is the Ginsburg
criterion in which diverging fluctuations of the order parameter is the root
cause. We argue, contrary to the above mentioned traditional view, that
diverging fluctuations in real physical systems near a critical point are
genuine consequence of the breakdown of the property of statistical
independence, and are faithfully reproduced by the mean-field theory. By
looking at the problem from the point of view of "statistical independence" the
divergence of fluctuations in real physical systems near criticality becomes
immediately apparent as a connection can be established between diverging
correlation length and diverging fluctuations. To address the question of why
mean-field theories, much successful qualitatively, fail to reproduce the known
values of critical indices we argue, using the essential ideas of the Wilsonian
renormalization group, that mean-field theories fail to capture the long length
scale averages of an order parameter near a critical point.
