Paradoxical Circulation Theory of Lift

The New Theory of Flight presented on The Secret of Flight shows that the classical circulation theory of lift by Kutta-Zhukovsky is unphysical and thus incorrect, which is also supported by the fact that it builds on a paradox:

• Kutta-Zhukovsky lifting flow around a 2d airfoil is obtained by augmenting non-lifting potential flow by large scale circulation around the airfoil.
• The sharp trailing edge of an airfoil is supposed to be necessary for generation of lift.  
• The lift is proportional to the circulation, and the circulation is determined so as eliminate the singularity of potential flow arising from the sharp trailing edge.
• Lift is thus paradoxically obtained by elimination of what has been introduced, that is by eliminating the singularity introduced by the sharp trailing edge. This is like obtaining an effect by first introducing something and then removing it, as if (+ 1 - 1) could be greeter than zero. 
• The paradox is supposedly resolved by claiming that the singularity is eliminated by effects of viscosity. 

The New Theory shows that lift is generated, not by a sharp trailing edge, but by wings with smoothly rounded trailing edges with diameter up to 10% of the chord length.