V. L. Chechulin, L. N. Yasnitsky

The limitations of neural networks resulting from the general fundamental limitations of predicative formal systems and formal methods were described; indicated meaningful interpretation of these restrictions can not be formalized in terms of neural networks through the processes taking place in the minds of the reflection of reality. The main limitations of neural networks follow from the limitations of algorithmic unsolvability, since neural networks are implemented by some algorithms. A connection of limitations of neural networks with Gödel's incompleteness theorem is found. Indicated on the interpretation of the theorem of Nagorny, on the algorithmic insolubility of the doubling of words in some alphabet, showing the inability to apply neural networks to the currently known models of the processes of consciousness (reflection). The study of limitations showed that neural networks are applicable in the case when they describe the phenomena reduced to the functional (predicative) dependencies. Described constraints allow us to specify the range of applicability of neural networks for applications in such area as predictive functional dependencies.