Dear colleagues,

I would like to declare that the famous Godel's incompleteness theorems with a 92 years history are wrong based on the following observations.

The equation (8.1) in [1] with the term?"subst(y,19,number(y))" has a logical error in it.?

Here, Godel supposes there is a formula with a free variable y, and also, he names the Godel number of this very formula as "y", which means he uses one symbol "y" for two different meanings, and formula y has been talking about itself from the first place, since Eq. (8.1) is actually the starting point of Godel's arguments.?

If we allow one symbol has two different meanings, we can construct a liar-paradox in one step, just name the statement "Formula G is false" as G.

This error invalidates Godel's whole arguments.

[1] K. Go ?del, “Uber formal unentscheidbare sa ?tze der principia mathematica und verwandter Systeme I,”?Monatshefte Fu ?r Mathematik, vol. 38, no. 1, pp. 173–198, 1931. English Translation "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" by Marin Hirzel, Nov. 27, 2000.?

Sincerely Yours

Xuezhi Yang with ID 110108197007188995

IEEE Senior Member?

Beijing, China

yangxuezhi@hotmail.com