Decidability without mathematics

The paper proposes a new definition of the conception of effectiveness (computability, general recursiveness, algoritmicity). A good name for this version of effectiveness is discernibility. The definition is based on the fact that every computation may be reduced to the operation of discerning the fundamental symbols and concatenation of formulas. This approach to effectiveness allows us to formulate the proof of undecidability in such a way that arithmetization of the syntax may be replaced by the use of concatenation in metalogic. (C) 2003 Published by Elsevier B.V.