is well-formed but not derivable though it is an instance of the tertium non datur. This fact suggests to attempt a similar treatment of descriptions: formulas which contain terms like zx(A (x) A ~A (x)) are considered as wff but the tertium non datur does not hold generally for such formulas. The whole classical propositional logic can be applied to formulas which do not contain any I-terms. For simplicity, we restrict our considerations to first order logic (the analogy to Ackermann's type-free logic concerns only the fact that the language is richer as in standard systems of logic and that for the set of expressions which are added the classical propositional logic is restricted to a "positive" one without tertium non datur). In certain sense it can be said that this system is an approximation to ordinary language where we can use the words "Pegasus" and "the round square" but where there are disagreements whether this means that Pegasus exists or that the round square is round. In contrast to Russell (Principia Mathematica "14.22) the formula