Page "Entscheidungsproblem" Paragraph 6

Turing's argument is as follows.

Suppose that we had a general decision algorithm for statements in a first-order language.

The question whether a given Turing machine halts or not can be formulated as a first-order statement, which would then be susceptible to the decision algorithm.

But Turing had proven earlier that no general algorithm can decide whether a given Turing machine halts.