Carnap, Popper, gödel: Can unity be refuted by incompleteness?

In this paper all the “acting” philosophers play their classical role: Gödel is present with his incompleteness theorems. Carnap is present with the positivist view of unity of science, and specifically with the thesis about a universal language. Finally, Popper tries to refute Carnap’s thesis with the help of Gödel’s. Unfortunately this debate did not take place in real, only one claim and reponse was made in Shilpp’s volume. I attempt to clarify this question in the present paper. The main focus is on Carnap’s view. I will show that it is possible to hold a thesis about a possible universal language if this is meant in a weaker sense: as a syntactical framework. The concept of “language” in Carnap’s view is also examined, and I come to the conclusion that it was used both in a wider and both in a narrower meaning. I also try to clarify this conceptual issue.
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