According to Kurt Gödel, Bertrand Russell misinterpreted the incompleteness theorem, but did it in ʻa very interesting manner’. To understand what he meant we need to consider their attitudes to defining truth. Even more revealing is the discussion of two fundamental approaches to logic: one is universalistic, and assumed by both Russell and Gödel, and the other is model‑theoretical, Alfred Tarski’s style. It turns out that a misleading or erroneous interpretation can be interesting, as it reveals something fundamental. William Byers claims that truly great ideas in mathematics and about mathematics are in a way false, as they lead to errors, but at the same time they can help to make advances in math. Logicism provides a good example. In addition it may be mentioned that when Russell argued in its favor, he committed a logical fallacy.

In this paper, the problem of aliasing and folding effects in spectrum of sampled signals in view of Information Theory is discussed. To this end, the information content of deterministic continuous time signals, which are continuous functions, is formulated first. Then, this notion is extended to the sampled versions of these signals. In connection with it, new signal objects that are partly functions but partly not are introduced. It is shown that they allow to interpret correctly what the Whittaker– Shannon reconstruction formula in fact does. With help of this tool, the spectrum of the sampled signal is correctly calculated. The result achieved demonstrates that no aliasing and folding effects occur in the latter. Finally, it is shown that a Banach–Tarski-like paradox can be observed on the occasion of signal sampling.