““Interesting-sounding, supposed applications of the incompleteness theorem [here earlier taken explicitly to refer to the incompleteness theorems as a whole] outside mathematics, therefore, often ignore the essential condition of encompassing some basic arithmetic, and formulate the theorem incorrectly as a theorem about formal systems in general. When they do take this condition into account, authors may resort to formulations such as 'Our hypothesis is that the universe is at least as big as arithmetic, so that it is affected by incompleteness' or 'The philosophy should incorporate arithmetic, or else it is already limited'. The first of these makes no apparent sense, while the second amounts to feeble criticism of a system of philosophy that it cannot be a complete guide to life or the universe since it fails to decide every arithmetical statement. Such implications of the incompleteness theorem will be further commented on in Chapter 4.””
