ABSTRACT
But if numbers are so fundamental, then we have to allow ourselves to ask, “What are numbers, and what are they good for?” The question may seem stupid or naive, but it is neither. The number theorist Richard Dedekind formulated the question in this way as the title of his famous book Was sind und was sollen die Zahlen? And the question has no simple answer. As indeed it cannot; it may well be that the regularities in the world can be phrased and understood in terms of numbers, but if so, then “one, two, three” will certainly not suf¤ce. In fact, the so-called natural numbers (one, two, three, and so forth), which seem to us so concrete and obvious, already present problems-philosophical problems, of course, but also very concrete problems.
