 To illustrate this, consider the case of Zeno’s classical paradox on Achilles and the Tortoise (see the entry  Zeno’s paradoxes  for details). In this paradox we seem able to prove that the tortoise can win a race against the 10 times faster Achilles if given an arbitrarily small head start. Zeno used this paradox as an argument against the possibility of motion. It has later turned out that the paradox rests on an inadequate understanding of infinity. More precisely, it rests on an implicit assumption that any infinite series of positive reals must have an infinite sum. The later developments of the mathematics of infinite series has shown that this assumption is invalid, and thus the paradox dissolves. The original acceptance of Zeno’s argument as a paradox was a symptom that the concept of infinity was not sufficiently well understood at the time. In analogy, it seems reasonable to expect that the existence of semantic and set-theoretic paradoxes is a symptom that the involved semantic and set-theoretic concepts are not yet sufficiently well understood. 