Could it be that our thinking contains irresolvable contradictions? The paradoxes of the infinite are a good candidate for this. Kant claimed in his transcendental dialectic that we cannot think the infinite consistently. Hegel, on the other hand, offers a fascinating positive dialectic that aims to think the infinite without contradiction. However, with Cantor, who revolutionized the modern conception of the infinite, the paradoxes return. Guido Kreis demonstrates that our concepts of the infinite are indeed inconsistent relative to our best theories and simultaneously introduces the fundamental forms of modern dialectic through this negative dialectic.