The two-system hypothesis states that there are two kinds of reasoning systems, the first of which is evolutionarily old, heuristically (or associatively) based, automatic, fast, and is a collection of independent systems. The second is evolutionarily new, perhaps peculiar to humans, is rule-based, controlled, slow, and is a single token system. Advocates of the two-system hypothesis generally support their claim by an inference to the best explanation: two systems are needed to explain experimental data from the reasoning, heuristics, and biases literature. The best evidence for this claim comes from simultaneous contradictory belief (henceforth SCB) (Sloman 1996, 2002). I argue that Sloman has not provided us with cases of SCB. In each of his examples there is no evidence that the beliefs are held simultaneously. I then offer the outline for an experimental setup that would offer compelling evidence for the existence of SCB and thereby support the two-system hypothesis.