Anthropic reasoning in multiverse cosmology and string theory∗

Anthropic arguments in multiverse cosmology and string theory rely on the weak anthropic principle (WAP). We show that the principle, though ultimately a tautology, is nevertheless ambiguous. It can be reformulated in one of two unambiguous ways, which we refer to as WAP1 and WAP2. We show that WAP2, the version most commonly used in anthropic reasoning, makes no physical predictions unless supplemented by a further assumption of “typicality”, and we argue that this assumption is both misguided and unjustified. WAP1, however, requires no such supplementation; it directly implies that any theory that assigns a non-zero probability to our universe predicts that we will observe our universe with probability one. We argue, therefore, that WAP1 is preferable, and note that it has the benefit of avoiding the inductive overreach characteristic of much anthropic reasoning.