A philosopher of science examines falsifiability. A theory claims All swans are white. After observing 10,000 white swans but one black swan, by what factor does the falsity probability increase if the model assumes universal statements with no exceptions? (Assume initial falsity probability is 0.01, and black swan doubles it.)

["A philosopher of science examines falsifiability. A theory claims All swans are white. After observing 10,000 white swans but one black swan, by what factor does the falsity probability increase if the model assumes universal statements with no exceptions? (Assume initial falsity probability is 0.01, and black swan doubles it.)", "When a theory states something universal—such as "All swans are white"—it sets a critical standard for truth under scientific scrutiny. Recent attention in the US reflects a growing cultural and intellectual interest in how we evaluate claims that rely on absolute assertions. This focus isn’t surprising: in an era of information overload and skepticism toward unchecked claims, the concept of falsifiability—coined by prominent 20th-century thinkers—has resurfaced as a vital tool for assessing reliability. The sudden appearance of this topic across news, academic blogs, and educational platforms points to rising curiosity about how scientific truths hold up when tested against reality.", "Why are philosophers of science closely examining falsifiability right now? The surge aligns with broader public attention to evidence-based reasoning, fueled by debates in climate science, AI ethics, and medical research. The striking example of 10,000 white swans followed by a single black swan illustrates a core truth about knowledge: even overwhelming confirmation does not guarantee eternal certainty. When one counterexample emerges, especially one that challenges a foundational claim, it recalibrates our understanding—dramatically shifting what was once considered immutable truth into something provisional.", "So how does the falsity probability change? Assume a starting falsity probability of 0.01—representing a barely detectable complement to universal truth. When a black swan is discovered, this probability doubles, reflecting a scientific doubling of doubt: from 1% to 2%. But this doubling is not just arithmetic—it’s interpretive. It signals a critical inflection: the theory’s claim now carries a dramatically heightened falsity weight, not in absolute certainty, but in how likely it is to survive further testing.", "To unpack this simply: the initial model treats the claim as potentially true despite rare exceptions. The emergence of the black swan doubles the estimated epistemic risk. However, this increase is relative, not absolute. Modern scientific philosophy recognizes that no"]