In the early twentieth century, the logical positivists of the Vienna Circle located the power of science in "verification": a statement was meaningful and scientific to the degree that it could be confirmed by observation. The young Karl Popper (1902–1994) saw that this criterion was flawed. For no finite set of observations can conclusively confirm a universal law — no number of white swans proves "all swans are white," yet a single black swan refutes it.

Popper's "Logik der Forschung" (later in English The Logic of Scientific Discovery), published in Vienna in 1934, placed this asymmetry at the centre of the philosophy of science. What makes a theory scientific is not that you can find evidence supporting it, but that an observation capable of proving it false is possible from the outset. A good theory makes bold predictions; it puts itself at risk. Einstein's theory of relativity — because it predicted the bending of light near the Sun and dared to be tested — was, for Popper, science itself.

By contrast, theories that can explain every outcome and that no observation could refute — Popper's examples were astrology, certain forms of psychoanalysis, and historical determinism — were not strong but weak; to explain everything is to forbid nothing. Science is thus not an accumulation of certain truths but a continual process of elimination: theories are never proven, only left standing as not-yet-refuted.

This view shook the tradition of grounding knowledge in induction and redefined science as a fallible, open-ended adventure. When Thomas Kuhn argued in 1962 that science does not in fact advance so cleanly but proceeds by leaps of paradigm, the debate between the two shaped the century's philosophy of science. Popper's criterion of "falsifiability" remains the most common litmus test for whether an idea is scientific.