Negative evidence, auxiliary assumptions and scientific theories

One black swan is enough to defeat the claim that all swans are white. A thousand white swans cannot establish that claim conclusively: the next one might be black. That is the difference between positive and negative evidence that opens A. Negative evidence conflicts with what a claim leads us to expect; it does not simply mean evidence we dislike.

Popper takes that difference further. He treats positive evidence as having no evidential value and negative evidence as disproof. The author calls this application hyperbolic. We can see why: even an enormous number of white swans would not prove that every swan is white, but does that make those observations completely worthless? Evidence can support a claim without settling it beyond all possible doubt.

Popper also puts attempts to disprove theories at the center of scientific research. A scientific theory must make predictions that can be tested in that way. Keep this position separate from the author's criticism. The objection is not that testing predictions is useless. It is that a failed prediction does not usually identify exactly which part of our reasoning failed.

Here is the complication. Scientists generally derive a prediction from a theory plus additional assumptions: perhaps their instruments work, their measurements are accurate, and no unaccounted-for force interferes. If the result is wrong, something in that package must be wrong. But which part? A faulty instrument would not necessarily disprove the theory being tested.

The swan example can help make that concern concrete. Before treating an apparently black swan as decisive, we would want to know that the observation is reliable. A white swan painted black would create a different problem from a naturally black swan. The point is not to invent excuses for every theory. It is to recognize that a real test depends on more than the theory alone.

A's main point: Popper overstates the power of negative evidence because a failed prediction may reveal a faulty auxiliary assumption rather than a false theory.

B gives us two cases in which a prediction fails, but the eventual responses differ. Start with Uranus. Astronomers use Newton's laws along with assumptions about masses, orbits, velocities and nearby planets. Their predicted orbit does not match the observed one. Newton might be wrong, but so might the assumption that there is no nearby planet affecting Uranus.

They pursue the second possibility. Neptune is then found in the location needed to reconcile the calculation with observation. The missing planet supplies the missing influence. Newton's laws survive this test because the problem lay in an auxiliary assumption. The original mismatch was real; it just did not establish that Newton's laws were false.

The Mercury case initially looks similar. Again, Newton-based predictions fail, and astronomers propose an unseen planet, Vulcan. But Vulcan is never found. This time the successful calculation comes from Einstein's general theory of relativity together with the old auxiliary assumptions. The theory changes while those assumptions remain. This is not Newton's theory succeeding after relativity is added as one more background fact: B expressly describes Newton's theory of gravity being rejected.

B's main point: Failed orbital predictions led scientists to revise an auxiliary assumption in the Uranus case and replace the underlying theory in the Mercury case.

The two cases give A's distinction practical meaning. Negative evidence tells scientists that their prediction failed, but further investigation helps determine whether the theory or an additional assumption needs changing. B also ends with increased confidence in Einstein's theory. That is positive support, even though increased confidence is not the same as conclusive proof.