Key Principle
Corroboration is an appraisal of how well a theory has survived severe tests — tests that had a genuine chance of refuting it. It is not verification (corroboration never makes a theory "true"), and it is not a probability (see The Formal Probability Calculus and Zero-Probability Proof for the formal proof). Corroboration depends on three factors: (1) the severity of tests passed, (2) the theory's degree of testability, and (3) whether the tests were genuinely designed to refute the theory.
A test is severe when the prediction tested would be improbable (surprising) without the theory. Confirming what everyone already expected proves little; confirming what would be astonishing without the theory proves much.
Why This Matters
If corroboration were a probability, then tautologies — which have probability 1 and content 0 — would be the best-corroborated statements. But tautologies tell us nothing about the world. The fact that corroboration is not a probability is what preserves the link between scientific merit and informative content: only theories that risk much can be corroborated much.
This is the final nail in inductivism. There is no rational procedure for making theories "probable" by evidence. Theory choice is governed by testability and survival, not by accumulated confirmation. Science advances by conjecture and refutation, never by approaching certainty.
Good Examples
Einstein's eclipse prediction: The bending of starlight by gravity was a precise, risky prediction. If light had not bent by the predicted amount, general relativity would have been refuted. The prediction was improbable without the theory, making the 1919 confirmation a severe test and a high degree of corroboration (Chapter 10).
The corroboration formula: C(x,y) = (P(y,x) - P(y)) / (P(y,x) - P(xy) + P(y)). The numerator P(y,x) - P(y) measures how much more the evidence is expected given the theory than without it — the theory's explanatory surplus. A tautology yields C = 0 regardless of evidence; a bold law can reach C approaching 1 if it predicts maximally surprising evidence (Appendix *ix).
Confirmability ceiling: A theory's maximum possible corroboration equals P(x̄) — the probability of the theory being false, i.e., its content. Only theories with high content (low probability) can achieve high corroboration. This encodes "risk yields reward" in a formula (Appendix *ix).
Counterpoints
"But I want to know the probability that a theory is true": Popper's answer: for universal laws in an infinite universe, that probability is zero — always and necessarily (Appendix *vii). Corroboration tells you something different and more useful: how well the theory has survived attempts to destroy it.
Bayesian updating: Bayesians update the probability of a hypothesis given evidence. Popper argues this confuses the logical probability of a theory (zero for universal laws) with its corroboration (which can be high). The two measures track different things and cannot be reconciled (Appendix *ix).
Limits of formalization: Popper acknowledges that no formal measure fully captures the "ingenuity and sincerity of attempts at refutation." The quality of tests remains partly a matter of scientific judgment, not algorithm (Appendix *ix).
Key Quotes
"The old scientific ideal of episteme — of absolutely certain, demonstrable knowledge — has proved to be an idol." — Karl Popper, Chapter 10
"I think that we shall have to get accustomed to the idea that we must not look upon science as a 'body of knowledge', but rather as a system of hypotheses; that is to say, as a system of guesses or anticipations which in principle cannot be justified, but with which we work as long as they stand up to tests." — Karl Popper, Appendix *i
"I regard the doctrine that degree of corroboration or acceptability cannot be a probability as one of the more interesting findings of the philosophy of knowledge." — Karl Popper, Appendix *ix
Rules of Thumb
- A theory's track record (corroboration) tells you how well it has been tested, not how likely it is to be true
- Prefer theories that have survived severe tests — tests designed to refute them under conditions where failure was genuinely possible
- High corroboration does not guarantee future success; it only tells you the theory has not yet been caught out
- Never equate the number of confirming instances with degree of corroboration — severity matters more than quantity
Related References
- Content, Testability, and Degrees of Falsifiability — Why content determines how much corroboration a theory can achieve
- The Formal Probability Calculus and Zero-Probability Proof — The formal proof that corroboration cannot be a probability
- Falsifiability and the Logic of Deductive Testing — The deductive testing method that corroboration appraises