Imre Lakatos, answered from the texts and cited to the page.
The negative heuristic is the methodological rule within a scientific research programme that forbids the scientist from directing refutation — the modus tollens — at the programme's hard core.1 Every research programme has a hard core: a set of metaphysical commitments held immune from falsification by the decision of its proponents.2
When anomalies appear, and they always appear, the scientist does not turn the refutation against Newton's laws of dynamics or his law of gravitation, for instance. Instead, the modus tollens is redirected toward the protective belt of auxiliary hypotheses and initial conditions that surround the core.3 Those auxiliaries bear the brunt of tests; they get adjusted, re-adjusted, or replaced entirely, while the core stands firm.
Newton's programme illustrates the point with maximum clarity. Faced with an ocean of anomalies at its inception, the Newtonians did not abandon the core — they worked with brilliant tenacity to overturn the observational theories that had generated the apparent counterevidence, turning each difficulty into a new corroboration.4 Bohr behaved identically: when Evans produced what looked like a refutation of Bohr's hydrogen theory, Bohr did not inspect the anomaly as a potential falsifier of his hard core; he immediately suspected the auxiliary conditions of the experiment — the ionized helium in the tube — and he was right.5
What the negative heuristic protects, then, is not irrationality but the programme's capacity to develop. It is primarily the positive heuristic — the agenda for how the protective belt is to be constructed and extended — that drives the scientist's choice of problems, not the anomalies themselves.6 Only when the positive heuristic exhausts its momentum does the scientist properly attend to accumulated anomalies and ask whether the programme has become degenerating.
Popper's picture — "All swans are white" refuted by one black swan — is, as I put it in my LSE lectures, absolute nonsense as an account of how major physical theories actually live and die.7
The negative heuristic of the programme forbids us to direct the modus tollens at this 'hard core'.I SCIENCE: REASON OR RELIGION, pp. 54–55
All scientific research programmes may be characterized by their 'hard core'.I SCIENCE: REASON OR RELIGION, pp. 54–55
Instead, we must use our ingenuity to articulate or even invent 'auxiliary hypotheses', which form a protective belt around this core, and we must redirect the modus tollens to these.I SCIENCE: REASON OR RELIGION, pp. 54–55
Newtonians turned, with brilliant tenacity and ingenuity, one counterinstance after another into corroborating instances, primarily by overthrowing the original observational theories in the light of which this 'contrary evidence' was established.I SCIENCE: REASON OR RELIGION, p. 55
Bohr, without even looking or asking for the details of the experiment, wrote a letter in which he claimed that it was quite clear that there should have been some ionized helium in the tube of the experiment that Evans had carried out.For and Against Method - LSE Lectures + Lakatos-Feyerabend Correspondence, pp. 117–118
It is primarily the positive heuristic of his programme, not the anomalies, which dictate the choice of his problems.Philosophical Papers Vol I - The Methodology of Scientific Research Programmes, p. 118
In Popper's view, on the contrary, the acme of a scientific theory is 'All swans are white,' because one single observation of a black swan refutes it. This is absolute nonsense.For and Against Method - LSE Lectures + Lakatos-Feyerabend Correspondence, pp. 117–118